Bargaining through Approval

Abstract

International audienceThe paper considers two-person bargaining under Approval Voting. It first proves the existence of pure strategy equilibria. Then it shows that this bargaining method ensures that both players obtain at least their mean utility level in equilibrium. Finally it proves that, provided that the players are partially honest, the mechanism triggers sincerity and ensures that no alternative Pareto dominates the outcome of the game

Reaching Consensus Through Simultaneous Bargaining

“…If the two sets do not intersect then the final outcome is selected using the uniform lottery over the union. Núñez and Laslier (2014) show that every equilibrium outcome of this game is individually rational and, if players are partially honest, not Pareto dominated by any pure alternative. The definition of sincerity in this setting is borrowed from the approval voting literature (Brams and Fishburn, 1983).…”

“…If the two sets do not intersect then the final outcome is selected using the uniform probability measure over the union. We show that this game retains every desirable property in Núñez and Laslier (2014) while also obtaining full efficiency when players are partially honest. Again, we borrow the definition of sincerity form the approval voting literature and say that a strategy is sincere if whenever it includes some lottery it also includes every lottery that is at least as good.…”

“…In contrast, Núñez and Laslier (2014) show that approval voting (Brams and Fishburn, 1983;Laslier and Sanver, 2010) can be reinterpreted as a bargaining protocol when there are only two voters. It is a one-shot bargaining game where each agent approves a subset of the finite set of alternatives.…”

“…This paper departs from Núñez and Laslier (2014) and considers a one-shot game in which each player selects a set of lotteries over the pure alternatives.…”

Dominance solvable approval voting games

“…Due to their simplicity, this pair of examples summarizes many of the interesting insights of voting theory. For instance, approval voting is less problematic than the other results since it gives better incentives for coordination (see also Babichenko & Schulman, 2015;Börgers, 1991;De Clippel, Eliaz, & Knight, 2014;Laslier, Núñez, & Pimienta, 2017;and Núñez & Laslier, 2015 for mechanism design in the framework of simple elections).…”