arXiv subjects

Héctor Hermida-Rivera

Publications and source records attributed to Héctor Hermida-Rivera.

5 recordsLinked to original sources

arXiv2026

Self-Equivalent Voting Rules

In this paper, I introduce a novel stability axiom for stochastic voting rules, called self-equivalence, by which a society considering whether to replace its voting rule using itself will choose not to do so. I then show that the unique voting rule satisfying the democratic principles of anonymity, efficiency, monotonicity, and neutrality as well as the stability principle of self-equivalence must assign to every voter equal probability of being a dictator (i.e., uniform random dictatorship). Thus, this paper suggests one reason why most democratic societies normally choose whether to replace their voting rule using a voting rule other than itself, or in binary elections against just one other voting rule.

econ.TH↗

arXiv2025

A Note on Qualified Majority Voting Rules

This note characterizes every qualified majority voting rule in environments with just two alternatives through anonymity, responsiveness, and q-neutrality. Crucially, the latter imposes independence of the labels of the alternatives if and only if some alternative is strictly top-ranked by at least q voters. Thus, this note generalizes May's (1952, Theorem, p. 682) characterization of the simple majority voting rule to qualified majority voting rules. In doing so, it shows that qualified majority voting rules are distinguished by their degree of neutrality.

econ.TH↗

arXiv2025

Binary Self-Selective Voting Rules

This paper introduces a novel binary stability property for voting rules-called binary self-selectivity-by which a society considering whether to replace its voting rule using itself in pairwise elections will choose not to do so. In Theorem 1, we show that a neutral voting rule is binary self-selective if and only if it is universally self-selective. We then use this equivalence to show, in Corollary 1, that under the unrestricted strict preference domain, a unanimous and neutral voting rule is binary self-selective if and only if it is dictatorial. In Theorem 2 and Corollary 2, we show that whenever there is a strong Condorcet winner; a unanimous, neutral and anonymous voting rule is binary self-selective (or universally self-selective) if and only if it is the Condorcet voting rule.

econ.TH↗

arXiv2025

The Implementability of Liberalism

This note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A social choice rule is choice liberal if and only if for every player, there exists at least one pair of outcomes such that if this player strictly prefers one over the other, the one he prefers is socially desirable and the other one is not. A social choice rule is Nash implementable if and only if there exists a mechanism such that at every preference profile, the set of Nash equilibrium outcomes coincides with the set of socially desirable ones. The proof constructs an intuitive Nash implementing mechanism.

econ.TH↗

arXiv2025

Minimal Stable Voting Rules

In this paper, I characterize minimal stable voting rules and minimal self-stable constitutions (i.e., pairs of voting rules) for societies in which only power matters. To do so, I first let players' preference profiles over voting rules satisfy four natural axioms commonly used in the analysis of power: non-dominance, anonymity, null player and swing player. I then provide simple notions of minimal stability and minimal self-stability, and show that the families of minimal stable voting rules and minimal self-stable constitutions are fairly small. Finally, I conclude that political parties have evolved to ensure the minimal self-stability of otherwise not minimal self-stable constitutions.

econ.TH↗