Voting Paradox

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A social dilemma characterised by 'public goods' and 'free-riders' and the fact that it is in the rational best interest for an individual sharing a public common good to free-ride
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(165) This example demonstrates the Condorcet paradox: A dominant second-choice candidate will not always exist because group preferences are not always transitive.
(176) By locating the Condorcet-winning opinion, "the narrowest grounds doctrine identifies as the opinion stating the holding that opinion which represents a dominant, and thus stable, second choice." (177) Professor Stearns also takes a rather optimistic view of the Marks doctrine by concluding that it can apply to at least some cases in which the concurring opinions do not fall neatly within each other like "Russian dolls." (178) In fact, unlike many other scholars, (179) Stearns maintains that the Marks doctrine will only produce indeterminate holdings in a very small category of plurality decisions--those that exhibit the Condorcet paradox, in which no Condorcet winner exists.
(166.) See STEARNS, CONSTITUTIONAL PROCESS, supra note 137, at 45 (explaining possibility of intransitivity shown by Condorcet paradox lies at core of social choice theory).
(191.) See supra text accompanying notes 159-166 (demonstrating Condorcet paradox).
In a world in which relatively few people were formally educated and fewer still could honestly describe themselves as intellectuals, it is perhaps not surprising that both Thomas Jefferson and James Madison were familiar with the noted French philosopher and mathematician,(1) the Marquis de Condorcet.(2) As Minister to France, Jefferson personally knew Condorcet.(3) Jefferson owned several of Condorcet's works, including the famous Essai sur l'application de l'analyse a la probabilite des decisions rendues a la pluralite des voix written in 1785.(4) The Essai describes what has become known as the "Condorcet Paradox,"(5) the seminal insight underlying what Condorcet described as "social mathematics" and what is presently known as social choice theory.(6)
Part III revisits Arrow's Theorem to demonstrate the similarities between the Condorcet Paradox and the problem of the empty core.
In the 1950's, at the same time that social choice theory was reemerging in economic theory, economists discovered a phenomenon nearly identical to the Condorcet paradox within private markets.(53) The problem, known as the "empty core,"(54) demonstrates that in certain circumstances, participants in private markets may be unable to arrive at any conclusive set of contractual arrangements and may-therefore cycle indefinitely.(55) The only significant difference between this phenomenon and the Condorcet Paradox, is that the "empty core" takes place among private market participants rather than among lawmakers.
The empty core problem is a generalization of the Condorcet Paradox.(70) In the ice cream cake hypothetical, for example,(71) if the coalition (Alice, Bob) decides that it will impose chocolate upon the group, Carole can lure Alice away and make the new coalition (Alice, Carole) better off by selecting coffee.
Relatively few studies have shown conclusive evidence for the Condorcet paradox in real life.