Indecision Theory: Explaining Selective Abstention in Multiple Elections

We present a new model of voting which explains the so-called "roll-off" phenomenon: Selective abstention in multiple elections. We first characterize when a Bayesian voter prefers to abstain, and find that such choice necessitates correlation in the voter's beliefs between election outcomes and candidate policies. We then show that if a voter is ambiguity averse, he may abstain under more general circumstances. In fact, ambiguity aversion about the candidates' policy positions can make abstention look to the voter a smaller "mistake" than voting for one of the candidates. We investigate the conditions under which this happens, and find that it does when the voter sees the candidates as sufficiently complementary in their ambiguity. As this will likely happen in those elections on which the voter has poor or nil information, our model provides a possible explanation for selective abstention.