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Open AccessEditor’s ChoiceArticle

The Condorcet Jury Theorem with Information Acquisition

by Jun Chen

Games 2021, 12(4), 79; https://doi.org/10.3390/g12040079 - 25 Oct 2021

Cited by 1 | Viewed by 3125

We analyze a committee decision in which individuals with common preferences are uncertain which of two alternatives is better for them. Members can acquire costly information. Private signals and information choice are both continuous. As is consistent with Down’s rational ignorance hypothesis, each member acquires less information in a larger committee and tends to acquire zero information when the committee size goes to infinity. However, with more members, a larger committee can gather more aggregate information in equilibrium. The aggregate information is infinite with the size going to infinity if and only if marginal cost at “zero information acquisition” is zero. When the marginal cost at “zero information acquisition” is positive, the probability of making an appropriate decision tends to be less than one. Full article

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22 pages, 358 KB

Open AccessArticle

Information Use and the Condorcet Jury Theorem

by Keiichi Morimoto

Mathematics 2021, 9(10), 1098; https://doi.org/10.3390/math9101098 - 13 May 2021

Cited by 2 | Viewed by 4333

Abstract

Using a simple model of a coordination game, this paper explores how the information use of individuals affects an optimal committee size. Although enlarging the committee promotes information aggregation, it also stimulates the members’ coordination motive and distorts their voting behavior through higher-order beliefs. On the determination of a finite optimal committee size, the direction and degree of strategic interactions matter. When the strategic complementarity among members is strong, a finite optimal committee size exists. In contrast, it does not exist under strategic substitution. This mechanism is applied to the design of monetary policy committees in a New Keynesian model in which a committee conducts monetary policy under imperfect information. Full article

(This article belongs to the Special Issue Economic Modelling: Theory, Methods and Applications)

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12 pages, 753 KB

Open AccessArticle

A Condorcet Jury Theorem for Large Poisson Elections with Multiple Alternatives

by Johanna M. M. Goertz

Games 2020, 11(1), 2; https://doi.org/10.3390/g11010002 - 23 Dec 2019

Viewed by 4808

Abstract

Herein, we prove a Condorcet jury theorem (CJT) for large elections with multiple alternatives. Voters have common interests that depend on an unknown state of nature. Each voter receives an imprecise private signal about the state of nature and then submits one vote (simple plurality rule). We also assume that this is a Poisson voting game with population uncertainty. The question is whether the simple plurality rule aggregates information efficiently so that the correct alternative is elected with probability tending to one when the number of voters tends to infinity. The previous literature shows that the CJT holds for large elections with two alternatives, but there is also an example of a large election with three alternatives that has an inefficient equilibrium. We show that there always exists an efficient equilibrium, independent of the number of alternatives. Under certain circumstances (informative types), it is unique in elections with two alternatives. The existence of inefficient equilibria in elections with more than two alternatives is generic. Full article

(This article belongs to the Special Issue Political Economy, Social Choice and Game Theory)

23 pages, 1349 KB

Open AccessArticle

Voting in Three-Alternative Committees: An Experiment

by Johanna M.M. Goertz and Kirill Chernomaz

Games 2019, 10(2), 20; https://doi.org/10.3390/g10020020 - 1 May 2019

Cited by 2 | Viewed by 7177

Abstract

We design an experiment to test how voters vote in a small committee election with three alternatives. Voters have common preferences that depend on an unknown state of nature. Each voter receives an imprecise private signal prior to the election and then casts a vote. The alternative with the most votes wins. We fix the number of voters in our experiment to be five and focus on differences in the information structure (prior and signal distributions). We test three different treatments (different prior and signal distributions) that pose different challenges for the voters. In one, simply voting for one’s signal is an equilibrium. In the other two, it is not. Despite the different levels of complexity for the voters, they come relatively close to the predicted strategies (that sometimes involve mixing). As a consequence, the efficiency of the decision is also relatively high and comes close to predicted levels. In one variation of the experiment, we calculate posterior beliefs for the subjects and post them. In another, we do not. Interestingly, the important findings do not change. Full article

(This article belongs to the Special Issue Political Economy, Social Choice and Game Theory)

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