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.

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 "[[W:Chicken (game)|chicken]]" or "snowdrift" game (especially if voters are not sure which of the two subfactions is larger).

== Analysis ==

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%; " |

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

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

| style="border-right: solid black 1px; text-align: right; " | cooperate

| style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; " | 9, 9

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

| style="border-right: solid black 1px; text-align: right; " | defect

| style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; " | 10, 9

| style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; " | 0, 0

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

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":

* 33: A>B>>C

* 22: B>A>>C

* 45: C>>A=B

== Definition ==

=== Formal 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'''

# There are 3 candidates: A, B, and C.

# The A voters and the B voters, combined, add up to more than half of the voters in the election.

# The A voters are more numerous than the B voters. The C voters are more numerous than the A voters, and more numerous than the B voters.

# The A voters vote B over C. The B voters refuse to vote A over anyone.

# None of the C voters vote A or B over the other.

==== '''Requirement''' ====

=== Further analysis ===

=== Methods passing criterion ===

Some methods that pass the Chicken Dilemma Criterion: