Good afternoon. Good afternoon. Welcome to the Carnegie Endowment. My name is Carlos Lozada. I'm a book critic at The Washington Post and a visiting scholar here at Carnegie. It was my great pleasure to moderate this conversation about polarization on an international scale, not just an American thing. And in particular about this new book, Democracies Divided, the Global Challenge of Political Polarization, edited by Thomas Crothers and Andrew O'Donoghue, and published by Brookings Press. I should note that this book came out on September 24th, which I'm sure by accident coincided with the day that House Speaker Nancy Pelosi announced the impeachment inquiry against President Donald Trump, and also the day that the Supreme Court in the UK ruled that Prime Minister Boris Johnson's suspension of parliament was unlawful. So, Tom, if you were trying to prove a point about the perils that polarized societies posed for democracies, good timing. Let me briefly introduce our panel. Tom Crothers at center is Senior Vice President for Studies at Carnegie, where he oversees all of Carnegie's research programs and directs the Democracy Conflict and Governance Program. Ann Applebaum is a columnist for The Washington Post and a Pulitzer-winning historian, author of books such as Gulag History and Red Fam Installants War in Ukraine. On the subject of polarization, incidentally, I've urged you to read an essay she published in The Atlantic a year ago titled A Warning from Europe. Naomi Hussain is a political sociologist at the Institute of Development Studies Sussex and currently based at the Accountability Research Center at American University. She's the author of The Aid Lab, understanding Bangladesh's unexpected success. And Sarah Yerkes is a fellow in Carnegie's Middle East program, where her research focuses on Tunisia's political, economic, and security development, as well as state-society relations in the Middle East. So Tom's going to open things up with a presentation. Then each of our panelists will weigh in with their comments. Ann is going to have to leave us a little bit early. Then I'll have some questions as well, and I hope you will too. I'll try to keep us on track time-wise. And at the end, there will be books for sale. Always be closing at a special discounted price. So thanks again for joining us. Ann, Tom, over to you. Good afternoon. Welcome, everyone. In the wake of the 2016 US presidential election, like many Americans, I think I became preoccupied by the problem of polarization in the United States. And I could see that we were headed for a period of even further intensification of this issue in the country. So being a comparativist rather than a scholar of American politics, I decided to try to gain some comparative perspective on the topic. Some initial research I did indicated to me that many other democracies were facing severe polarization. So I thought it would be worth taking a comparative look. Now, democracy researchers in the last five years or so have turned their attention, unfortunately, but out of necessity, to analyzing democracies' troubled fortunes in the world. And as they've done so, they've focused a lot on different issues, the decline of traditional political parties, of citizen alienation from those parties, rising illiberal populist forces in a number of countries, state capture and the problem of systemic corruption in democracies, and new authoritarian influences across borders that are harmful to democracy. But they haven't given that much attention to polarization per se. And I think when we look at the different syndromes and debilities affecting democracy globally, we need to add this to the list and understand it in its own terms as its own phenomenon with its own dynamics and realities. So I put together this research project, including this book to look at the project. And I started by identifying a set of countries I wanted to look at and found a group of really terrific country experts to look at those countries. The book considers nine countries in Asia, India, Indonesia, Bangladesh, in Africa, Kenya, in the Middle East, Turkey, in Europe, Poland, in Latin America, Brazil, Colombia, and in North America, the United States. And I also enlisted the efforts of Andrew O'Donohue, who's the co-editor, who was a young researcher here at Carnegie last year and we worked closely together on this and Andrew made terrific contributions every step of the way. He has since finished his fellowship here and moved to Turkey. He said he wanted to move to an even more polarized country. So he's in Turkey and Istanbul at the Istanbul Policy Center, doing further work on these topics. So we focused on four main questions about polarization. One is to look at the roots or the bases of division in different societies. The second was to then examine the trajectories of polarization, how it tends to move forward over time, what are the drivers of it, what are the patterns of it. Third, the consequences. And then fourth, the remedies or at least attempted remedies. So what I'd like to do here is give you some highlights of these findings. Now let me start by saying that we focused on severe polarization. A certain amount of polarization or political division among the contending main political parties or forces is normal in a democracy. Voters need to be able to make choices. They ought to have choices on offer and it's normal for contending parties to differ with each other, differentiate from each other. But a certain degree of polarization may be good for democracy, but once it becomes very intense, it becomes highly problematic. So we focus on this severe polarization. Now there's no bright line between kind of normal polarization and severe and dysfunctional polarization, but there are characteristics of very severe polarization that are very familiar once you look at them. And I know we've been aided in this research by some terrific work. Two scholars have done Jennifer McCoy and Marat Summer have also done some work on comparative polarization and they put forward ideas about severe polarization, which are useful. Some of the characteristics of severe polarization is that there's almost no common ground between the two main contending political forces. There's a high intensity of negativity or negative views of each side of the other that all other divisions in the society become subsumed by these overarching, the two overarching sort of groups that the division is sustained over time. It's not just the work of a single political leader in a short-term way or the characteristic of a particular political moment, but rather it lasts and becomes entrenched in that the division involves both elite polarization and societal polarization, usually starting at the top and working its way throughout the society, but not always. In such contexts, when you have a binary severe polarization of this type, the division becomes an identity and affiliation and the feeling of being attached to one side or the other is belonging to a group which defines your views of the world and defines yourself. And it becomes about what kind of person you are. And so disagreeing with people on the other side becomes less about, I disagree with you on these particular policies, but instead I'm different from you.  The term that's commonly used and it's a problematic term, but it's used so much in the United States. It does help crystallize it, is that politics becomes tribal. Now, in fact, many societies that have tribal politics are not all that polarized. So it's a confusing term, but nevertheless, when people in the United States say our politics become tribal, they are getting at this concept of identity differentiation and a dug in severe polarization. When you look around the world, let's take a brief tour to see where you find societies that are experiencing at least some degree of serious polarization. In Latin America, you see a lot. Venezuela is unfortunately a textbook case of very severe polarization. Argentina in some ways, since the days of Perón has been a very polarized society and gone through at least many episodes of serious polarization. Bolivia in recent years, Colombia throughout much of its modern history, Ecuador more recently, in these days, both Brazil and Mexico seem to be experiencing a path of polarization. In Asia, Thailand has been racked and divided by serious polarization. Bangladesh, as we'll hear more about, Sri Lanka has gone through this. The Philippines maybe in a highly polarizing moment, it's not clear yet actually. India seems to be headed on this path. There's some warning signs in Indonesia as well. In the Middle East, Turkey, of course, very highly polarized country. Israeli politics, very polarized. Palestinian politics, intensely polarized. Lebanon in some ways, a very polarized society. Egypt, in its short period of pluralism from 2011 to 2013, is intensely polarized. Iraq, Syria, Yemen, and elsewhere. In Africa, just to move quickly, Kenya as I've talked about, one of our case studies, Mozambique for a long time has experienced quite a bit of polarization between the two sides. Zimbabwe, Cameroon seems to be in a polarizing process. Burundi and Rwanda went through intensely polarized periods. Cote d'Ivoire, off and on over the last 20 years. In Europe, Poland, of course, one of the case studies in the book. Hungary to some degree, that's a complicated case. Great Britain in some ways is experiencing a very polarizing moment with Brexit. Belgium, been polarized in different ways. Alphanon, Bosnia, Serbia these days. France and Italy are debatable. Complex cases we might come back to. And in North America, the United States. But Canada has had, particularly in the last decade, under the conservative government, episodes of polarization. Australia also experiencing some polarization as well. So there's a lot of it around. There are a lot of countries experiencing this phenomenon. Not all democracies, obviously, but it's very common. Now, what can we say about the roots or the bases of polarization? The research shows that usually it's one of three roots tends to divide a country in these ways. One is ethnicity, the other is religion, and the third is ideology. Many people assume that ethnicity is the most common basis for severe polarization, but it's not really. It's actually not that common as a basis of severe polarization, although it does exist. The Kenyan case that we examine is a case of ethnic-based polarization. Bosnia is another. But religion is actually more common. And it's not so much two different religions in a society as two different views of the role of religion in life, usually a more secular view and a more religious view of society and politics that becomes the dividing line. That's what we see in India today with Hindu nationalism versus the secular, pluralist conception of India, Turkey's division between the AKP and other political forces. And religion plays a role in division in Poland and in the United States and in many other places. But then also ideology is common. Sometimes it's ideology focused on socioeconomic issues, often related to social class differentiation like in Venezuela where there's a sense of the sort of the poor versus the rest in the country polarization. But sometimes it's sociocultural ideological issues that have to do with a different sort of sociocultural view of the society, contending visions, Poland has experienced some of that as has the United States with the so-called culture wars over many decades now. So ethnicity, religion, ideology, all of these can become identities in different ways. And there's often a mistake in using the word identity. People think you only mean ethnicity and religion, but ideology can become an