Incentives for Participation and Abstention in Probabilistic Social Choice
Voting rules are powerful tools that allow multiple agents to aggregate their preferences in order to reach joint decisions. A common flaw of some voting rules, known as the no-show paradox, is that agents may obtain a more preferred outcome by abstaining an election. Whenever a rule does not suffer from this paradox, it is said to satisfy participation. In this paper, we initiate the study of participation in probabilistic social choice, i.e., for voting rules that yield probability distributions over alternatives. We consider three degrees of participation based on expected utility, the strongest of which even requires that an agent is strictly better off by participating at an election. While the latter condition is prohibitive in non-probabilistic social choice, we show that it can be met by reasonable probabilistic functions. More generally, we study to which extent participation and Pareto efficiency are compatible. To the best of our knowledge, this is the first work in this direction.