Charles Kurzman and Ijlal Naqvi have "examined results from parliamentary elections in all Muslim societies":
Given the choice, voters tend to go with secular parties, not religious ones. Over the past 40 years, 86 parliamentary elections in 20 countries have included one or more Islamic parties, according to annual reports from the Inter-Parliamentary Union. Voters in these places have overwhelmingly turned up their noses at such parties. Eighty percent of these Islamic parties earned less than 20 percent of the vote, and a majority got less than 10 percent -- hardly landslide victories. The same is true even over the last few years, with numbers barely changing since 2001.
True, Islamic parties have won a few well-publicized breakthrough victories, such as in Algeria in 1991 and Palestine in 2006. But far more often, Islamic parties tend to do very poorly. What's more, the more free and fair an election is, the worse the Islamic parties do. By our calculations, the average percentage of seats won by Islamic parties in relatively free elections is 10 points lower than in less free ones.
(Hat tip: 3QD)