voting paradox.
Suppose that three people, Alice, Brian, and Cait, are choosing between three candidates, Primus, Secunda, and Tertius, for a job. Alice prefers Primus to Secunda to Tertius. Brian prefers Secunda to Tertius to Primus. Cait prefers Tertius to Primus to Secunda. So a majority prefer Primus to Secunda, and a majority prefer Secunda to Tertius, and, paradoxically, a majority prefer Tertius to Primus. So preferences obtained by majority voting between pairs do not give a coherent ranking. Or, to put it differently, the outcome depends on the order in which the options are presented. If the first choice is between Primus and Secunda then Secunda will be eliminated and Primus will win when compared with Tertius. But if the first choice is between Primus and Tertius then Primus will be eliminated and then Secundus will win when compared with Tertius. These facts are special cases of Arrow's theorem, which shows that there can be no perfect voting system.... ...
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