An alternative explanation of the chance of casting a pivotal vote

Uncertainty about the outcome of elections is commonly represented by person-by-person randomization, where people’s probabilities of voting for the left party in a left–right contest are assumed to be uncorrelated but the same. An alternative representation of uncertainty about the outcome of elections relies upon nation-wide randomization shifting the entire schedule of voters’ monetary valuations for one party over the other, up or down, and altering the parties’ vote shares accordingly. The alternative is broadly commensurate with historical evidence about the chance of casting a pivotal vote, gives rise to a chance of casting a pivotal vote that is small but not, as often supposed, infinitesimal, explains an important source of bias in elections and preserves a role for self-interest, as well as duty, in the decision whether to vote or abstain.