Reciprocal Score Voting: Difference between revisions
→Analysis
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In the case of any asymmetry in support, the reciprocity ratio is <math>R(j,\phi) < 0</math> for the faction which did not cooperate, and <math>R(j,\phi) = 1</math> for the faction that did cooperate. Therefore, not cooperating penalizes the side which did not cooperate more. In this way, factions are encouraged to cooperate as much as possible to maximize mutual support, forcing them to strike a balance between supporting their favorite as well as supporting alternatives as much as they can. In the case of opposing factions, the mutual lack of cooperation has no effect.
This system is [[monotonicity criterion|non-monotonic]] and suffers from a very unusual "reverse [[spoiler effect]]" (see "chicken dilemma" below), in which a larger faction may lose an election by not supporting smaller supportive factions. Therefore, larger factions are encouraged to promote smaller factions as much as possible in order to win.
The <math>\min(\cdot, 1)</math> condition above is required so that support is never amplified by asymmetry. This is also necessary so that a smaller faction cannot parasite on the support of a larger faction, which will never rate the smaller faction above its own. A smaller faction artificially rating a larger faction too highly will only receive exactly as much support as the larger faction is willing to give to it.
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