identity. In Venezuela being a chavista or not a chavista, that's an identity statement which is rooted in an ideological division in the society. The United States stands out, not in a positive way and that our polarization is unusual and that all three of these elements are lined up on one side or the other. And the United States belonging to sort of a feeling of attachment to one side or the other or the political divide is often related to ideology, sort of small government versus big government ideas. But religion also plays a role. Sociologists in the United States say that if you wanna ask one question of an American voter to understand how they're likely to vote, he would ask about their religious affiliations and practices. And third, ethnicity, particularly race in this country has been a highly polarizing issue. So the United States has what we call in the book the Iron Triangle of American Polarization of ethnicity, race, and ideology which is quite damaging, quite serious. What about trajectories and drivers? Well, there's no single pattern of polarization. Of course, there's diversity and it's interesting when you look closely. In some countries, a profound division in the society exists at the very time of the birth of the country and that division haunts it through all of its life. Kenya is a bit like that one. Kenya gained independence in 1963. It went through several years of coalition government bringing the Kukuyu and the Luau together, but that broke apart three years later. And ever since Kenya has been broken over the rock of this division between contending groups and polarization. So all of Kenya's history as a country, there's the original sort of founding rift in the country that has never been overcome. Other countries have a deep division or two competing visions of the country, but for various reasons it doesn't rise to the surface and become a source of intense polarization until some later point. India to some extent is like that. All the way back in the 19th century, Indian thinkers about the prospects of Indian independence and debated should India be a Hindu nation or should be a pluralistic nation? And that was there in the 1940s, that debate Gandhi came down on a certain side of that debate and won out. And so for decades of its modern history, India was a secular, pluralist democracy and only fairly late in its sort of modern history, the issue of Hindu nationalism emerged in the society in a more strident way and began to push itself into political life. So India had lived with a sort of founding rift that only rose to the surface later. Turkey is a bit like that as well. The two visions of Turkey are more Islamist vision, more secular vision were there in the 1920s when Ataturk founded the modern Turkish Republic, yet only came to push itself to the surface in the 1990s and early 2000s when the AKP gained force and pushed forward this division. So sometimes the founding rift is there and activated from the beginning. Sometimes it's under the surface for a long time and sometimes it's not evident that division was there before but it appears. These days that polarization in Poland, it's not really clear how much the division that today the devils Polish politics was really present before, something we can talk about, but there are other cases where polarization emerges in a country that didn't seem to have such rifts until suddenly you experience them. Whatever the particular pattern, in most cases, polarizing leadership is a crucial driver and polarization becomes the project of often a singular figure who embodies one side of the divide and pushes polarization as his, it's always his in our research at least, his political project, his way of advancing himself, gaining power and advancing his cause. Think here of Ula Chavez or Modi in India or Erdogan in Turkey, leaders who embody the very division that they're talking about and drive forward polarization. In the polarization playbook, it's pretty simple. Demonize your opponent, make the division very extreme. Demonize your opponent, stretch the truth if needed, engage in conspiracy theories as needed, but demonize the other side, find symbolic identity issues and push hard on them, choose certain issues that seem to be the hot buttons in the identity debate in the society like in India the building of a project to build a Hindu temple on the side of a mosque, back in the 80s and 90s, projects like that that really inflame the division, push them hard. The third characteristic of the playbook is relentlessness. Polarizing leaders wake up every day and polarized, it's what they do, it's their governing strategy, it's what they live for, they don't rest and there's no halftime polarization, it's a full-time job. Polarization is a psychological project of constructing a narrative that subsumes other differences in divisions in society and it creates a vision of two competing forces in a society, one of which must win in order to gain real power. And it takes years to entrench a polarizing narrative, to socialize people into it, to condition people to believe in it, to advance it, so polarization doesn't just happen in the society, it is happened to by actors who decide that they're going to polarize a country. What can stop it? What are the guardrails? Well, they're soft guardrails, norms of moderation, norms of tolerance, of truthfulness, of respect for rules. These norms are steamrolled by polarizing leaders who just crush norms of moderation, norms of truthfulness, norms of fair play and they just smash over the soft guardrails. The harder guardrails are institutions, of course, above all an independent legal system or independent legal institutions that can put checks on power and say to a polarizing project, this you cannot do. And so attacking independent legal institutions becomes a key element of course of a polarizing playbook. Independent or nonpartisan election administration is also a key institution that sets limits and says, you know, you have to win an election fair and square. Elections have to have these characteristics and so independent election administration is also targeted in different ways. And third, of course, the constitution. Here's the overall framework that tries to constrain these divisions within a democracy and most polarizing leaders of successful reform or deformed constitutions and put in new constitutions. So Bangladesh, for example, pressure on election administration in Poland, pressure on judicial independence, Turkey and Hungary, new constitutions and so forth. So these institutional guardrails become the targets. Consequences of polarization. I won't spend too much time on these because you probably already have a good sense of them but I'll just mention them. Political grid law or non-cooperation between angry divided sides. Institutional deformation and degradation. Politicized foreign policy, interesting polarization often drags foreign policy into the polarizing law and uses it for its own purposes. We've seen a bit of that here in the United States in the last few weeks. Declining social cohesion. You begin to see a society with lower social trust and tensions within the society and often rising sociopolitical violence, which is a typical characteristic of a highly polarized country. We identify in the research a kind of ladder of ultimate outcomes. If you say where is polarization going in the country? Once the country is moving down this road, there's sort of five destinations you can get to. The worst is civil war, like in Colombia in the 1950s and 60s. Cote d'Ivoire, various times in the last 20 years. Second destination you can get to is military intervention, the military stepping in and saying, stop the polarizing madness that happened in Bangladesh in 2006, 2007, happened in Thailand, happened in Egypt. Now these aren't benign interventions by the military, but they're often justified as saying polarization has gotten out of control and needs to be stopped. So military intervention, domestic coups. The third outcome is one party winning out the battle over the other and enforcing a kind of illiberalism and squeezing the life out of the democratic system. That's what we've seen in Turkey, seen it in Mozambique to some degree. We might be seeing it in Hungary, probably seeing it in Kenya in the last 10 years to some degree. So the system gets out of balance and one party squeezes the other, squeezes the life out of the democratic system. Fourth outcome, majoritarianism or maturitarian drift, where a degree of intolerance infiltrates the democracy and the dominant group begins to impose a certain kind of intolerance despite democracy. We see that in India. And then a fifth is just basically democratic dysfunction. We can poorly function in institutions, social cohesion going down and so forth. You see that I would say in the United States. We've seen it in Belgium off and on in the 20th century and other countries that are able to keep the basic rules of democracy but drift into democratic dysfunction. So the outcomes are not good. The trajectory of polarization is sobering. Then we turn finally then to the remedies. I wish I had some great news for you here that I've just been holding forth the recipe here, the answer that somehow nobody's thought of before. But I don't. Once polarization becomes really entrenched in the body politic of a society, it's very difficult to eradicate because it becomes a set of beliefs and processes and patterns and norms that are quite deep. Kenya is an example of a country that for 50 years now has just lived through dysfunctional polarization again and again and can't seem to escape it. Argentina almost feels cursed by the divisions that go back to parentism and the origins of parentism and it can't seem to escape that division. The big remedy, but it's usually elusive, is leadership change. It's the imagined leader who somehow depolarizes the society and reaches across the divide in some way and brings the country back together. That's what most people dream about in such cases. But it's rare. It's very rare to find instances of that. We might be seeing that now in Ecuador or under Corea, the previous president is a very polarizing leader, sort of populist polarizing project. He chose his successor, Daniel Moreno, who came into power but was just cut from a different cloth and has tried to bring the country back together somewhat and depolarize the country. And interestingly, he's from the party that was polarizing and so that's given him a certain credibility because when the leader's from the other side, whoever was driving the polarization just doesn't accept them. So it's very hard to... the idea that a depolarizing leader can come from the other side and bring the country back together. Very hard to find good examples of that historically. Other remedies, of course, and you see this in most polarized countries, including this one, some of these at least, political party dialogue efforts, efforts to bring parties together to talk to each other, to agree on basic standards of behavior. Lots of congressional dialogues and briefings and efforts to support bipartisanship at the congressional level, both at the national and state level in the United States. You see this. Institutional reforms to strengthen the guardrails. You say, well, if these are the crucial guardrails, then we need to reinforce independent legal institutions, maybe reinforce the independence of the judiciary in various ways. Some countries trying to do that. Reinforcing independent election administration to make sure it's not corrupted and so forth so you can try to strengthen guardrails. And then lots of civic action to try to overcome polarization. Lots and lots of civic dialogues to