# Difference between revisions of "Chicken dilemma"

## Definition

Supporting definitions:

1. The A voters are the voters who prefer candidate A to everyone else. The B voters are the voters who prefer candidate B to everyone else. The C voters are the voters who prefer C to everyone else.

2. A particular voter votes sincerely if s/he doesn't falsify a preference, or fail to vote a felt preference that the balloting system in use would have allowed hir to vote in addition to the preferences that s/he actually votes.

Falsifying a preference means voting X over Y and not preferring X to Y.

Failing to vote a felt preference means preferring X to Y and not voting X over Y.

Premise:

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

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

3. The A voters and the B voters all prefer both A and B to C.

4. 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.

5. Voting is sincere, except that the B voters refuse to vote A over anyone.

6. Candidate A would be the unique winner under sincere voting (...in other words, if the B voters voted sincerely, as do all the other voters).

7. The C voters are indifferent between A and B, and none of the C voters vote A or B over the other.

Requirement:

B doesn't win.

[end of CD definition]

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' co-operativeness. The A voters wanted to vote both A and B over the candidates disliked by both the A voters and B voters. Thereby they helped {A,B} against worse candidates. But, with methods that fail CD, the message is "You help, you lose".

Some methods that pass the Chicken Dilemma Criterion:

ICT, Symmetrical ICT, MMPO, MDDTR, IRV, Benham's method, Woodall's method