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    Don't Vote - It's Completely Irrational

    One of the interesting things about voting is that there isn't a good reason for it, especially from the perspective of modeling human behavior that's common in fields like economics.  In order to illustrate why this is true, I've put today's Presidential election into a simple game theory framework:

    I've modeled both an Obama voter and a Romney voter, but the models are the same.  The idea here is that the best payoff occurs when a voter's candidate wins.  However, there is also a cost to voting - time, lost wages, travel expenses, psychic cost - represented by c.  We've assumed that cost is variable, but less than the payoff of getting one's candidate in office.  The result is that the best payoff for each voter is to not vote, but still end up with their candidate winning.

    Doesn't voting actually increase the likelihood that your candidate will win?  Not really.  The closest Presidential election was Kennedy over Nixon in 1960.  Kennedy won by just over 100k votes nationally.  Even then, that means the odds of an individual vote being the deciding vote is less than 0.00001%.  It's usually even less.  Given that your vote is incredibly unlikely to decide the outcome, you're always better off not voting because you avoid the costs associated with voting

    You might quibble that this model doesn't account for the electoral college, but that makes things worst for most voters.  There is absolutely no rational incentive to vote for President in states like California or Texas.  Of course, the electoral college does amplify the effect of voting in swing states, but it doesn't really improve the odds - situations like Florida in 2000 notwithstanding.

    So, why do so many people vote?  There are some possible explanations.  Satoshi Kanazawa offers the possibility that we are not in fact forward-looking utility maximizers, but backward-looking adaptive learners, meaning that we're really voting on the last election.  Fighting the last war anyone?  It also has to do with feeling like a loser or like a winner depending on whether you feel your behavior was rewarded in the past.

    Whatever, the reason - and it sure isn't a rational belief that your actions will affect the outcome of the election, because they objectively will not - millions of people still turn out to vote.  So, sound off here and let us know why you're jamming a stick in the eye of homo economicus today.

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    We like to run up the score, trounce the other team, bash their skulls in, grind up their kneecaps, percolate their sinus cavities, and other juicy imagery. I'm surprised after all these years game theory still doesn't reflect the game as much as the theory.

    I recall a particularly insightful article that noted the flocking of reporters to Iowa each election year to get the opinion of "typical Americans" - middle aged white male farmers driving tractors, whereas the author noted there are more World of Warcraft players in lower Manhattan than there are white middle-aged farmers in all of the US, but he couldn't remember the last time the press flocked to him to ask the opinion of real World of Warcraft Americans on the pressing issues of the day.

    Personally I believe "c" will decrease into a barely manageable integer between 1 and 100, so instead of "swing states", we'll have a group of "swing personalities" (no, no chemical imbalance jokes please) to fit in a room and decide the next "leader of the free world" (which now that we own most of the Mideast, should only leave out Burma, China, Russia/Belorus & South Korea?). Maybe we could invoke a game of capture the flag or Parcheesi, and pocket the obscene amounts of money spent pretending to debate issues and solve world problems. Just like Numberwang.

    Presidential elections and Numberwang do seem to be on the path to convergence.

    It is 2012 - the Mayans will have their way with us as foretold, whether we believe in astrology and mysticism or not. Let's play Mayan Numberwang!!!

    BTW, if you're going to play this perfesser ruse, shouldn't it be "1-c" and "0+c"? Seems having negative voters draws some disturbing questions.

    Perhaps I failed to properly explain the model.  It's a simultaneous form game, like in the Prisoner's Dilemma.  The grids contain payoffs, not the number of voters.  ( 0 - c ) is correct because the payoff is negative in the case that you vote, and thus pay the associated costs, but your candidate of choice loses.  As a consequence of this, the best possible payoff is to not vote and avoid the associated costs, but win anyway.

    Ah, so instead of the cheery "you win by playing", you stand to lose a lot - sometimes better to sit it out than have your leg gnawed off by a wild boar. If I can use a popular allusion...

    But go ahead and exercise your right and duty to vote - it can only end up... painful.

    Though realistically there can be gains from playing - putting a seat in play that was assumed to be an easy win, causing the winning opponent to put in more resources next season. A plus for both your party and the consultants/advertisers you make rich each season, and the journalists who make their yuan off a close race. You of course have burned out your chances by a fickle populace who discard your once promising career on the dustbin of history, close being only good in horseshoes and handgrenades. But somewhere, a little karma has been set free....

    The model, though useful in some respects, is clearly "wrong" in the sense that it's not predictive of human behavior.  Millions of people vote anyway, even when the associated costs are incredibly high - like being forced to stand outside in inclement weather for hours.  A model that was more predictive would need to find a way to explain why the payoff when voting appears to be higher than the associated costs.  If it were, then you could arrive at an equilibrium strategy that involves voting.

    Taking a simple approach based on Kanazawa's work, you might add a term to represent some kind of psychological payoff effect so that the amended payoff term when voting is something like ( b - c ), where voting and winning yields ( 1 + b - c ) and losing yields ( 0 + b - c ).  For any voter where b > c, voting is now the equilibrium strategy.

    Another interesting consequence of adding this "psychic" term is that it becomes advantageous to find ways to reduce c if you want to increase turnout.  There's no reason to think that reducing associated costs will change the incentive to vote in the model as I originally presented it.  You can let c = 0, but then voting and not voting are equivalent strategies.

    Even without fully identifying what might be captured by the additional term b, you now have a model that can potentially explain why people might vote, what conditions cause them to vote ( b > c ) and what effect lowering the associated costs of voting might have.


    It (along with paying taxes) allows us to feel entitled--more entitled than those who don't vote, that is--to bitch.  Or even offer constructive suggestions.

    It can earn us greater social acceptance or standing, there being a certain embarrassment in some peer/neighbor/family networks owing to not voting.  In others, not voting may be seen as a badge of honor.  

    It coheres with our inner Kantian, the part of some of us that judges the appropriateness of our actions at least in part by whether they seem "universalizable":  "What would happen if everyone, believing as I do that their vote will not affect the outcome, opted not to vote?"

    To some of us who have breathed in arguably too much of this representative government  air in our lifetimes, it feels good and right.  Or at least better than not voting.



    These are all good potential explanations.  See my response to Peracles above about expanding the model in attempt to capture some of these psychic rewards.

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