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Condorcet’s Paradox has been formally studied by an amazing number of people in many different contexts for more than two centuries. Peter Fishburn introduced the basic notion of the Paradox to me in 1971 during a course in Social Choice Theory at Pennsylvania State University. My immediate response to seeing the simple example that he presented was that this phenomenon certainly could not be very likely to ever be observed in reality. Peter quickly suggested that I should work on developing some representations for the probability that the Paradox might occur, and very soon thereafter that pursuit began. It is only after 35 years of effort, with a lot of help from Peter, that I now feel that a good answer can be given to the challenge that was presented in that classroom in 1971. Many people have suggested to me over the years that a book like this should be completed, since the source material is spread over such a wide variety of disciplines of a- demic journals and books that it is very difficult for people to know what has been done, and has not been done, in this area of determining representations for the probability that Condorcet’s Paradox would ever be observed in reality.

Voting --- Mathematical models. --- Condorcet, Jean-Antoine-Nicolas de Caritat, --- Polls --- Elections --- Politics, Practical --- Social choice --- Suffrage --- Caritat, Jean-Antoine-Nicolas de, --- Condorcet, Antoine-Nicolas Caritat de, --- Condorcet, C.-F., --- Condorcet, Marie Jean Antoine Nicolas, --- Condorcet, --- De Caritat, Jean-Antoine-Nicolas, --- Kondorsė, Zhan Antuan, --- Economic theory. --- Mathematics. --- Political science. --- Operations research. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Game Theory, Economics, Social and Behav. Sciences. --- Political Science. --- Operations Research/Decision Theory. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Administration --- Civil government --- Commonwealth, The --- Government --- Political theory --- Political thought --- Politics --- Science, Political --- Social sciences --- State, The --- Math --- Science --- Economic theory --- Political economy --- Economic man --- Game theory. --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Decision making

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Politics --- Economic schools --- Operational research. Game theory --- politieke wetenschappen --- economisch denken --- speltheorie --- operationeel onderzoek

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This monograph studies voting procedures based on the probability that paradoxical outcomes like the famous Condorcet Paradox might exist. It is well known that hypothetical examples of many different paradoxical election outcomes can be developed, but this analysis examines factors that are related to the process by which voters form their preferences on candidates that will significantly reduce the likelihood that such voting paradoxes will ever actually be observed. It is found that extreme forms of voting paradoxes should be uncommon events with a small number of candidates. Another consideration is the propensity of common voting rules to elect the Condorcet Winner, which is widely accepted as the best choice as the winner, when it exists. All common voting rules are found to have identifiable scenarios for which they perform well on the basis of this criterion. But, Borda Rule is found to consistently work well at electing the Condorcet Winner, while the other voting rules have scenarios where they work poorly or have a very small likelihood of electing a different candidate than Borda Rule. The conclusions of previous theoretical work are presented in an expository format and they are validated with empirically-based evidence. Practical implications of earlier studies are also developed.

Elections. --- Game theory. --- Welfare economics. --- Economics. --- Social Choice/Welfare Economics/Public Choice. --- Electoral Politics. --- Game Theory. --- Operations Research/Decision Theory. --- Economic policy --- Economics --- Social policy --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Electoral politics --- Franchise --- Polls --- Political science --- Politics, Practical --- Plebiscite --- Political campaigns --- Representative government and representation --- Operations research. --- Social Choice/Welfare Economics/Public Choice/Political Economy. --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making. --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making

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