Majoritarian Bargaining Research Articles

An Experiment on Gender Representation in Majoritarian Bargaining

Women are underrepresented in business, academic, and political decision-making bodies across the world. To investigate the causal effect of gender representation on multilateral negotiations, we experimentally manipulate the composition of triads in a majoritarian, divide-the-dollar game. We document a robust gender gap in earnings driven largely by the exclusion of women from alliances rather than differential shares within alliances. Experiments with different subject pools show that distinct bargaining dynamics can underlie the same inequitable outcomes; gender-biased outcomes can be caused by outright discrimination, but they can also be driven by more complex dynamics related to differences in bargaining strategies. Although replacing the male with a female majority all but eliminates the gap in one pool, it has minimal effect in the other. These findings show that there is no “one-size-fits-all” solution to the gender gap we uncovered and highlight the importance of studying bargaining dynamics in detail. This paper was accepted by Marie-Claire Villeval, behavioral economics and decision analysis. Funding: A. Baranski recognizes financial support from Tamkeen [under the New York University Abu Dhabi Research Institute; Grant CG005]. J. Tremewan acknowledges funding from the Agence Nationale de la Recherche [Grant ANR-21-CE03-0018 (Project ENDURA)]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01800 .

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

We analyze the data sets of all majoritarian Baron and Ferejohn (Am Political Sci Rev 83(4):1181–1206, 1989) experiments through 2018. By exploiting the variation of the experimental parameters, we are able to identify how group size, discount factor (cost of agreement delay), voting weights, and communication affect bargaining outcomes and dynamics. The outcomes are qualitatively in line with the stationary subgame perfect equilibrium, i.e., minimum winning coalitions are modal; proposers demand larger shares than non-proposers; and most agreements are reached without delay. Experience and communication between players move outcomes closer to the equilibrium. However, bargaining dynamics are not stationary. Behavior following a disagreement is history-dependent in the form of retaliation towards failed proposers and their supporters, which, if rationally expected, may deter proposers from demanding high shares.

An Experiment on Gender Representation in Majoritarian Bargaining

An Experiment on Gender Representation in Majoritarian Bargaining

The impact of group identity on coalition formation

Bargaining and coalition building are a central part of modern politics. We argue that majoritarian bargaining is important for the formation of coalitions and that group-identity preferences have an impact on partner selection. We tested the effect of gender, race, and ideological distance in a majority-rule bargaining experiment and found that ideological distance significantly affected the likelihood and amount offered to potential partners. We concluded that formateurs are not necessarily purely rational actors pursuing policy goals and/or the benefits of office. Rather, they also care about the identity of their partners, preferring others who are like themselves.

Majoritarian Bargaining over Budgetary Divisions and Policy

We report the results of a field-in-the-lab experiment in which subjects bargain over a two-dimensional agenda: a donation to a political interest group and the division of a sum of money. We show that subjects sacrifice monetary gains to secure preferred policies and that behaviorally elicited preference intensity correlates with bargaining behavior. We find an ideological majority advantage and a status quo premium. Minorities benefit most from negotiating on two dimensions because the budgetary division problem allows compromise. Finally, we show that induced preferences over artificial policies fail to capture the bargaining dynamics that arise when real ideological choices are involved.

The Determinants of Multilateral Bargaining: A Comprehensive Analysis of Baron and Ferejohn Majoritarian Bargaining Experiments

We collected and analyzed the data sets of all majoritarian Baron and Ferejohn (1989 Am. Pol. Sci. Rev.) experiments through 2018. By exploiting the variation of experimental parameters such as group size and discount factor we are able to test whether or not the theoretical point predictions and comparative statics hold and find virtually no support for the theory. Novel findings are reported about the effect of group size and discounting on distribution of the surplus, the proposer's share, agreement delay, and voting behavior. We also report on off-equilibrium behavior (after subjects fail to agree) and identify strong history-dependent behavior in the form of punishment and loyalty to previous proposers.

