A Computational Analysis of Strategic Nominations: Modeling Equilibrium and Complexity in Organizational Elections

TL;DR

This paper analyzes organizational elections with probabilistic outcomes, demonstrating the complexity of equilibrium existence, providing algorithms for certain cases, and bounding inefficiency in strategic nominations.

Contribution

It introduces a formal model for strategic nominations, proves NP-completeness of equilibrium existence, and offers algorithms and bounds for specific classes of voting rules.

Findings

Pure-strategy Nash equilibria may not exist with three or more groups.

Deciding equilibrium existence is NP-complete.

An FPT algorithm computes equilibria under certain conditions.

Abstract

We study organizational elections in which each group nominates one candidate and receives as payoff its members expected utility under a probabilistic winning rule. We empirically justify a standard monotonicity assumption by simulating two- and three-group elections, finding that a candidates aggregate voter utility correlates monotonically with win probability. For three or more groups, we show that pure-strategy Nash equilibria (PSNE) may fail to exist even under egoistic preferences, and that deciding PSNE existence is NP-complete in a succinct (general form) representation. For cross-monotone winning-probability functions, we give simple sufficient conditions for PSNE existence and an FPT algorithm to compute one, parameterized by the number of irresolute groups and nominating depth. Finally, for crossmonotone, order-preserving winning-probability functions, we bound the price of anarchy of egoistic games by the number of groups.