bridge communities and do reconciliation at the local level. And then media reforms, efforts to encourage media to be a force that drives people, ideas and information away from the extremes. And greater research and study. Polarization is not very well understood in a lot of places where it occurs. In Turkey, for example, the very polarized country, there's a lot of polarization within Turkey. For example, our Turkish researchers tell us and very few surveys that show because the government denies there's any polarization, doesn't encourage such research or frowns on it. And so sometimes just basic information can be useful. So there are many efforts and ways you can sort of combat polarization, but the news is discouraging in terms of how easy it is or how rapid that occurs. So that leads me just to closing thought that this comparative journey, which I've described to you on roots, trajectories, consequences and remedies, has left me more rather than less sobered about polarization in this country. I think I've gained a better appreciation of how deep a problem can become and how terrible the outcomes can be. And that the United States does have certain characteristic features. I mentioned the iron triangle of polarization. Some of our institutional weaknesses, like a traditional tremendous weakness in our election administration, it's sort of puzzling given how sophisticated and wealthy of a democracy we are in some ways. The fact that independent legal institutions are becoming more politicized and you see that guardrail under stress. And the fact that polarization in the United States has now been with us for really 50 years in its modern form and has been socialized into the country's body politic in different ways. What we're going over is a very deep project, not something one election is going to take care of or one set of particular political reforms. So we're heading into an electoral process that will intensify polarization further. But at some point, we as a country are going to have to take very seriously the larger project of what overcoming polarization in the United States will mean. Is it for my remarks? We're going to now turn to our three commentators. I think starting first with Naomi Hussain and then we'll have time for audience question and answer afterwards. Thanks for your attention. Thanks very much, Tom. I think you can hear me, I feel like I'm echoing very loudly. It's great to have Bangladesh included in a volume of this kind because I always think I've been in D.C. for four years and I think that Bangladesh gets very little attention and I should point out in case nobody believes me that Bangladesh is in fact important. It's the seventh largest democracy currently or maybe after the last election, we should call it erstwhile or aspirational democracy but it's a huge place, one of the fastest growing economies in the world. And the reason it's in this book is that we've had in the last 30 or so years a process of polarization in Bangladesh, political polarization that has resolved itself really down more or less into a single dominant political grouping, the Awami League Party, which has been in power for the last 10 years. But the process of polarization has been quite traumatic and destructive for Bangladeshi politics and society. But I should say first of all that we haven't always been a very polarized society in key moments in political history in Bangladesh. There have been these moments where the society really came together, first in the liberation struggle against the British and then in a big struggle for national liberation against the neocolonial rule of West Pakistan in 1971. And these were moments when really the society pulled together, they were very violent episodes, millions of people died, there was lots of destruction. But it resulted in quite a strong elite and popular consensus, a kind of social contract around some of the basics, like food security, economic development, social policy, disaster management, all the things that really mattered in Bangladesh. So we've had this strong elite consensus, strong popular consensus as well, which is why the political divisions that arose in the period after 1991 are kind of a puzzle. I think this is really why Tom wanted the Bangladesh case in this book. So since we returned to multi-party democracy in 1991, so it's been, what is that now? Oh my goodness, it's been 30 years. And in that time there's been a real polarization, really a competition between the Awami League party, now in power, and the party that led the national liberation struggle and the Bangladesh Nationalist Party, which was kind of a party that emerged out of a civilized military rule in the late 1970s. And these two have been fighting it out over the last 30 years or so. And in each election since 1991, these two parties together have had a growing share of the popular vote. They've been very hotly contested elections, the growing level of political violence. And in each election up until 2014, they turfed the incumbent out. The citizen said, no, thanks, let's have the next guys. It's their turn at the trafic, if you like. The political opposition now hasn't been in power for 10 years and is kind of almost totally decimated, criminalized, and very weakened. So really this Awami League party has emerged as the winner out of this polarization process. What's really interesting about Bangladesh is, unlike your fine country, we don't have the Troy Curve, what did you call it? The Iron Triangle, there you go. It's quite a homogenous society. It's really quite hard to see what the basis, the roots of this polarization might be. It's quite a homogenous society and that's a result of the long years of political struggle. There's a lot, as I said, of consensus in the population within the elite about how to run the economy. There's no ideological difference of any significant degree around social policy and all that. And this reflects the kind of the homogeneity, the close-knit nature of Bangladesh elite, the fact that it has quite a lot of affinities with the rural masses. In some ways it's more perhaps like Japan or South Korea perhaps but there have been differences historically over the role of religion in public and in social life and it's really there that political elites have tried to activate to amplify differences when it suited them. And so really when we look at the polarization that's happened in Bangladesh, it does appear to have been very much a political elite strategy for holding on to power. We had, since 1996, in recognition of the fact that this polarization and this fracturesness is really quite unmanageable, we established this quite innovative caretaker government system. So for three months in the election cycle a non-party caretaker government would take over and run the country because the two parties couldn't be trusted to police themselves. And this worked basically once, really. Nevertheless, it was in place for many cycles. In 2006, the then ruling party, the BNP, decided to pack the courts. The higher courts tended to supply the officials so they packed the courts with their men in order to rig the election. Political violence rose, the military stepped in and took over for two year period. At which time they had the great idea of reforming the political parties, cleaning them all up and trying to get them to be more democratic internally. And the result of that was the BNP was completely weakened and the Awami League came to power in 2009 and then abolished the caretaker government system. So now there is no external or neutral party to police the elections and in 2018, in December, there was an election which the Awami League, the incumbent won something like 95 or 96% of the vote. I'll say no more about that. It's not really clear to anyone, really, if this caretaker government system, as a solution to political polarization, if it made it worse or if it made it better my feeling is that it made it worse because the political parties never learned to behave themselves, never learned to police their own behavior, never developed the institutions they need to do that. But also that it weakened these institutions of accountability like the Supreme Court which to that point had been quite robust institutions of accountability in the country. So this effort to improve democracy had actually ended up weakening these other institutions. I think when we look towards the future, I think what's really important now is that Bangladesh has had quite a lot of success with its development policies, it's very inclusive, quite good on gender equality, poverty reduction, climate change and so on, managing things pretty well for a country with the kinds of challenges it has. But it's always done so with quite a strong social, state, society, coalition partnerships between social actors and the state. Now the party that is in power is very strong, the state is getting stronger and the ambition appears to be to go its own way without the interference of civil society or political opposition and so on to be, if you like, a developmental estate. And I think this is where we're going now with Bangladesh and I think this is one of the outcomes of the process of political polarization there. Sarah? Thank you for having me. And so Tunija is the case that has an experience of polarization and I'll talk a little bit about why that is and why that perhaps going forward in the future, polarization might actually be a good thing for Tunija. So without going into the entire history of the post-revolutionary period, I will just note that Tunija sort of flirted with severe polarization in the early years after the revolution. So first of all the Ben Ali regime who came before the revolution pitted Islamists and secularists against each other, jailing and torturing Islamists or else forcing them into exile. So when Islamists were allowed back onto the political scene after the revolution, this divide that had been permeating sort of played itself out in a really ugly way, resulting in the assassination of two leftist politicians in February and July of 2013. Many Tunija then blamed the Islamist government for failing to adequately address the rise of Salafism in Tunija and as a result the Islamist government actually stepped down, they brought in the technocratic government and the democratic transition at that point was actually almost derailed. We also at this same time saw the rise of the Nida Tunis party, which was a party set up by the previous president, Bezgi Qaeda Sebsi explicitly to be anti-Nachda Islamist party. So this kind of set Tunija up for this us versus them mentality that we've seen play out in other cases. But the reason that the democratic transition didn't derail is actually the reason, the same reason that we have not seen polarization take place in Tunija. So why not? The first reason, the most important reason I think is leadership. What we saw is that even as the former president, Bezgi Qaeda Sebsi was denouncing the Islamist, was denouncing the Nahda, creating his own party that's only platform as far as we could tell was to be anti-Nachda. In secret he was also meeting with the leadership of the Nahda. And the end result of this is that Tunija adopted a consensus model. This idea that they were going, these two leaders behind the scenes at first and then overtly in public later on were trying to heal rather than divide the country. The result of this was that consensus became Tunija's sort of guiding light. What we see today is that the political class pretty much across the board has almost developed an allergy to polarization. And Tunija actually is in the midst of holding their next elections. On Sunday they had their last, the legislative