Communication in Multilateral Bargaining with Joint Production

We experimentally investigate the effect on efficiency of pre-bargaining communication in a multilateral majoritarian bargaining game with joint production under two conditions: observable and unobservable productive investments. In both conditions, communication mainly fosters fair sharing and is rarely used by proposers to pit voters against each other. A virtuous cycle of proportional surplus sharing arises in treatments with observable investments regardless of whether communication is possible leading to high efficiency gains over time. In the absence of investment observability, communication is widely used by subjects to truthfully report their investments, which coupled with calls for equitable sharing, allows for substantial efficiency gains. These results contrast sharply with previous findings on bargaining over an exogenous fund where communication leads to highly unequal outcomes, competitive messages, and virtually no calls for fair sharing.

Subgame perfect equilibria in majoritarian bargaining

We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory experiments show various deviations from this equilibrium, where different offers are typically made and delay may occur before acceptance. We address the issue to what extent these findings are compatible with subgame perfect equilibrium and characterize the set of subgame perfect equilibrium payoffs for any value of the discount factor. We show that for any proposal in the interior of the space of possible agreements there exists a discount factor such that the proposal is made and accepted. We characterize the values of the discount factor for which equilibria with one-period delay exist. We show that any amount of equilibrium delay is possible and we construct subgame perfect equilibria such that arbitrary long delay occurs with probability one.

Subgame Perfect Equilibria in Majoritarian Bargaining

We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory experiments show various deviations from this equilibrium, where different offers are typically made and delay may occur before acceptance. We address the issue to what extent these findings are compatible with subgame perfect equilibrium and characterize the set of subgame perfect equilibrium payoffs for any value of the discount factor. We show that for any proposal in the interior of the space of possible agreements there exists a discount factor such that the proposal is made and accepted. We characterize the values of the discount factor for which equilibria with one-period delay exist. We show that any amount of equilibrium delay is possible and we construct subgame perfect equilibria such that arbitrary long delay occurs with probability one.

On Majoritarian Bargaining with Incomplete Information

This article studies a finite horizon version of Baron and Ferejohn's (American Political Science Review 83 (1989), 1181-206) majoritarian bargaining with incomplete information. Of many findings, we show that (i) allowing for delay can be optimal for a proposer; (ii) the revelation of a type depends on two conflicting concerns, the offer concern a la Spence's signaling (the higher the type the better) and the coalition inclusion concern in a majority consent (the lower the type the better); and (iii) players take actions to distinguish themselves via delay, but separating equilibria often fail to exist due to incapability or unprofitability of exercising delay.

ON MAJORITARIAN BARGAINING WITH INCOMPLETE INFORMATION*

This article studies a finite horizon version of Baron and Ferejohn's (American Political Science Review 83 (1989), 1181–206) majoritarian bargaining with incomplete information. Of many findings, we show that (i) allowing for delay can be optimal for a proposer; (ii) the revelation of a type depends on two conflicting concerns, the “offer” concern à la Spence's signaling (the higher the type the better) and the “coalition inclusion” concern in a majority consent (the lower the type the better); and (iii) players take actions to distinguish themselves via delay, but separating equilibria often fail to exist due to incapability or unprofitability of exercising delay.

Demand bargaining and proportional payoffs in majority games

We study a majoritarian bargaining model in which players make payoff demands in decreasing order of voting weight. The unique subgame perfect equilibrium outcome is such that the minimal winning coalition of the players that move first forms with payoffs proportional to the voting weights. This result advances previous analysis in terms of one or more of the following: a) the simplicity of the extensive form (finite horizon with a predetermined order of moves); b) the range of the majority games covered; c) the equilibrium concept (subgame perfect equilibrium is sufficient for a unique prediction).

Inequity Aversion May Increase Inequity in Majoritarian Bargaining

Inequity aversion models have been used to explain equitable payoff divisions in bargaining games. I show that inequity aversion can actually increase the asymmetry of payoff division in majoritarian bargaining games.

Demand Competition and Policy Compromise in Legislative Bargaining

I propose a new majoritarian bargaining model in which more than one implicit proposal can be on the table at the same time. Institutional differences from system to system affect the order of play, the equilibrium majorities, and the policy outcome. The ex post distribution of payoffs within a winning coalition is, however, invariant to fundamental institutional differences, and it is always proportional to the distribution of relative ex ante bargaining power. The bargaining process is modeled as a sequential demand game, in which players are called to propose a policy and to specify their desired share of the private benefits related to being in office. The order of play is endogenous, and the distribution of payoffs within an equilibrium majority usually does not depend on who is the proposal maker. The role of the head of state and the advantages to center parties are also studied.