NANCY Seminar – Eric KAMWA (BETA)

Event details :

Title: Equilibrium under Preference Approval Voting and Fallback Voting

Abstract: Two major debates have opposed theorists in voting theory or the aggregation of individual preferences. The first pitted the Marquis de Condorcet (1785) against the Chevalier de Borda (1781) regarding the “best” rule for aggregating preferences. This debate seems to have found its conclusion in the impossibility theorems of Arrow (1963) and Gibbard (1973)–Satterthwaite (1975): there is no perfect aggregation rule. More recently, the other debate involved Donald G. Saari & Van Newenhizen (1988) against Brams et al. (1988): what is the “best” way to express preferences? The first group of authors advocates an approach based on individual rankings (strict, complete); the second group, on the other hand, opts for an approval-based approach that allows individuals to approve/disapprove as many options as they deem acceptable from the set of options submitted for their evaluation. The works developed around these two approaches have primarily focused on situations where the object of preference aggregation is the choice of a single option or a unique social optimum.

Brams and Sanver (2009) proposed an approach for expressing individual preferences that combines the two dominant approaches; individuals approve and rank (or rank and approve) the options. Brams and Sanver (2009) also proposed two aggregation rules that fit within this new approach: Preference Approval Voting (PAV) and Fallback Voting (FV). Brams and Sanver (2009), Sanver (2010), Kamwa (2019, 2023) have shown, among other things, that the PAV and FV rules seem to perform better than Approval Voting (AV) and the most popular ranking-based rules such as Plurality and Borda rules.

Under PAV and FV, some individuals, sincere in their rankings, may strategically choose where to draw the line between approved and disapproved candidates to try to elect their preferred candidates. These individuals may induce a better outcome by contracting or expanding their approval sets. In such a case, the outcome is said not to be in equilibrium (Brams and Sanver, 2009). An outcome is in equilibrium if the approval strategies of each preference class of individuals that produce it constitute a Nash equilibrium.

The contribution of this article is twofold. We characterize the cases where an outcome under PAV or FV is in equilibrium. Among other things, we show that when voters’ preferences are sincere and the strategies admissible, if an Absolute Condorcet winner exists, they constitute an outcome in equilibrium under both PAV and FV; if PAV chooses an AV outcome that is in equilibrium, it is also in equilibrium under PAV. Our characterization also extends to the notion of a set of critical strategies. By exploring the case of three-candidate elections with an infinite electorate where voter preferences are sincere and admissible strategies, we obtain results indicating that FV and PAV are more likely to lead to an outcome in equilibrium than AV.