Difference between revisions of "Chicken Dilemma Criterion"

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One type of election scenario which is particularly fraught is 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 "chicken" or "snowdrift game (especially if voters are not sure which of the two subfactions is larger). That is, 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), 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;" align=right cellspacing=0 cellpadding=8 width=225
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|-
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|style="width:33%;                                                    "|
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|style="width:33%;                      border-bottom: solid black 1px;"| Swerve
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|style="width:33%;                      border-bottom: solid black 1px;"| Straight
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|style="border-right:  solid black 1px; text-align: right;            "| Swerve
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|style="border-right:  solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| 0, 0
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|style="border-right:  solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| -1, +1
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|-
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|style="border-right:  solid black 1px; text-align: right;            "| Straight
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|style="border-right:  solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| +1, -1
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|style="border-right:  solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| -10, -10
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|-
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|style="font-size: 90%;" colspan=3 |''Fig. 2: Chicken with numerical [[Risk dominance|payoffs]]''
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|}
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== Definition ==
 
== Definition ==

Revision as of 14:59, 11 October 2016

One type of election scenario which is particularly fraught is 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 "chicken" or "snowdrift game (especially if voters are not sure which of the two subfactions is larger). That is, 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), many voting systems lead to the following payoff matrix:


Swerve Straight Swerve 0, 0 -1, +1
Straight +1, -1 -10, -10
Fig. 2: Chicken with numerical payoffs



Definition

Supporting 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:

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

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

5. 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 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:

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


Because CD is so simple, such a simple situaton, could there be another simple implmentation of it?

...maybe one that doesn't speak of numbers of voters in the factions?

CD is sufficient, as-is, but here is a non-numerical definition:

CD2:

Supporting definition:

The A voters are the voters who vote A over everyone else. The B voters are the voters who vote B over everone else. The C voters are the voters who vote C over everyone else.

Premise:

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

2. If the A voters and B voters all voted both A and B over C, then C couldn't win.

3. The ballot set is such that if C withdrew from the election and the count, A would win.

4. The A voters vote B over C.

5. The B voters don't vote A over anyone.

Requirement:

B doesn't win.

[end of CD2 definition]