Chicken dilemma: Difference between revisions

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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.

An example of a chicken dilemma scenario, in the format of "#voters:true preferences":

An example of a chicken dilemma scenario, in the format of "#voters:true preferences" (see [[Strong/weak preference option]] for notation):

* 33: A>B>>C

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Some methods that pass the Chicken Dilemma Criterion:

ICT, [[Symmetrical ICT]], [[MMPO]], MDDTR, [[IRV]], [[Benham's Method|Benham's method]], [[Woodall's method]]

ICT, [[Symmetrical ICT]], [[MMPO]], MDDTR, [[IRV]] and most [[:Category:Condorcet-IRV hybrid methods|Condorcet-IRV hybrid methods]] ([[Benham's Method|Benham's method]], [[Woodall's method]])

== Notes ==

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:

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

26 A>B

25 B

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49 C</blockquote>If two A-top voters instead vote B-top, B wins instead of C.

49 C

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Most advocates of the CD criterion would likely counter that it's a more common issue to encounter CD-type scenarios because of strategic voting rather than honest voting, therefore these are worthy prices to pay for the strategic resistance.

Another major issue is that the chicken dilemma is indistinguishable based on the ballots from a situation where a majority subfaction begins to support a 3rd party. The above example with different candidate names: <blockquote>26 Green Party>Democrats

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If two A-top voters instead vote B-top, B wins instead of C.

25 Democrats

49 Republicans </blockquote>The chicken dilemma criterion assumes that the Democrat-top voters are trying to withhold their support from the Green Party, and thus it punishes their "lack of cooperation" by electing the Republicans. Yet really, the Democrats don't support the Green Party in this example, and the Green Party-top voters merely wished to elect either the Green Party or the Democrats, and would not have wanted their support for their 1st choice to hurt their 2nd choice. So it can be argued that in fact, a voting method should fail the CD criterion and always elect the "non-cooperating" faction's preferred candidate to avoid this spoiler effect. Most [[:Category:Defeat-dropping Condorcet methods|defeat-dropping Condorcet methods]], [[Rated method|rated methods]], and to some extent, [[:Category:Condorcet-cardinal hybrid methods|Condorcet-cardinal hybrid methods]] fail the criterion. See also [[Asset voting]] for some discussion on this; the majority can be thought of as a "majority semi-solid coalition".

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Most advocates of the CD criterion would likely counter that it's a more common issue to encounter CD-type scenarios because of strategic voting rather than honest voting, therefore these are worthy prices to pay for the strategic resistance.

[[Category:Voting system criteria]]