Chicken dilemma: Difference between revisions

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.

 

 

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.

 

 

 

B doesn't win.

 

 

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:

{| id="Payoff matrix" style="background:white; float: right; clear:right; text-align:center;" width="225" cellspacing="0" cellpadding="8" align="right"

|-

| style="width:33%; border-bottom: solid black 1px;" | defect

|-

| style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; " | 8, 10

|-

|-

| colspan="3" style="font-size: 90%;" |''Fig. 2: Chicken with numerical [[Risk dominance|payoffs]]''

There are various ways to deal with this situation. For instance:

 

 

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" (see [[Strong/weak preference option]] for notation):

 

 

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".

 

Some methods that pass the Chicken Dilemma Criterion:

 

[[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.

 

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

 

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]]