ONE lowly state senator from southern California, upon seeing the state's new electoral maps and realising that no incumbent member of Congress currently lives in a district to be drawn around her home, spontaneously declared: “I'm in, I'm in, I'm in, I'm in,” and thus became a candidate for the House of Representatives in Washington, DC. Other state senators, assemblymen and US representatives were rather less effusive. Several suddenly found themselves sharing a district with political allies who may now become rivals, or facing a much less sympathetic electorate.

This chaos among California's incumbent politicians is a good sign. For the new lines of 177 districts, released on June 10th and to be finalised by August 15th, were drawn, for the first time, by a genuinely independent commission of citizens, not by state legislators. The panel's mandate is to make compact, contiguous districts that preserve natural “communities of interest” such as ethnic groups, and to ignore politics altogether. The commissioners do not even have voter-registration statistics or the addresses of incumbents. The revolutionary new idea is that, instead of politicians choosing their voters, voters should choose their representatives.

This marks a dramatic change in the history of American democracy. The practice of rapacious boundary-drawing dates back to the Founding Fathers. Patrick Henry, who famously demanded liberty or death, tried to draw a congressional map of Virginia to deny his foe James Madison election. In 1812, the partisans of Elbridge Gerry, then governor of Massachusetts, drew a state-Senate district so bizarre that its salamander shape led to the term “gerrymandering”, which persists to this day.

By contrast, a related flaw, called malapportionment, was largely fixed in the 1960s. Until then, districts across America had very different populations but equal representation, so that some (mostly rural) communities were over-represented in legislatures and Congress, while others were under-represented. But in 1964 the Supreme Court enshrined the principle of “one person, one vote”. It requires districts to have the same population, so that their boundaries must be redrawn after every census (ie, once a decade).

Because most states still let their legislators do this redrawing, gerrymandering has remained a problem. In democracies with proportional representation (as in continental Europe), maps are not very important. But in America's “winner-takes-all” system, where the candidate with a plurality of votes becomes the representative and all other votes count for nothing, maps are crucial. Thus legislators like to draw lines that, in the jargon, “pack” more of their supporters into one district to make it safe, or “crack” a hostile block of voters into several districts, and so, with many variants, forth.

Such gerrymandering can be extremely partisan when the majority party in a legislature draws districts that favour its candidates, as the Republicans did in Texas a decade ago. But it can also happen on a bipartisan basis, when both parties agree on maps that favour the incumbents. California's legislature did this in 2001, producing cynically squiggly districts that made most of the seats safe for whichever Republicans or Democrats already held them. In the 612 races of California's last four elections, only seven seats have changed from one party to the other.

Over the years, several states have tried to scrub their maps clean of such shenanigans. Iowa was first in 1980, making redistricting largely apolitical, although the legislature must still approve all maps. But Iowa is a homogenous and geographically simple state, and its system was not copied. Some 19 other states, aside from California, have established commissions, either as the main mapmakers or as advisers to the legislature. But most of these panels are still, one way or another, appointed by politicians, with varying degrees of independence. Arizona's commission, the result of a ballot measure in 2000, was the most promising, but its maps were fought over for seven years in the courts.

So now comes California's reform, which could be “the great experiment that other states will follow”, according to Tim Storey, a redistricting analyst at the National Conference of State Legislatures. Also approved directly by voters, in two separate ballot measures, this commission consists of 14 members, chosen in a complex but rigorous process, partly by lottery. In its diligence and transparency, it has been above reproach.

The hope among many voters, of course, is that more districts will thereby become competitive, forcing politicians to become more moderate. It helps a lot that California has also adopted a non-partisan primary system with the same aim. Analysis by the Public Policy Institute of California, a think-tank, shows that the maps do indeed make several additional districts toss-ups (see chart), with Democrats benefiting slightly more.

On the other hand, Californians may also have set themselves up to be disappointed, says Paul Mitchell at Redistricting Partners, a consultancy. The new system is certainly “shaking up the ant farm, but it's still an ant farm,” and political extremism has many causes, not just gerrymandering. One only needs to look at the US Senate, whose members are all elected statewide, and therefore not gerrymandered at all, to see that. But at least from now on voters are a bit more likely to feel that they had a genuine choice, and that they deserve what they chose.