A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-12-01
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| Series: | Games |
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| Online Access: | https://www.mdpi.com/2073-4336/11/1/2 |
| _version_ | 1818288102689472512 |
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| author | Johanna M. M. Goertz |
| author_facet | Johanna M. M. Goertz |
| author_sort | Johanna M. M. Goertz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-13T01:51:03Z |
| format | Article |
| id | doaj.art-910d2e059dec41d7abd283ee1b41eac7 |
| institution | Directory Open Access Journal |
| issn | 2073-4336 |
| language | English |
| last_indexed | 2024-12-13T01:51:03Z |
| publishDate | 2019-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Games |
| spelling | doaj.art-910d2e059dec41d7abd283ee1b41eac72022-12-22T00:03:31ZengMDPI AGGames2073-43362019-12-01111210.3390/g11010002g11010002A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple AlternativesJohanna M. M. Goertz0Department of Economics and Finance, Gordon S. Lang School of Business and Economics, University of Guelph, 50 Stone Road East, Guelph, ON N1G 2W1, CanadaHerein, 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.https://www.mdpi.com/2073-4336/11/1/2efficient information aggregationsimple plurality rulepoisson gamescondorcet jury theorem |
| spellingShingle | Johanna M. M. Goertz A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives Games efficient information aggregation simple plurality rule poisson games condorcet jury theorem |
| title | A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives |
| title_full | A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives |
| title_fullStr | A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives |
| title_full_unstemmed | A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives |
| title_short | A Condorcet Jury Theorem for Large <i>Poisson</i> Elections with Multiple Alternatives |
| title_sort | condorcet jury theorem for large i poisson i elections with multiple alternatives |
| topic | efficient information aggregation simple plurality rule poisson games condorcet jury theorem |
| url | https://www.mdpi.com/2073-4336/11/1/2 |
| work_keys_str_mv | AT johannammgoertz acondorcetjurytheoremforlargeipoissonielectionswithmultiplealternatives AT johannammgoertz condorcetjurytheoremforlargeipoissonielectionswithmultiplealternatives |