Ideologically driven gerrymandering over the past several decades has produced an in­creasing number of relatively homo­genous congressional districts represented by legislators with little to fear from most ­challengers.

But anyone who thinks more diverse districts are ­rough-­and-­tumble rings of fierce political competition has another thing coming. Political scientists Michael J. Ensley of Kent State University, Michael W. Tofias of the University of Wiscon­sin, Milwaukee, and Scott de Marchi of Duke University write that in districts where the political landscape is especially hard to understand, potential challengers rarely materialize, and when they do, they are more likely to ­lose.

The trio gauged the complexity of congressional districts by examining opinion-poll data on residents’ views on economic issues such as taxation and on cultural questions—­what to do about abortion, guns, and school prayer. Districts where the two areas of belief were highly correlated have “simple” political landscapes; a candidate in such a district can make accurate pre­dictions about how consti­tuents feel about gun control based on how they feel about taxes. In districts where people have, say, uni­formly conservative economic views but heterogenous social values, poten­tial challengers face a problem. In these “compli­cated” districts, putting together an accurate picture of people’s views requires a lot more polling than in a simple district (a process that can be quite expensive).

The 2000 election bore out the authors’ argument. In districts with greater political complexity,  a serious challenger was far less likely to emerge, and those who did fared much worse come Election Day. In the ever artless language of political scientists, “If we compare a district with a complexity score two standard deviations below the mean to a district with a score two stand­ard devia­tions above the mean, there is a 2.5 percent difference in the incumbent’s expected share of the vote.” Simply put, the more com­plex a district, the better the in­cumbent fared. Ensley and colleagues ex­plain, “By definition, an incum­bent has done a good job of finding a successful platform at least once.” Best of luck to the ­go-­get­ters who want to throw their hats in the ring.