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By William V. Gehrlein

The ebook is a compilation of the examine that has been performed within the research of Condorcet's Paradox for 2 centuries. It starts with a old evaluate of the invention of Condorcet's Paradox within the 18th Century, offers an exhaustive survey of diverse empirical reports which were performed to discover genuine occurrences of the ambiguity, and compiles all the examine that has been performed to enhance mathematical representations for the likelihood that the anomaly can be saw. The e-book is exclusive because it focuses realization strictly in this one balloting paradox, and it combines all the diverse methods which have been used to check this very attention-grabbing phenomenon.

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Example text

The voters’ payoffs or losses depend upon whether the issues are passed or defeated by majority rule, and once a vote has been taken on an issue the outcome is final for that issue. These payoffs or losses could reflect the benefit or loss for the constituency that a voter represents. The issues are independent, so that each is passed or defeated without regard to the outcome of any other issues. Fig. 11 lists the payoffs and losses for an example in which three voters are considering six issues, ^A, B, C , D, E , F ` , following an example from Riker and Brams (1973).

He was imprisoned and was found dead in his cell two days later. 5. Condorcet’s Other Paradox 23 can be found in Schapiro (1934), Morley (1965), Baker (1975), Badinter and Badinter (1988), Rosenfield (1989), and McLean and Hewitt (1994). Given the long history of the debate over which voting rule makes the most sense to use, it is quite fascinating that the debate still continues. Felsenthal and Machover (1992) argue strongly for the use of Condorcet’s suggestion of finding the PMRW. Saari (1995b) argues strongly for the direct use of Borda Rule in all elections.

By introducing the Whitten Amendment, a PMR cycle was created, and Whitten was thereby able to take advantage of the sequential elimination election process on amendments to be assured that the original bill passed. Riker (1958) estimated that the House of Representatives and the Senate may have voting results that appear to have PMR cycles in more than ten percent of cases when two or more amendments are considered with an original bill. However, some of these cycles are contrived as a result of strategic manipulation, as in the case discussed above.

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