Most of us are familiar with the process of making budgetary decisions by committee. A group of people, each with their own preferences and goals and representing different interests, must decide among themselves how to allocate resources. Such committees are typically rule bound: Decisions are made by majority rule or by unanimous consent, or some other mechanism.
Economists have theories about how humans behave in these situations and what decision-making mechanisms lead to the most efficient outcomes. Caltech professor of economics Marina Agranov tests these theories. "I'm trying to understand whether these theories have what we call empirical bite and how theories may need to be modified to better predict human behavior."
"When there is a fixed budget, the unanimity rule gets a lot of criticism, and for good reason," Agranov explains. "With a unanimity rule, each person has veto power. It's enough that one voter rejects a proposal for it to fail. Even if a proposal is reasonable and fair, such that no one should vote against it, humans are human. They may take issue with a proposal for emotional reasons or because of group dynamics, for example. Deciding by the vote of the majority is the more efficient rule in this instance, the rule most likely to result in timely outcomes."
But what happens when a budget is not fixed but could, for example, become larger in the future? How might budget committee members bargain with one another given such uncertainty?
"Theoretically," Agranov says, "in a world with stochastic-that is, changing and uncertain-budgets, the unanimity rule offers some benefits. Under majority rule in such scenarios, committee members often rush to approve small budgets out of fear that, if they delay, they may be excluded from future coalitions. These rushed decisions frequently lead to inefficiency. In contrast, unanimity requires all members to agree, which can encourage the committee to delay decisions until the budget grows larger, resulting in better outcomes, on average, for everyone."
This is the economic theory that Agranov and her colleagues set out to test in the lab. "The lab has a notable advantage compared to the field, where we would be examining human behavior in real-world settings," Agranov says, "In the lab, I can fix the rules of the game, control the budgets, and observe people negotiating and making decisions. If we find that the theory fails in the very simple environment of the lab, it is unrealistic that it would hold water in the field."
In order to model the situation of bargaining under uncertainty, Agranov's team recruited 288 participants and organized them into groups of three-member budget committees. All of the participants sat at their own computer, with no face-to-face interaction with other committee members, who were not identified to them (although they could communicate with one another via chat). Each round of the game began when one person was selected, at random, to be the agenda-setter. The agenda-setter could either create a proposal for how to divide the budget the committee was given or could choose to delay making a proposal. If the proposal was made, the other committee members were then asked to vote on the proposal, that is, either accept or reject it. The minimum number of votes required to pass the proposal was either two (the majority voting rule) or three (unanimous support). If the agenda-setter chose to delay bargaining or the proposal did not receive the minimum number of votes required, then the committee moved on to the next bargaining round with a 20 percent chance that the bargaining was over, and all committee members would receive nothing. "This last element of unpredictability mimics the discounting rate idea according to which people prefer to get a dollar today rather than tomorrow," Agranov explains. The 20 percent chance of ending the game is equivalent to valuing $1 as 80 cents in the next period.
Different experiments varied the process governing the evolution of the budget across bargaining rounds. In all experiments, participants started with a $24 budget in the first bargaining round. In some experiments, if the bargaining reached the second round, third, or any further round, then there was a 50/50 chance that the budget would either rise to $48 or remain at $24. In other experiments, there was a 50/50 chance that the budget would either rise to $96 or remain at $24. Finally, these experiments with stochastic budgets were compared to the benchmark in which the budget was always $24 regardless of the bargaining round.
These scenarios are meant to model committees that meet regularly. "We are most interested in standing committees, committees that don't just meet one day and never interact with one another again," Agranov explains. "They have repeated interactions. Most committees are like this, so understanding how bargaining operates in standing committees provides more insight into real-world group dynamics."
Experimental data, in this case, align with theory: Although the presence of a unanimity rule cripples the work of a one-and-done committee effort to distribute resources by giving each party veto power, it allows for more fruitful ongoing bargaining in a standing committee. Most importantly, committees that use a unanimity voting rule are more patient and, as a result, are more likely to appropriate large budgets than committees that use a majority voting rule. How do people get to these efficient outcomes? "In our experiment, if you have three people and $24, the most egalitarian distribution is going to be $8 for each person," Agranov says. "Under majority rule, you should not advocate for an egalitarian distribution, because if you can get only one other person on board with your proposal, the two of you can take a higher share of the total. But when you introduce more uncertainty about future budgets, people make more egalitarian offers. This incentivizes all committee members to be patient and wait for the large budget to arrive even if sometimes it means getting zero payoff because of the discounting kicking in."
The reason for this enhanced egalitarianism in the stochastic situation is linked to the delay in reaching consensus, Agranov says. "If you offered only one person a positive share and you excluded the third person, in the next round the person you excluded is likely to retaliate against you. So you are actually better off being more egalitarian today to ensure that if your immediate proposal fails, tomorrow's proposal will be more likely to include benefits to you."
The paper describing this research, " Bargaining in the Shadow of Uncertainty ," is in the November 2024 issue of American Economic Journal: Microeconomics. Co-authors include Hülya Eraslan of Rice University and Chloe Tergiman of Penn State University. Research was funded by the National Science Foundation.
