Power illusion in coalitional bargaining: An experimental analysis

Abstract

One feature of legislative bargaining in the real world is that the distribution of seats or voting weights often does not accurately reflect real bargaining power. Game-theoretic predictions about payoffs and coalition formation are insensitive to such purely nominal differences. The converse idea that nominal differences might matter is referred to as 'power illusion'. We conduct an experimental test of the classical Baron-Ferejohn model with five player groups. We compare treatments with differences in nominal power holding real power constant. We find strong evidence for the existence of power illusion in almost all aspects of bargaining behavior even if subjects got familiar with the game. This implies that attention needs to be paid to nominal power differentials in the design of weighted voting systems.

The determinants of multilateral bargaining: a comprehensive analysis of Baron and Ferejohn majoritarian bargaining experiments

“…11 See Maaser et al (2019) for a recent experiment in which voting weights are varied. A similar conclusion is reached as the one derived from our comprehensive analysis.…”

Recognition probability in legislative bargaining

“…Diermeier and Gailmard (2006) and Kim and Kim (2022) show that a high disagreement value might induce unfavorable offers from other agents, which can result in lower expected payoffs (Miller et al 2018). Maaser et al (2019) find that inexperienced subjects' bargaining behavior is sensitive to the nominal differences in voting weights, when there is no difference in real bargaining power defined by pivotality.…”

Gender and Nominal Power in Multilateral Bargaining

“…At the beginning of each period, each subject was randomly assigned her voting weight for that period (see [8] for a methodological discussion of random vs. fixed roles). Notes: The table shows how data from [4] are pooled in the current analysis.…”

“…From a game-theoretic perspective, purely nominal differences in voting weights should not matter. If they are nevertheless found to influence behavior and outcomes, this indicates the presence of a "power illusion", a possibility that has previously been studied in the context of structured multilateral bargaining [4][5][6] and in unstructured bargaining [7,8]. Guerci et al [9] focuses on how experimental subjects learn about nominal weights, without a bargaining context.…”

“…Among the studies that considered nominal power differences in Baron-Ferejohn bargaining, evidence for power illusion is mixed. While [5] found power illusion effects to apply only to inexperienced subjects [4] (hereafter: MPT) reported that nominal differences can continue to influence agents' behavior in spite of experience. In [6], the effect of nominal weights is a secondary aspect, as main interest is to test the effect of adding a new player to a weighted voting game.…”