elections. The final results are not out yet, but it's been interesting to watch how this is playing out today, five years after the first presidential election. The Islamist party in Nahda this time has received the top vote, but only with about 18% of the vote. And no clear path to a sufficient coalition. So what we are seeing is that many Tunisian commentators are very scared. What they're worried about is that we might end up having to divide a government, we likely will. There might not be a consensus model going forward. And what does that mean? This could be a very dangerous situation for Tunija. But the third reason the country has not devolved into polarization is that frankly it's just not that divided. And I think this is very important. There's a lot of similarities there, but some have, but Tunija has not resulted in polarization the same way that Bangladesh has. Tunija is 99% student Muslim and has long prided itself on being a secular state. But most Tunisians have not actually considered themselves secular. When they're asked in polls, they don't identify as being secular. And I'll give you a recent example of this, that the former president tried to pass a law that would have granted equal inheritance rights to women and men, changing the law in Tunisia. However, according to polling data, 63% of Tunisians were against this law. So this country that holds itself up as being a secular model most people didn't actually want to pass this law. That would sort of change, push away from religion and change the equality there. So what it shows you is that the social divides in Tunisia are actually far more nuanced and complex than simply the Islamist secularist divide that I think we often hear about. Now it's not to say that there are no divides. There certainly are. Primarily they're geographic. We see big divides between the coastal regions and the interior. This is not unique to Tunisia. But these divides have not actually manifested themselves in political polarization. And the final reason, which is related to this, is that highly personalized political parties exist in Tunisia, but they don't have clear platforms or policies. It's very difficult for them to be polarized because they frankly don't stand for anything. And again, they're in the midst of elections right now. I interviewed the heads of almost all of the major political parties a few months ago, and what I found is that none of them could really articulate a platform. They've tried.  But there aren't really clear divisions between what the different parties stand for. And I'll just caveat this to say that we have seen this election one party, Abir Musi's free historian party, who supports a return to authoritarianism. That party has started to gain ground. That party will actually be in parliament this time. They will have seats. We don't know the final results at this point. So we could actually be seeing Tunisia setting itself up for a bigger political divide in the future. They do stand for something that is contrary to what the rest of the parties really stand for. But let me end with talking about why I think that polarization actually would be good for Tunisia. So as this book notes, polarization helps clarify voters' choices and develop stronger party attachments, which is something that is lacking in Tunisia. People are increasingly turning away from traditional political parties towards independent candidates. In their 2019 municipal elections, the first ever municipal elections, the independence while they're not a single group, performed better than either of the two primary parties. Today, we've just had presidential elections a few weeks ago. There's a runoff system, so we'll find out the final candidate in a few weeks, but next week. But what we found was that one of the two candidates who made it to the runoff doesn't have a political party. He's an independent. He didn't have a campaign. So what you're seeing is that people, again, are turning away from what have been established political parties in large part because of the fact that parties don't stand for anything. Voters don't know who to identify with. They don't really feel like there's much of a difference between the parties, so they're sort of turning away from the traditional political system. We also saw this manifest itself in what I consider to be pretty low voter turnout. In the presidential elections the first round held a few weeks ago, only 39% of eligible voters came out to vote. The country's second ever democratic election. That number might be on par with the United States or other established democracies, but that's quite low for a country that's only having its second contest. So we'll just close by arguing that I think Tunisia could use some polarization in the guise of political parties or camps with clear, strong, and differentiated positions to help bring Tunisia through its next step of its transition, and we might in fact see this play out in the next government. Thank you. Well, I've been given the topic of Europe, which is broad and large. I'll just start by one comment about something that Tom said. The question of, it's very striking when you look at his book and when you look at so much of what's happening not just in Europe but around the world is why we see these similar patterns in politics happening everywhere at the same time. So why India and Poland and the United States and the Philippines all at once. And the more I look at it the more I think it has a lot to do with politics moving from being grounded in real institutions, whether it's trade unions or church organizations as it was in Europe for many decades, social democrats and Christian democrats, they had those parties based on real institutions, labor movement and church movement, and as people stop as those real institutions in real life stop mattering politics moves increasingly online. And online people are looking for new identities, they are they're finding and arranging their lives in different ways, they're identifying with groups that they find online. I think that's one of the things that all of these countries have in common. In the conversation about Europe people they're not the same thing. They are related though because there are populists in Europe who are using polarization as a tool. And I think the most important point about the polarizing movements in groups that we see in Europe is that almost everywhere you look they're happening because they are useful to somebody. So very often these are political divisions or social divisions, these are ethnic and religious divisions that have been there for a long time, maybe even many centuries or at least many decades. And one a politician or a group of politicians has seized on them and sought to promote them as a way of gaining power. I mean Poland is an excellent example of that because the divisions that you have in Poland between people who are very religious or someone let religious are very have been there for a long time. It's actually a very homogenous country. There's no tradition of Polish civil war of people fighting each other. It's a country that's been very united against invaders. But what we've seen is one political party over the last two decades actually has sought to very systematically polarize the country and to take power on those grounds. And then to use that support as a way of beginning to end democracy so that it will stay in power definitely.  So and this is a, and as I said the divisions that are not in any way inherent they weren't necessarily there before they've been built up and created through social media, through alternative media and then more recently when they take power through the use of state television. In both cases the ruling party takes over state television and turns it into a kind of almost communist style propaganda machine. I mean in Poland there's really only one team, you know there's opposition parties don't appear on state television anymore and because it's a it reaches only about sorry, the other way around there's about 10% of the country, maybe 15 that can only see state television doesn't get any other television. It's a very influential voice and so they've used polarization to first to come to power then to so conspiracy theories and now they're attempting to use it to end, they will particularly if they win next week in Poland they will use it to end the remaining institutional obstacles of democracy they've said it, I mean they will destroy the independent judiciary, they will try to destroy the rest of the media, they will try and make sure that the free media, independent media is taken over by someone they admire and so on. So it's a you know the point about it is not that it's something inherent, it's not that it was always there it's something that's used. So with this in mind you can also look you can see something very similar happening in the United Kingdom, I mean the Brexit story is really not about imposing a liberal democracy on Britain but it is once again interesting because if you looked at the country before the Brexit vote if you looked at all the polling that was done up until 2016 you did not see deep divides of anger about Europe, it just wasn't I mean some people were there's a small fraction maybe on both ends people who loved Europe, people who hated Europe but it wasn't something that consumed the whole society and the referendum and the complicated politics that have followed have made it that, so in other words this is again something that has been, has become a political tool for a particular group and it's now in the interests of the so-called Brexiteers the very pro-Brexit politicians and also voters to use very, I mean the confusing thing is they use similar language now to the kind of language you hear in Poland and Hungary so they talk about liberal elites who are out of touch with the country and of themselves as the only true British or in many cases just English this is very often a party of English nationalism and we are the only real, you know we want the good of the country and everybody else or traders or sorry I mean Boris Johnson himself has started using that language even though this isn't a kind of language that he ever used before, he was not known as a polarizing or divisive figure when he was mayor of London quite the opposite he was somebody who thought of London as a global city and sought to represent there was no, there was no hint that this would be, that he would be a prime minister who would talk like that but he does now, you know and again once again it's because this is now an effort to keep the Tory party in power and to make sure from a small group that Brexit happened so again you see it as a kind of tool and I would say you also see polarization being used as a tool even in cases where it's not a, you know, where it's a minority view one of the issues that I've spent a lot of time looking at over the last couple of years is the issue of Russian involvement in European politics and there are a number of cases probably the most interesting one is Germany where you have small political parties that use this kind of polarizing language we are the real Germans everybody else is, you know, our traitors and those are the parties that have, you know, either very obvious online Russian support of the kind we're now familiar with from the US election or in some cases even financial support so the AFD in Germany, there are a couple of MPs who have direct, you know, we now know there have been a couple of scandals around direct financial support from Russia so it's now this, you know, this polarizing language and polarizing tactics are now something the Russian government uses in, you know, where it can in particular