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Chicken dilemma: Difference between revisions
general talk about chicken dilemma first
imported>Homunq (chicken payoff matrix) |
imported>Homunq (general talk about chicken dilemma first) |
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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); 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;" align=right cellspacing=0 cellpadding=8 width=225
|-
|style="width:33%; "|
|style="width:33%; border-bottom: solid black 1px;"|
|style="width:33%; border-bottom: solid black 1px;"|
|-▼
|style="border-right: solid black 1px; text-align: right; "| Swerve▼
|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%; "|
|style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "|
|-
|style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "|
|style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| 0, 0
▲|style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| -1, +1
▲|-
▲|style="border-right: solid black 1px; text-align: right; "| Straight
▲|style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| +1, -1
▲|style="border-right: solid black 1px; border-bottom: solid black 1px; background:white; font-size:120%; "| -10, -10
|-
|style="font-size: 90%;" colspan=3 |''Fig. 2: Chicken with numerical [[Risk dominance|payoffs]]''
|}
There are various ways to deal with this situation. For instance:
- Some voting systems, such as approval voting, ignore the problem. Perhaps the assumption here is that it will be impossible to organize a defection without prompting a retaliation, and thus that both sides will prefer to cooperate. ("Mutual assured destruction"?)
- Some voting systems, such as [[Majority Choice Approval]], try exploit the fact that each faction is not a single coordinated entity, but a group of individual voters. The idea is that if a small number of voters defect, they should be ignored; hopefully, in that situation, majority cooperation will be a stable strategy.
- Other voting systems, such as [[ICT]], try to exploit the fact that in a real-world election, A and B are never perfectly balanced; one subfaction is always larger. In this case, a voting system can encourage the smaller group to cooperate by threatening to elect C (punishing both groups) if the smaller group defects. The criterion below is passed only by this kind of voting system.
== Definition ==
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