Brendan Nyhan and Jacob Montgomery talk sense here. I am perhaps too influenced by Steven Rosenstone’s 1983 book, Forecasting Presidential Elections, which is the first thing I read on the topic. In any case, I agree with Nyhan and Montgomery that the difference in vote, comparing a centrist candidate to an extreme candidate, is probably on the order of 1-2%, not the 4% that has been posited by some.

Andrew Gelman is a professor of statistics and political science and director of the Applied Statistics Center at Columbia University. He has received the Outstanding Statistical Application award from the American Statistical Association, the award for best article published in the American Political Science Review, and the Council of Presidents of Statistical Societies award for outstanding contributions by a person under the age of 40.