European countries to promote polarization as a way of paralyzing you know, paralyzing a country you know, the AFD is never going to win I don't think it's ever going to be a majority party but with 13 or 14% it destabilizes the parliament it makes it hard for the government to form coalitions it is able to have a big voice and a big impact on German politics and my guess is that's the aim of Russian support for Marine Le Pen Party in France or for Salvini's party in Italy similar, you know, these are parties that have important native roots, I don't want to deny that but they are also now kind of a funnel for outside influence as well so to conclude, I would say that this is, there's now almost a playbook, there's a kind of polarization playbook that is being used by particular people in particular circumstances either as I say in Poland and Hungary as a way of taking power and eventually making money as well, the Hungarian government is profoundly corrupt its leadership uses its political power to make money or as a way of taking charge in a messy situation as in the UK or as a way of exerting outside influence and having some influence on a given country's politics from an outside power Russia is doing it now there's no reason why China or somebody else won't do it in the future I'll stop there thank you very much, I'll just have a few questions for the panel and then we'll have questions from the audience and my questions are open to whoever cares to engage in them so Tommy in your presentation you noted that some degree of polarization is useful is even healthy as parties build their brands and as twitches are clarified for voters as part of why Sarah thinks Tunisia could use a little helping of polarization but that when it goes too far it becomes corrosive for democracy you said there are no bright lines but are there hazy lines? are there something that you see that is evident maybe across some of these different case studies where you see potential tipping points once these identities become activated because otherwise it seems like something that's most easily identified in hindsight which is sort of analytically elegant but practically frustrating well one way to think about that question Carlos is to take a case of a country that has a fairly high degree of quote normal polarization but at the time did not lapse into this chronic severe polarization that was the UK in the 1980s UK in the 1980s presented voters of the choice nearly at ease between Margaret Thatcher and Michael Fulton it's kind of like a nine and a two on the one to ten ideological spectrum and these were far apart from each other they were two different economic visions of the United Kingdom and socioeconomic visions that were really startling I was living in the UK at the time and an American used to coming from sort of governance that just always required at least some compromise from Congress the gap between these two visions and the decisiveness by which the Thatcher government was moving to impose its policies or to implement its policies in the country was startling yet it didn't become an identity division in this corrosive sense in that it didn't subsume all other differences in the country and you didn't have to give up other features of your identity to belong to one or the other and it didn't craft a narrative of other so Margaret Thatcher didn't craft a narrative of that you know because you're a working class person who's been voting for labor for 45 years you're a dangerous other she wanted those votes too she was just trying to expand the Conservative Party's reach and say we could be good for you too and so it was actually an inclusive attempt on her part to sort of say these aren't just about the upper middle class in this country we're actually the real champions of the working class because we're going to get this economy out of its doldrums and provide real growth for the country so she never turned it into a sociocultural sort of project of where the Conservatives didn't at the time of you have to agree with us on a whole series of things to be one of us and if you're not with us you're terrible you're a terrible person so somehow you look for those signs in when you see a political leader or political party constructing a platform or a vision and say how much does it other the other side how much does it demand affiliation on sort of other issues that are not central to its core sort of policy project I guess are the things I would look for I'll move to another question so one of my favorite lines I heard today is polarizing leaders wake up every day and they just start polarizing sort of implicit in that is a deliberate action of choice and in that sense should we think of polarization as always being a top-down process right or what is the always is an input a political tool that is deployed what is the interplay otherwise between the breakdown of elite consensus as you described and sort of once polarization becomes a mass event then how does the causal arrow start flipping if it does so my having watched it happen in a couple of places so I literally moved through it my view is that it's not so much the politicians who started as the journalist is really the wrong word but the writers slash political technologists slash ideologists slash you know the kind of people who write stuff on social media I mean there's a description of the identity that begins to happen and whether it's being directed politically which sometimes it is or not there are I mean in this country you would call it the alt-right so the alt-right begins organizing people online begins using a different kind of political language and you know begins indulging and spreading conspiracy theories and you know seems to me they precede Trump I mean you have them first and then you have Trump who's able to use this you know this new way of talking about the United States and new way of shaping people's identity that has been created online and who then runs with it when he runs for president I mean something similar to that happened in Poland where you had these little far-right fringed magazines that began with a conspiracy theory about this plane crash that killed one of the Polish presidents and they began pushing this conspiracy theory and using it and repeating it and implying that there was a huge cover-up and that meant that really everybody in the Polish government was a traitor and implying that there was a you know an enormous secret plot basically to take over the country and it sounds ridiculous when I say it here but it was extremely influential it mattered a lot it moved a third of the country and it was the people who created and spread that conspiracy theory who were really critical it wasn't so much that it was a political decision in that case I think it was it was closely tied to one particular political party but it's really the people who can create the language of polarization and the people who can create the identity that draws people in that's the really influential group it's important to note that in some cases there's a strong element of grievance and that the degree of grievance fuels the idea that you need to be polarizing so by in Venezuela for example in the early 1990s it had become a society in which many Venezuelans were very angry at the political elites and felt that they'd be given a bad deal for many years by them and there was a you know there was a lot of accumulated anger that then Chavez stepped forward, attached itself to and he sensed that and he became the leader of that grievance and said the only way we're going to get justice for our side is we have to take extreme measures because these people are going to stifle us if we don't and so grievance propels the justification for the extreme measures or Hindu nationalism in the 1980s began to emerge more clearly as a social movement within India again it's just as answers some writers, thinkers with activists saying wait a minute, we've been, you know this is a Hindu country and Hindus are we're getting at the back of the line and other people with this affirmative action and all this for other unfavorable cast and the Muslims they're stepping ahead of us and how come Hindus are not being put first in their own country and they built a narrative of grievance that we the majority in the country are mistreated by those who bend over backward for the minorities and Hindu nationalism needs to step forward with our grievance and that energy and that sense of grievance fuels the idea that we need a leader who can break some chains I remember Indian, it was an intellectual project before it was a political project I think it's the case the same with Brexit actually but in India the historical project it's a project with long historical roots and I think this point about grievances is very important, what happened in Bangladesh was we had a significant number of war crimes in 1971 which were never there was never any kind of justice for that and when the Awami League finally came to power with a big majority in 2009 they set up what they called an international crimes tribunal war crimes tribunal and tried some of the political opposition for war crimes a very imperfect transitional justice process as they always are kind of rough justice was achieved but this has been deeply politically polarizing and I think it's not these divisions didn't exist but other divisions also existed in Bangladesh why did the parties not polarize around class for instance plenty of class divisions plenty of geographical divisions as well but this historical grievance around religion, the role of Islam in state and social life was the thing that was reactivated it was a very I don't think the now ruling party thought that this would be something that would win them this sort of power it was this festering grievance that went on for a long time but other things could have been chosen that these were the issues around which the penalization eventually occurred out of that on the case I think we've seen sort of the top down nature around grievance matters as well this idea that the Islamist party had every right to be agreed they were in jail, they were tortured when they came back in and there was this threat of polarization they stepped out of power they made the decision to not be in power anymore to save the transition recognizing this was becoming more and more polarized and this was also I mean I think was occurring at the same time that Egypt was going through its own test with the Muslim Brotherhood in power with President Morsi so I do think that this idea that polarization can come from the top is important but also preventing polarization this idea I don't know many other cases where you've seen the leadership choose to relinquish its own power in order to kind of protect this and move forward we've also seen them now roll back their position they came in as an Islamist party they then switched to becoming a party of Muslim Democrats and now they want to just be called a conservative party you're seeing these different sort of how do you deal with this how do you kind of prevent this stuff some people think it's just to play the long game but others think it is genuine in order to kind of keep Tunisia in the process and prevent it Last question I'll ask there seem to be ways in which polarization creates its own defense mechanisms I think hit on this in different ways today you can have a leader who sort of you know stokes polarization whether it's pre-existing or sort of it becomes infused in the society and you know as a project of corruption or authoritarianism and as a result the remedies that oversight or other political norms and institutions become harder to use precisely because different