Approval voting allows voters to support as many candidates as they wish. One advantage of the method is that voters have weak or no incentives to vote insincerely. However, the exact meaning of this statement depends on how the voters' preferences over candidates are extended to sets. We show...

Approval voting allows voters to support as many candidates as they wish. One advantage of the method is that voters have weak or no incentives to vote insincerely. However, the exact meaning of this statement depends on how the voters' preferences over candidates are extended to sets. We show...

In this short paper, we analyze the implications of dropping the axiom of faithfulness in the axiomatization of approval voting, due to P. C. Fishburn. We show that a ballot aggregation function satisfies the remaining axioms (neutrality, consistency and cancellation) if and only if it is either...

In this note we discuss two examples of appoval voting games. The first one, with six voters and three candidates, has a unique stable set,where each voter approves only his most preferred candidate. This strategy coincides with the sophisticated one, while other strategy combinations, leading...

We assume that people have a need to make statements, and construct a model in which this need is the sole determinant of voting behavior. In this model, an individual selects a ballot that makes as close a statement as possible to her ideal point, where abstaining from voting is a possible...

We assume that a voter’s judgment about a proposal depends on (i) the proposal’s probability of being right (or good or just) and (ii) the voter’s probability of making a correct judgment about its rightness (or wrongness). Initially, the state of a proposal (right or wrong), and the...

We present a simple voting environment where the Condorcet winner exists. Under plurality rule, the derived game has a stable set where such a candidate is elected with probability one. However, no stable set of the approval game elects the Condorcet winner with positive probability.

It is commonly accepted that the multiplicity of equilibria is ubiquitous in preference aggregation games with any voting method. We prove that this multiplicity is greatly reduced under some mild restrictions over social preferences when each voter can vote for as many candidates as she wishes...

We prove two results on the generic determinacy of Nash equilibrium in voting games. The first one is for negative plurality games. The second one is for approval games under the condition that the number of candidates is equal to three. These results are combined with the analogous one obtained...

This work provides necessary and sufficient conditions for the dominance solvability of approval voting games. Our conditions are very simple since they are based on the approval relation, a binary relation between the alternatives. We distinguish between two sorts of dominance solvability and...