Voting as a Lottery

Voting is a lottery in which an individual who is uncertain about how the others vote wins if she belongs to the majority or loses if she falls into the minority. The risk of losing can be reduced by increasing the majority threshold. This however has the negative effect of also lowering the chance to win. We find that an individual prefers higher majority thresholds when she is more risk averse, less powerful, or less optimistic about the chance that others will vote like her. De facto, raising the majority threshold is a form of protection against the higher risk of being tyrannized by an unfavorable majority. We include these preferences for majority thresholds in a Nash bargaining game that describes constitutional negotiations over voting rules. Individuals that largely avert the risk of being tyrannized behave reluctantly during negotiations, and succeed in getting higher protection through a threshold raise.