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The Kemeny–Young method is a voting system that uses preferential ballots and pairwise comparison counts to identify the most popular choices in an election. It is a Condorcet method because if there is a Condorcet winner, it will always be ranked as the most popular choice. This method assigns a score for each possible sequence, where each sequence considers which choice might be most popular, which choice might be second-most popular, which choice might be third-most popular, and so on down to which choice might be least-popular. The sequence that has the highest score is the winning sequence, and the first choice in the winning sequence is the most popular choice. (As explained below, ties can occur at any ranking level.) The Kemeny–Young method is also known as the Kemeny rule, VoteFair popularity ranking, the maximum likelihood method, and the median relation. ==Description== The Kemeny–Young method uses preferential ballots on which voters rank choices according to their order of preference. A voter is allowed to rank more than one choice at the same preference level. Unranked choices are usually interpreted as least-preferred. Another way to view the ordering is that it is the one which minimizes the sum of the Kendall tau distances (bubble sort distance) to the voters' lists. Kemeny–Young calculations are usually done in two steps. The first step is to create a matrix or table that counts pairwise voter preferences. The second step is to test all possible rankings, calculate a score for each such ranking, and compare the scores. Each ranking score equals the sum of the pairwise counts that apply to that ranking. The ranking that has the largest score is identified as the overall ranking. (If more than one ranking has the same largest score, all these possible rankings are tied, and typically the overall ranking involves one or more ties.) In order to demonstrate how an individual preference order is converted into a tally table, it is worth considering the following example. Suppose that a single voter has a choice among four candidates (i.e. Elliot, Meredith, Roland, and Selden) and has the following preference order: These preferences can be expressed in a tally table. A tally table, which arranges all the pairwise counts in three columns, is useful for counting (tallying) ballot preferences and calculating ranking scores. The center column tracks when a voter indicates more than one choice at the same preference level. The above preference order can be expressed as the following tally table. Now suppose that multiple voters had voted on those four candidates. After all ballots have been counted, the same type of tally table can be used to summarize all the preferences of all the voters. Here is an example for a case that has 100 voters. The sum of the counts in each row must equal the total number of votes. After the tally table has been completed, each possible ranking of choices is examined in turn, and its ranking score is calculated by adding the appropriate number from each row of the tally table. For example, the possible ranking: # Elliot # Roland # Meredith # Selden satisfies the preferences Elliot > Roland, Elliot > Meredith, Elliot > Selden, Roland > Meredith, Roland > Selden, and Meredith > Selden. The respective scores, taken from the table, are * Elliot > Roland: 30 * Elliot > Meredith: 60 * Elliot > Selden: 60 * Roland > Meredith: 70 * Roland > Selden: 60 * Meredith > Selden: 40 giving a total ranking score of 30 + 60 + 60 + 70 + 60 + 40 = 320. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Kemeny–Young method」の詳細全文を読む スポンサード リンク
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