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{{wikipedia|Chicken (game)}}
The "chicken dilemma" refers to a situation where two similar candidates share a majority, but are opposed by one candidate which has a plurality against either of the two. This can happen when there is a majority split into two subfactions (below called A and B), competing against a united minority (below called C) that is bigger than either of the subfactions.
This scenario has been called the "chicken dilemma" because in many election systems, the two majority subfactions are in a situation that resembles the classic game of "chicken" (see "[[W:Chicken (game)
== Definition
The A voters are the voters who vote A over everyone else. The B voters are the voters who vote B over everyone else. The C voters are the voters who vote C over everyone else.
===Premise ===
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B doesn't win.
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If we assume each faction has a single, coordinated strategy defined as "cooperate" (vote both candidates A and B above bottom) or "defect" (bullet vote, with only the favorite above bottom); and that each faction values its preferred choice at 10, its less-preferred choice at 8, and candidate C at 0, many voting systems lead to the following payoff matrix:
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{| id="Payoff matrix" style="background:white; float: right; clear:right; text-align:center;" width="225" cellspacing="0" cellpadding="8" align="right"
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| colspan="3" style="font-size: 90%;" |''Fig. 2: Chicken with numerical [[Risk dominance|payoffs]]''
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There are various ways to deal with this situation. For instance:
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The chicken dilemma happens when there is a [[Condorcet winner]] and a majority Condorcet loser, but not a majority Condorcet winner. In many voting systems, supporters of one of the two similar candidates have a dilemma, like a game of "chicken": they can either "cooperate" and support both similar candidates, helping to ensure the opposing plurality candidate loses but risking a win by the less-preferred of the similar ones; or they can "betray" and support only their favorite candidate, trying to take advantage of cooperation by the other side.
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An example of a chicken dilemma scenario, in the format of "#voters:true preferences" (see [[Strong/weak preference option]] for notation):
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In the chicken dilemma scenario described in the premise of the Chicken Dilemma Criterion (CD), defined above, if B won, then the B voters would have successfully taken advantage of the A voters' cooperativeness. The A voters wanted to vote both A and B over the candidate disliked by both the A voters and B voters. Thereby they helped {A,B} against the worse candidate. But, with methods that fail CD, the message is "You help, you lose".
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Some methods that pass the Chicken Dilemma Criterion:
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[[Reciprocal Score Voting]] soft-fails if C is about as large as A+B and there is insufficient mutual support, but passes if A+B is a sufficiently large majority with sufficient mutual support, which is always encouraged by the system.
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One direct implication of the chicken dilemma criterion is a [[spoiler effect]]. This is because if A drops out of the race, then B becomes a majority's 1st choice and wins in any majority criterion-passing method. Further, there is also usually incentive for Favorite Betrayal, since A-top voters generally benefit from putting B 1st. That would be the case in IRV for:<blockquote>26 A>B
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See also [[Asset voting]] for some discussion on this; the majority can be thought of as a "majority semi-solid coalition".
[[Category:Voting system criteria]]
[[Category:Game theory]]
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