TY - JOUR
T1 - Strategic Candidacy Equilibria for Common Voting Rules
AU - Lang, Jérôme
AU - Maudet, Nicolas
AU - Polukarov, Maria
AU - Cohen-Hadria, Alice
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.
PY - 2025/5/8
Y1 - 2025/5/8
N2 - In strategic candidacy games, both voters and candidates have preferences over possible election outcomes, and candidates may strategically choose to join or leave the election. Following the model by Dutta et al. (Econometrica 69:1013–1037 2001) and (Journal of Economic Theory 103:190–218 2002), this paper presents a first systematic analysis of such games for a list of common voting procedures. We address the question of whether such games possess a pure strategy Nash equilibrium in which the outcome is the same as if all candidates run (which we call genuine equilibria). We give a number of negative results: unless the number of candidates is small (less than 3, 4 or 5, depending on the voting rule), there may be games without such stable outcomes. When the existence of genuine equilibria is not guaranteed, we also consider a weaker stability version, namely the existence of a pure strategy Nash equilibrium. Although most of our results are on the negative side, we identify one prominent rule that guarantees the existence of a genuine equilibrium, for any number of candidates, and for an odd number of voters: the Copeland rule. However, strong equilibria, where no coalition of candidates has a profitable collective deviation, are not guaranteed to exist, for almost any voting rule, including Copeland. Finally, we establish for the first time a strong relationship between equilibria of candidacy games and a form of voting control by adding or removing candidates, where candidates must consent to addition or deletion, and we initiate the study of resistance to this new version of control in elections.
AB - In strategic candidacy games, both voters and candidates have preferences over possible election outcomes, and candidates may strategically choose to join or leave the election. Following the model by Dutta et al. (Econometrica 69:1013–1037 2001) and (Journal of Economic Theory 103:190–218 2002), this paper presents a first systematic analysis of such games for a list of common voting procedures. We address the question of whether such games possess a pure strategy Nash equilibrium in which the outcome is the same as if all candidates run (which we call genuine equilibria). We give a number of negative results: unless the number of candidates is small (less than 3, 4 or 5, depending on the voting rule), there may be games without such stable outcomes. When the existence of genuine equilibria is not guaranteed, we also consider a weaker stability version, namely the existence of a pure strategy Nash equilibrium. Although most of our results are on the negative side, we identify one prominent rule that guarantees the existence of a genuine equilibrium, for any number of candidates, and for an odd number of voters: the Copeland rule. However, strong equilibria, where no coalition of candidates has a profitable collective deviation, are not guaranteed to exist, for almost any voting rule, including Copeland. Finally, we establish for the first time a strong relationship between equilibria of candidacy games and a form of voting control by adding or removing candidates, where candidates must consent to addition or deletion, and we initiate the study of resistance to this new version of control in elections.
UR - http://www.scopus.com/inward/record.url?scp=105004413526&partnerID=8YFLogxK
U2 - 10.1007/s00224-025-10220-3
DO - 10.1007/s00224-025-10220-3
M3 - Article
SN - 1432-4350
VL - 69
JO - THEORY OF COMPUTING SYSTEMS
JF - THEORY OF COMPUTING SYSTEMS
IS - 2
M1 - 23
ER -