At this point, you\u2019re probably asking why we keep looking at method after method just to point out that they are not fully fair. We must be holding out on the perfect method, right?<\/p>\r\n
Unfortunately, no. A mathematical economist, Kenneth Arrow, was able to prove in 1949 that there is no voting method that will satisfy all the fairness criteria we have discussed.<\/p>\r\n Arrow\u2019s Impossibility Theorem<\/strong> states, roughly, that it is not possible for a voting method to satisfy every fairness criteria that we\u2019ve discussed.<\/p>\r\n<\/div>\r\n<\/section>\r\n To see a very simple example of how difficult voting can be, consider the election below:<\/p>\r\n <\/p>\r\n Notice that in this election: [latex]10[\/latex] people prefer A to B [latex]10[\/latex] people prefer B to C [latex]10[\/latex] people prefer C to A<\/p>\r\n<\/section>\r\n No matter whom we choose as the winner, [latex]\\frac{2}{3}[\/latex] of voters would prefer someone else! This scenario is dubbed Condorcet\u2019s Voting Paradox<\/strong>, and demonstrates how voting preferences are not transitive (just because A is preferred over B, and B over C, does not mean A is preferred over C). In this election, there is no fair resolution.<\/p>\r\n It is because of this impossibility of a totally fair method that Plurality, IRV, Borda Count, Copeland\u2019s Method, and dozens of variants are all still used. Usually the decision of which method to use is based on what seems most fair for the situation in which it is being applied.<\/p>","rendered":" At this point, you\u2019re probably asking why we keep looking at method after method just to point out that they are not fully fair. We must be holding out on the perfect method, right?<\/p>\n Unfortunately, no. A mathematical economist, Kenneth Arrow, was able to prove in 1949 that there is no voting method that will satisfy all the fairness criteria we have discussed.<\/p>\n Arrow\u2019s Impossibility Theorem<\/strong> states, roughly, that it is not possible for a voting method to satisfy every fairness criteria that we\u2019ve discussed.<\/p>\n<\/div>\n<\/section>\n To see a very simple example of how difficult voting can be, consider the election below:<\/p>\n <\/p>\n Notice that in this election: [latex]10[\/latex] people prefer A to B [latex]10[\/latex] people prefer B to C [latex]10[\/latex] people prefer C to A<\/p>\n<\/section>\n No matter whom we choose as the winner, [latex]\\frac{2}{3}[\/latex] of voters would prefer someone else! This scenario is dubbed Condorcet\u2019s Voting Paradox<\/strong>, and demonstrates how voting preferences are not transitive (just because A is preferred over B, and B over C, does not mean A is preferred over C). In this election, there is no fair resolution.<\/p>\nArrow\u2019s Impossibility Theorem<\/h3>\r\n
\r\n\r\n
\r\n <\/td>\r\n [latex]5[\/latex]<\/td>\r\n [latex]5[\/latex]<\/td>\r\n [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n \r\n 1st choice<\/td>\r\n A<\/td>\r\n C<\/td>\r\n B<\/td>\r\n<\/tr>\r\n \r\n 2nd choice<\/td>\r\n B<\/td>\r\n A<\/td>\r\n C<\/td>\r\n<\/tr>\r\n \r\n 3rd choice<\/td>\r\n C<\/td>\r\n B<\/td>\r\n A<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n Which Method is Fair?<\/h2>\n
Arrow\u2019s Impossibility Theorem<\/h3>\n
\n\n
\n <\/td>\n [latex]5[\/latex]<\/td>\n [latex]5[\/latex]<\/td>\n [latex]5[\/latex]<\/td>\n<\/tr>\n \n 1st choice<\/td>\n A<\/td>\n C<\/td>\n B<\/td>\n<\/tr>\n \n 2nd choice<\/td>\n B<\/td>\n A<\/td>\n C<\/td>\n<\/tr>\n \n 3rd choice<\/td>\n C<\/td>\n B<\/td>\n A<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n