Reciprocal Score Voting: Difference between revisions
→= Chicken dilemma
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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.
=== Chicken dilemma ===
{| class="wikitable"
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: C = ''(1 - m)'' 10
If m > 0.5, A+B is a mutual majority. Either A or B can easily win over A provided there is enough mutual support. The goal then is to ensure they mutually support one another. (For example, if ''m'' = 52%, a modest majority, they may rate one another as low as 7 and one of them still win.
Without loss of generality (due to symmetry), we can assume the faction A is larger than B (''r'' ≥ 0.5). In this simplified scenario the faction ratings are simple to see: they can be read straight from the ballots (the table above).
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: A = ''m'' (''r'' 10 + (1 - ''r'') ''a'' min(1, ''b''/''a''))
: B = ''m'' (''r'' ''b'' min(1, ''a''/''b'') + (1 - ''r'') 10)
: C =
If faction B defects entirely by giving ''a'' = 0, the ratings become:
: A = ''m'' (''r'' 10 + 0)
: B = ''m'' (0 + (1 - ''r'') 10)
: C =
Such that B ceases to get any support from A. Thus, there is no incentive for B to defect, and they have an incentive to rate A highly. Even more curiously, suppose ''r'' = 3/4 such that A is a much larger subfaction than B. In most voting systems, such as [[Instant Runoff Voting]], A would be safe not supporting B, but this is not the case under Reciprocal Score Voting. If A defects with ''b'' = 0, the exact same results as if B defected occur! Therefore, even if A has an advantage over B, it it still in their best interest to support the minor faction as much as possible. This is akin to a "reverse spoiler effect", in which the larger mainstream party spoils the election by not supporting the smaller third party.
A "soft defection" (giving a low non-zero rating) would produce similar penalties accordingly, with a greater penalty for lower scores.
Since the incentive for defecting is eliminated, but the rewards for collaborating are preserved, Reciprocal Score Voting minimizes concerns with Chicken Dilemma scenarios. In any sufficiently large mutual majority scenario, the likelihood of either A or B winning will be very large (although not guaranteed due to the non-ranked nature of the system).▼
▲Since the incentive for
== Variants ==
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