Voting Systems-Sequential Pairwise Voting
المؤلف:
W.D. Wallis
المصدر:
Mathematics in the Real World
الجزء والصفحة:
177
16-2-2016
2200
In sequential pairwise voting several candidates are paired in successive runoff elections. There is an agenda (an ordered list of candidates). For example, if the agenda is A,B,C,D,... then the elections proceed as follows:
1. A against B
2. Winner of AB against C
3. That winner against D
...
Position in the agenda is very important. To see this, consider a four-candidate election with agenda A,B,C,D, in which all four candidates are equally likely to win. If repeated trials are made then we would expect the following results:
• A wins first runoff in half the cases
• A wins second runoff in half those cases—a quarter overall
• A wins the third runoff in half those cases—one-eighth overall.
So A has a 1 in 8 chance of winning. B also has a 1 in 8 chance. However, C has a 1 in 4 chance, and D has a 1 in 2 chance. In this case, being later in the list is very beneficial.
Rather than elections, this model is often used for sporting tournaments (the result of match is used instead of the result of a runoff election). One often sees playoff rules like:
(i) Second and third placegetters in preliminary competition play each other (“the playoff”)
(ii) the winner of playoff meets the leader from the preliminaries.
In this case it is reasonable that the preliminary leader should get an advantage.
However, when the model is used in voting situations, it is very subject to manipulation.
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