parts of the society now view themselves as illegitimate I mean you're seeing some elements of that in the United States is that it seems easy to get stuck there is this part of the democratic dysfunction that you talked about one of the outcomes of polarization or how do you deal with that when some of the legitimate methods of remedies of oversight and politics become harder to use in a context of polarization Yeah, the really destructive logic of polarization is that as you begin to polarize the idea that there's a group of people in the society or different people who are independent of that division and have a credibility for not being attached to it they begin to vanish and so therefore including civil servants, judges so you see in the United States if you ask an American today name two or five prominent Americans who are above the political fray it's getting harder and harder to find those people who you say just genuinely no one would accuse them only the right and the left would say yes that person's above the fray might have been a generation ago we might have thought of religious leaders, military leaders supreme court justices university presidents you know whatever head of a medical association but these days everyone is subject to scrutiny now they immediately go back and say where did you intern in the summer when you were 22 years old and you must have everybody has an affiliation somewhere you just need to find it and so therefore once nobody has independent credibility it's very hard to stand up for the institutions because those who stand up for the institutions are part of the polarizing fray and you say well they're just they're actually part of the polarizing fray they say they believe in independence of the judiciary they say they believe in independent election administration but we know they're real agenda and this is the really destructive logic of polarization is that the idea of independent standards institutions and viewpoints becomes deeply corrupted and when you see the difference like in this country where the supreme court is getting pulled into this and you see that the UK supreme court is a very different institution with a different role in UK life hasn't gone down that road you're just struck by the difference the UK and US are very similar in some ways but the UK supreme court is not caught in the polarizing now it may be but whereas the US supreme court is pretty far down the path very far down the path of being part of the polarizing dynamic in the country and so we've gone farther than we realize in some ways in this country that I think Americans realize because of the traditional sort of reverence in this country for certain institutions to realize when you stop and do a a gut check on this the healthiness of how much these institutions are outside the polarizing fray very few are seems only the military is still highly regarded but itself is the institution that has to stay out of politics and so people might think if only Jim Mattis would speak up now what would he say he's on a book tour so he has to say some but he's not saying much you know not as much as I think some people might think but here's a figure who maybe is outside the fray and perhaps 20 years ago Colin Powell served that kind of figure in the American imagination let's open it up for questions introduce yourself please and keep your comment in the form of a question third row there sir Hi, Vivek Madhul from Namathie, I really appreciate the discussion and the comparative perspective I had two questions you mentioned and mentioned that polarizations aren't the same thing as populism I was wondering about authoritarianism the relationship between polarization and authoritarianism do you see one as more means and one as more ends is one more lasting I don't think you mentioned that word but I was curious how you a lot of the strategies that you talked about polarizing leaders using involved assaults on democratic institutions but I was wondering how you saw the relationship between those and then the second one was in terms of remedies reforms to strengthen the guardrails rule of law institutions courts, electoral commissions and then you mentioned separately lots of civic action I was wondering about reforms that make more space for civic action for deliberative democracy for deepening democracy and whether that came up in the case studies at all the ultimate logic of a highly polarizing leader and his or her project can be authoritarian because of its disregard for guardrails and its insistence that we have to keep going to advance our project so Erdogan might not have been an authoritarian 20 years ago but he's ended up as one because of the natural logic of this process is taking him to a place where judiciary stands up to me well those are enemies against the project with the secular civil servants to you know one by one I have to crush these things for the sake of my project so polarizing leaders who sort of have no limits on their polarizing appetite end up as authoritarians if they can if they are able to gain that much power but some authoritarians didn't start as polarizers President Xi in China as an authoritarian leader who's not polarizing he doesn't need to be because the political system in China is different there isn't a division it's not a pluralist system and so many authoritarians are in societies that have not had pluralistic politics and so therefore don't have they may have underlying divisions within them but they're not they haven't had to use polarization in fact they often try to use many authoritarians try to use very inclusive language on the father of the country or on the one who over so authoritarians often are different they're trying to be unifiers because they're afraid of losing so I think there's but not all polarizers end up as authoritarians they're not able to get there the way China is good they don't have the political force or they're in some ways just more limited in their appetite for how much they want to conquer with respect to the second question regarding civic space and civic movements I think it's a very important point and you see both in response to the feeling in many democracies that the parties are not representing the citizens very well citizens are alienated from the parties efforts to create the liberty of democracy exercises and space is a way to try to connect people more to the system but you also see it as a way to try to release anger and pressure in the system so like the grand debates in France that Macron sort of oversaw this year in response to the yellow vest movement was an effort to kind of release and reduce the anger in the society by saying let's have a deliberative democratic exercise to give citizens a chance that you're angry at me I want to hear it I want to hear it in 20,000 forums around the country come and tell me what's bothering you I thought that was a smart move to try to sort of proactively say okay let's take the steam out of this pressure cooker here and let people go ahead at a local level and see what it adds up to so it was a response to that easier to do in a democracy than in the authoritarian system where the authoritarians can't really gauge if they did that they're afraid of what might come out kind of because they don't really know the degree of anger and they don't feel they can control it but a good democratic leader can do that ideally that's the case I think that also with the you know these cases of political polarization often show a kind of shrinking of independence of space if you like and the kind of polarization co-optation of civic actors was quite a common feature as we saw and I think there you have a problem of lack of trust, definitely a decline in trust even between your political opponents but you know just ordinary other citizens I think this is a really significant deterrent for doing this kind of engagement but the institutional guardrails question I gave you the example from among us that we tried and it really does when you put those sorts of institutions in the political firing line when they're politicized because they some ways hold the keys to power it really becomes very difficult then to protect those institutions I think while enabling them to function at the same time Yes Sir in the back Yes Thank you I'm from Iraq I'm from one of the most polarized countries in the world and I have experienced the entire spectrum of polarization since 1990 till now so I think there are two factors and I want to ask Tom about these factors which really made all that polarization for a long time we have different ethnicities different religious groups but we didn't have a real polarization I think it started with the dysfunction of the government when the government started to function well the people started to to real polarized so in our case I think it's the government dysfunction as a result of the invasion but at the same time in the world there is globalization dysfunction which also threaten all societies and especially the middle class which was one of the main pillar behind non-polarization so I think there is this socio-economic factor which is the middle class globalization which was a result of the dysfunction of the government in protecting their societies which made that polarization very clear everywhere not only in one country the dysfunction of globalization the dysfunction of the governments which lead to that polarization what do you think Tom? I tend to think of Iraqi politics as an example of where you have a deep divide that has been covered over by other political a political system that pushed that divide down in the society and suppressed it repressed it and then shocked the intervention that breaks apart that political system and then that divide emerges along with a lot of other divides in the society economic and regional and ethnic and so forth but the Shia Sunni divide which had been repressed under the state of modern Iraq is suddenly there and is activated by different actors there are many divides that could have been activated by some actors who feel they seem principal of our politics and so it was kind of shock therapy in a very divided society that's very dangerous to do in pluralism because different sides have to learn to accommodate each other over time and Iraq went through a very intensive period of reintroducing these divisions into a suppressed sort of plural system that where pluralism had been suppressed so I think there were many factors that suddenly led to this fracturing of Iraqi politics so intensely but in various ways could have mobilized along different lines in sort of post-invasion Iraq but for various reasons those lines were activated the religious lines and others and created the divisions within. You started off your discussion by talking about a comparative journey and covered a great number of nuances and factors I'm wondering if you at any point considered rating and scaling the amount of dysfunction or these various factors Yes, we did. We thought about a polarization index and neatly ranking all the countries in the world in 1993. We thought seriously about it because it would be a beautiful thing if you were able to do it but we concluded it's not possible that it's there are too many factors that would involve essentially subjective assessments of the intensity of political language for example which types of conflict are more salient than others we wouldn't be able to reach a level of sort of certainty or objectivity that we would need to make such an index and so it's just not a condition that lends itself to very precise that. I was just reading Nolan McCarty's book at Princeton on polarization in the United States it's 160 very well