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Public Choice Theory on Jury Theorem - Dictionary of Arguments

Parisi I 185
Jury theorem/Condorcet/Public choice theory/Farber: In the political sphere, the most common manifestation of the inherent limitation on collective choice is Condorcet's paradox (Shepsle, 2010(1), pp. 53-6 7). Because majority coalitions may shift depending on the alternative on the agenda, different majorities may favor option a to option b and option b to option c, but then prefer option c to option a. As the number of alternatives increases, or as the number of individuals voting increases, the chance of cycling, assuming randomly assigned preferences, mounts.
Problem: A key question is how democracies manage to create stable public policies given the risk of cycling.
False solution: An initial response might be to consider whether some more sophisticated voting mechanism could eliminate the problem. To make the idea of a voting procedure more specific, assume that the alternatives are assigned numbers, that a ballot consists of a list of these numbers which the voter then ranks, that voting is anonymous so all voters are treated the same, and that the voting procedure tells us, for any subset of options, which one is favored against the others. Example: Consider a decision situation with three options and three voters, each with different rankings for the options. Each option is one voter's first choice, one voter's second choice, and one's third choice. It is easy to see that no voting procedure can identify a winner in a three-way contest without relying on some additional factor to break the symmetry between the three alternatives. Cf. >Arrow’s theorem.
Problem: The fact that the options are identical in terms of all available information means that no one option can be singled out as the winner, no matter how complicated or clever the voting methodology.
Parisi I 186
Two-way contest/three-way contest: Suppose the contrary were true and that one alternative would beat both other alternatives. If that were true, we could decide the three-way contest simply by breaking it down into a round robin of two-way contests. But we have already seen that no voting procedure can decide the three-way contest, so we know that the round robin must also fail to yield a winner.
Majority rule: Although this result is often illustrated by the example of majority voting, the insight is clearly more general. In fact, so long as the decision process involves no information other than the preference rankings and gives equal weight to all of the voters, it plainly cannot avoid a cycle in a sequence of head-to-head votes when the preferences have s metrical voter support. >Arrow’s theorem/Public choice theory.

1. Shepsle, K. A. (2010). Analyzing Politics: Rationality, Behavior, and Institutions. 2nd edition.
New York: W.W. Norton & co.

Farber, Daniel A. “Public Choice Theory and Legal Institutions”. In: Parisi, Francesco (ed) (2017). The Oxford Handbook of Law and Economics. Vol 1: Methodology and Concepts. NY: Oxford University Press

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Public Choice Theory
Parisi I
Francesco Parisi (Ed)
The Oxford Handbook of Law and Economics: Volume 1: Methodology and Concepts New York 2017

Ed. Martin Schulz, access date 2021-06-20