researched pages just trying to assess to what degree polarization exists in the US and this is a country with more data than any political scientist could ever dream of and it's a very difficult question to measure the polarization in a country and sort of assign it a number on a scale and so forth. Thank you, I'm Tom Rekford with the Foreign Policy Discussion Group you made a passing reference to Thailand which is very polarized these days but I wonder if you considered Malaysia which is a very interesting case it too has been polarized ever since independence in 1957 the ruling Malay party was very dominant and then a couple of years ago came a great surprise a new political coalition was formed for an election and it attracted some of the urban Malays from the other side and it won so I just wonder if maybe it's worth a little more attention to Malaysia Yes we did think about including Malaysia only so many case studies fit in the book so we couldn't but it seems to be an interesting example of a kind of a stable not too corrosive form of a sort of a political settlement in Malaysia for a long time that began to decay over the last 10 or 20 years and as you say other actors began to form new coalitions that superseded the divide the ethnic divide that was the basis of the original political settlement in Malaysia because the formation of wider coalitions is one of the ways to get out of the polarizing bind this has sort of been the effort in Turkey you saw this year in the local elections with the opposition to AKP formed somewhat wider coalitions in some of the cities where they were running mayoral candidates and tried to say this isn't just the AKP versus the traditional secular establishment all political actors in Turkey you know have an interest in opposing the AKP for different reasons so they tried to get out of the narrow sort of box of binary polarization to create a broader coalition in Turkey there were still some other parties because of the Kurdish divide and other divides in the country that were outside that binary polarization so Malaysia is an interesting example of the polarization settlement that seems to be melting and being replaced with something that might be more pluralistic and less stuck yes I think on the second question on political financing I agree there are elements of the political financing system in the United States that are exacerbating the problem because of both studies show that political financiers who entered the system with large amounts of private money tend to be highly motivated particularly ideological actors who enter and pull the system to the size rather than towards the center and other factors in political campaign but at that point the Brexit vote of course was funded by external financing probably illegally so it has had an effect already a polarizing effect and your first question around the economic side is really complicated and interesting you don't have a chance to get into it here there are interesting cases like Turkey where the country was in its best economic period between 2001 after the economic crisis of 2001 in Turkey till recently it was a golden period of Turkish economic development but it was the most polarizing period so it was interesting that a growing pie in Turkey did not undercut a process of polarization even though Turks were doing great on the economic front same in India the summits in India you know reforms of the early 1990s that led to much more sustained and higher levels of Indian growth yet in other cases like Venezuela a sense of economic grievance and there it was more about inequality than overall levels of growth it had the grievance and did contribute to it so it's not a straight line relationship between a country's economic health and its vulnerability to polarization but you can see you have to study each one to think how is the economic factor playing into the polarizing dynamic I'm afraid that that is all the time that we have let me remind you that the book is available for sale here and please join me in thanking our panelists


Welcome back, we are looking at continued fractions and we would like to approximate every real number by continued fractions. But to begin with we were looking at towards the end of our last lecture, we were looking at approximating real numbers by means of rational numbers. Of course, we know that every rational is a continued fraction and so it is clear that every real number can be approximated by continued fractions. But what we would want to have is that the continued fractions that you get to approximate any real theta is obtained just by adding one last entry at each level. That is the expansion that is the limit of that is the sequence that we would like to construct to approximate any real theta. So we are not just looking at any set of any limit of continued fractions approximating a given real number theta but we would like to have this continued fractions to be related to each other in the sense that the nth continued fraction is obtained from the n minus 1 only by adding one last entry at the last level. So this is how we would want to do and as you see on the slide we would call such an expansion to be a continued fraction expansion of theta of course we still have to construct such an expansion. We still have to construct the sequence of continued fractions which converge to any given real number theta we would have for theta we would construct a sequence of continued fractions converging to theta in a very special way. So the sequence is going to be a very special sequence. But before that before even we go to the continued fraction expansion you all must have known that there is a decimal expansion for theta. Every real number has a decimal expansion what is a decimal expansion how do we define it let us spend some time and understand what the decimal expansion is this is something that we have been using right from our school and we found it very useful many times we find this decimal expansion quite useful especially when it is a finite decimal expansion. We need some notations so for any real number theta the square bracket theta is the greatest integer less than or equal to theta. So what we have is that this greatest integer theta has the property that it is less than or equal to theta and theta is strictly less than the greatest integer less equal theta plus 1. This is called floor function we also sometimes use this symbol to denote it there is another way which is called ceiling function which is the smallest integer less than or equal to theta smallest integer bigger than or equal to theta. So this will have the property that minus 1 is less than theta which is less than or equal to the ceiling function for theta whenever we have a list of marks obtained by our students and if the list involves some fractions in the end we convert every fraction to a full number. So we call it rounding up when you go to buy vegetables you do also rounding up but in the other direction if the bill comes out to be 503 you will simply say that Pansol alone. So that is the floor function that we are applying in some sense and when we round up the marks obtained by our students we take the ceiling function. So this is called the floor function and this is called the ceiling function. So these are two very important functions we are not going to discuss about the ceiling function at all in this course this is the only function that we are going to look at the floor function and our notation therefore is the square bracket theta. Remember it is the integer so you take all integers which are less than or equal to your theta and take the greatest one among them that is how we construct it. So let us look at some examples. If I have this 2.71828 if you remember this is the expansion for E the Euler number where it does not stop at the 8 that we have given but it goes beyond the floor function for this is equal to 2 because 2 is less than this number and 3 is not less than this number. So the greatest integer less than or equal to this quantity is 2. If you have your number to be 0.123 of course it is clear that the floor function now gives you the value 0. If you have an integer the floor function will return the same integer if the floor function of 2020 is 2020. A very important example coming up if you have the number minus 1.2 its floor function will give you minus 2 because minus 1 is not less than minus 1.2 minus 1 is bigger than minus 1.2.  So it is on the left hand side of your minus 1 therefore minus 1 is not less than that the greatest integer less than or equal to minus 1.2 is minus 2. So the floor function of minus 1.2 is minus 2 and finally the floor function of pi is 3. So remember that pi has this expansion 3.14 something something and therefore its floor function will give you the number 3. Now of course when you take any real number theta and look only at the floor functions applied to it then you have only integer and somehow you do not want to miss out on the information of theta. So we would also like to keep track of the fact the difference between your number theta and the floor function applied to theta and there is a notation for that this is denoted by curly bracket theta. By definition this is theta minus square bracket theta while talking we will call this to be the integral part of theta and this will be called the fractional part of theta. So for every real number we have these 2 things we have the integral part of theta which is an integer we have the fractional part of theta which is between 0 and 1 it can be 0 but it is not equal to 1 and your theta happens to be integral part of theta plus fractional part of theta. So these are functions and the integral part of theta fractional parts of theta so both these parts are uniquely determined by the given real number. So with this notations it is easy to describe the decimal expansion but I will not go into construction of these let me just tell you what we mean by decimal expansion. So decimal expansion of any real number theta is a sequence of integers a i which are sequence which are from 0 to 9 and with the property that summation a i 10 power minus i is theta. So where does this i here i should not be from 0 to 1 but it will be from some quantity onwards so i is going to be bigger than or equal to some minus n onwards. So we have this expansion which will be a minus n 10 power n plus a minus n minus 1 10 power n minus 1 plus dot dot dot plus a 0 into 10 power 0 which is just 1 plus a 1 into 10 power minus 1 plus dot dot dot this is our expression for theta. So for instance if you have the number 304.2397 this will be 3 into 10 power 2 plus 0 into 10 power 1 so I just ignore that 4 into 10 power 0 plus 2 into 10 power minus 1 plus 3 into 10 power minus 2 plus 9 into 10 power minus 3 plus 7 into 10 power minus 4 and we stop here because our number has a finite decimal expansion it is true that for any real n any real theta we would have such an expansion where your i will go up to infinity and this is again easy to construct because remember the sequence of rationals that we had constructed in last lecture. Here what we do is that you first of all look at the largest integer bigger less than or equal to your theta the integral part this integral part can be of course written as a sum of certain powers of 10 multiplied by some integers from 0 to 9 just as here in the example we have written 304 to be 3 into 100 plus 4 into 1 so once you do it for integer part now you have the remaining things so what we are doing is that we are constructing a sequence of rationals converging to your number theta in the following way we looked at the integer first that would give you that it is less than the distance between theta and your number is less than 1 then we would divide this in the interval the integral part of theta to integral part of theta plus 1 into 10 equal parts and we will see which of these so the interval of length 1 has now been divided into 10 sub intervals of length 1 upon 10 and your number theta has to belong to one such sub interval you take the beginning point the initial point of that sub interval here that sub interval would begin at 2 so from 304 to 305 we have exactly 10 parts the first one will begin at 304 next one begins at 304.1 the next one which begins at 304.2 that until 304.3 your number theta the number theta that we have here on in the slide belongs to that particular sub interval of length 1 by 10 then once you have found a sub interval of length 1 by 10 you divide that sub interval into 10 equal sub intervals that would give you the next decimal number in the expansion and so on so this is the way we would construct the expansion the sequence here the properties that the nth term of the sequence is less than or equal to your number theta by the distance at most equal to 1 upon 10 power n and as n goes to infinity this 1 upon 10 power n goes to 0 so you have that your sequence converges to the number theta so this is the decimal expansion that we have constructed we of course will take it for granted that such an expansion exists for every real number but note that we do not always have uniqueness of these decimal expansions there is this instance where 1 is equal to 0.999 and so on if you sum this up this is a geometric series and if you obtain the sum of this geometric series you will see that it is indeed equal to 1 so whenever you have a finite decimal expansion you have another decimal representation for the same number involving some sequence of integers ultimately ending with 9s so if you have the earlier example that we had taken if the last number was 3 then that 3 can be replaced by 2999999 so 0.3 is equal to 0.2999999 one way to understand this would be that the distance from 0.3 to 0.29 is 0.01 if you add one more 9 now the distance is 0.001 and you keep adding the 9s and your distance keeps reducing so when you go to infinity ultimately the distance goes to 0 so these two decimal expansions give you the same number now there are many differences between the decimal expansions and the continued fractions expansions that we are going to study so both have their applications the decimal expansions they seem quite useful in analysis for instance if you have seen the Cantor's proof which proves that the set of real numbers is uncountable this is called the diagonal argument of Cantor this proof uses decimal expansion on the other hand if we take the continued fraction expansions which we are going to study in this theme they seem more useful in arithmetic so as far as arithmetic is concerned we are going to see that continued fraction expansions are more useful this is something that we are going to see that the continued fraction expansions of real number of the given real number theta will provide good rational approximations so I told you in the last lecture that we are interested in finding p by q such that the distance of theta and p by q is less than 1 upon q square we are not happy with the distance being less than 1 upon q we want it to be less than 1 upon q square and we would call such rationales to give good approximation to theta and of course again there are many such approximations to theta which are good but if you impose one more condition then we will see later perhaps a few lectures later that the continued fraction expansions give you the only such nice approximations so this is something that we will see later but I must also tell you that there is this Brahmagupta pale equations which are x square minus n y square equal to 1 and you let n go to n vary over integers we are going to construct explicit solutions to such equations so the point is that n is given n is a fixed natural number and we consider the equation x square minus n y square equal to 1 and the question is to determine the set of integers x comma y satisfying this property if you look at rational numbers then this is some certain curve which we can easily draw if you are looking at real numbers then this is these are the points on some certain curve which we can easily draw but we are looking at integer solutions to this and so this is what is known as a Diphantine equation the solution to such equations forms the study of Diphantine equation which is initiated by the Greek mathematician Diphantas so this is an instance which we are going to study soon in our coming lectures but the point right now we want to understand is what is a good approximation and does there exist at least one such good approximation to a given real theta so that can be solved that has an affirmative answer by this theorem proved by the mathematician Dirichlet so let me recall the statement of the theorem let us understand the statement of the theorem we have a real number theta and we are looking at any integer bigger than 1 we fix any integer q bigger than 1 then we say that there are integers p comma q with the property that the denominator is less than q and this difference is at most 1 by capital Q this is the result that we want to prove so we want to say that there are these numbers p by q with the property that the denominator q I am calling q as the denominator and the reason for that will be clear very soon so this denominator is a positive quantity which is strictly between 0 and q and moreover mod q theta minus p is less than or equal to 1 upon capital Q the integer we started with so this proof involves one small trick consider the q plus 1 real numbers 0 1 fractional part of theta fractional part of 2 theta so on up to fractional part of q minus 1 into theta notice that these are indeed q plus 1 real numbers here we have first multiple of theta second multiple of theta until q minus 1 multiple of theta so these are q minus 1 numbers and we have 0 and 1 so once we add these we get q plus 1 numbers in all moreover these numbers are in the set 0 1 because we have observed that fractional parts of any real number is between 0 and 1 it is never equal to 1 but it is it can be equal to 0 so it is in closed 0 open 1 and here we have also taken 0 and 1 so we have these q plus 1 integers these q plus 1 real numbers and we will put them in these q sub intervals similar to what we had seen in the decimal expansion where we had divided each subsequent interval into 10 equal parts here we are dividing our interval 0 to 1 into q equal parts now we have q sub intervals and we have q plus 1 numbers and here is a principle which is often used in mathematics and therefore it has a name this is called pigeon hole principle which states that if you have n holes and there are n plus 1 pigeons sitting in these holes then at least one hole must contain two or more pigeons it is a very easy principle to prove but because it is used quite often it is convenient to have a name for that and simply say that we use the pigeon hole principle so here the pigeon hole principle will tell you that there will have to be at least two of these numbers that we have which will have to be in one such sub interval but those two numbers cannot be 0 and 1 because 0 is at one end and 1 is at another end so those two real numbers that you get at least one of them will have to be of the form in fractional part of m theta for some certain m so we then get not equal to n such that integral part of m theta minus fractional excuse me fractional part of m theta minus fractional part of n theta is less than or equal to 1 by q and if I now explain this notion the left hand side has notation fractional part which is nothing but m theta minus the integral part of n theta and then I have n theta minus the integral part of n theta which will now become plus this is less than 1 by q so we see that you have m minus n into theta minus some rational number let us call this rational some integer let us call that integer to be p and so we have this number here which is remember we had taken m and n from 1 to up to q minus 1 so the difference it could happen that your number that you had obtained is 0 or you may have the number that you had to be 1 and then another such number has to be some fractional part of m theta in that case m will be some number from 1 to q minus 1 if there is only one fractional part and one of the 0 and 1 you will have that the corresponding m is less than or equal to q minus 1 if you have both of those numbers to be fractional parts of m theta and n theta for different m and n then we of course know that their difference has to be again less than or equal to q so I will write it as q theta minus p to be less than or equal to 1 upon q so we have obtained our q to be some number which is less than or equal to q minus 1 which means that it is strictly less than the number capital q. So this is what we have obtained but how does it help us in getting a good approximation so let us see further this gives I will just divide by q throughout because q is strictly smaller than capital q 1 upon q is going to be strictly bigger than 1 upon capital q so hence we have obtained a rational number p by q for our real number theta satisfying this inequality. This is what we call to be a good approximation to our theta by a rational number what we have proved is that you choose any capital q for that capital q we have a good approximation where the denominator is strictly between 0 to capital q so we have a bounded denominator giving us a good approximation to our real theta. In fact, if you take this theta in fact you can choose p and q such that the integral the GCD of the p and q is 1 because if they had a GCD so if p comma q the GCD is d which is strictly bigger than 1 then mod q theta minus p which we know is less than or equal to 1 upon capital q the LHS would give you will take the GCD common and you will have q 1 theta minus p 1 less equal 1 by q which would give you mod of q 1 theta minus p 1 to be less than or equal to 1 upon d q which is of course less than 1 upon q. So, if you had a GCD non trivial GCD for p comma q you can cancel that GCD out and you have these numbers and of course we had our q to be less than small q was less than capital q and we would continue to have q 1 to also be less than capital q. So, we actually get once you have a pair of such integers p comma q giving you a good approximation you will be able to get the p and q where the GCD is 1 of course the rational number that you are going to get will be the same because p by q is now going to be equal to p 1 by q 1 but the important thing is that the denominator is further smaller. So, we are looking at smaller denominators giving you good approximations this is what we would want to do. In fact, if you have an irrational number then you have even a better such approximation. So, whatever we have proved so far for implies this corollary. So, for any real theta we have this rational number p by q with the property that the distance of theta and p by q is less than 1 upon q square and this q can in fact be chosen such that it is between 0 and capital q for any integer capital q bigger than 1 that you choose. So, the statement here given is a weaker statement we have actually proved something which is even stronger. Now, if you have an irrational number then there are infinitely many such good approximations on the other hand if your number happens to be a rational number then there are only finitely many such approximations. So, this dichotomy and further the study of continued fractions giving us such nice approximations and the remaining things will be done in the next lectures. See you then. Thank you very much.