User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
User:BetterVotingAdvocacy/Big page of ideas (view source)
Revision as of 23:43, 4 July 2020
, 3 years ago→Rated pairwise preference ballot
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One way to understand a voter's absolute score for a candidate is that they are expressing their degree of support for that candidate pairwise against a candidate they don't support at all.
== Miscellaneous ==
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Here is an example of a situation where, if voters are assumed to normalize their scores, it is possible to justify a non-majoritarian winner even with only ranked preferences: suppose there are very many voters, with there being a majority faction only one voter larger than an opposing minority faction. The majority's preference is A>B>C>etc. while the minority bullet votes B. In this case, B would almost guaranteeably win in Score under the above assumptions, even if decimal scores were allowed, so long as the majority's preference for B was non-infinitesimal, since this would cut into their ability to express their A>B preference.
(Work in progress, calculations and reasoning are off) Expressiveness of rated pairwise vs. other ballot types:
* One way to evaluate the expressiveness of various ballot types is to look at how many possible votes a voter can cast with a certain number of candidates. <ref>https://www.bridgealliance.us/ten_critiques_and_defenses_on_approval_voting See Critique #3.</ref> Rated pairwise, assuming a limited ballot design where voters can indicate their ranking of each candidate, and how they'd vote in a matchup between their 1st choice vs 2nd choice, 2nd choice vs 3rd choice, etc. (with matchups between candidates more than one rank apart calculated by adding up the margins of each intervening matchup i.e. the marginal preference a voter has for 2nd choice over 4th choice is calculated as the margin for 2nd>3rd + 3rd>4th), and if considering the "votes" a voter can cast as the possible rated pairwise preferences they can indicate on such a ballot, allows for at least 72 possible votes with 3 candidates, if allowing a scale of 0 to 3 in each matchup. This compares to a rated ballot with a scale of 0 to 3 itself, which allows for at most 62 possible votes.
** 72 comes from 60 + 12. There are 6 possible rankings of the candidates if disallowing equal-rankings (A>B>C, A>C>B, B>A>C, B>C>A, C>A>B, C>B>A), with each of these having 10 possible preferences (for A>B>C, this can be demonstrated as (with "|" used to separate each possible vote): (A>B 0, B>C 0, A>C 0 | A>B 1, B>C 0, A>C 1 | A>B 0, B>C 1, A>C 1 | A>B 1, B>C 1, A>C 2 | A>B 1, B>C 2, A>C 3 | A>B 2, B>C 1, A>C 3 | A>B 2, B>C 2, A>C 3 | A>B 3, B>C 2, A>C 3 | A>B 2, B>C 3, A>C 3 | A>B 3, B>C 3, A>C 3). In addition, there are a number of rankings that involve equal-ranking (A=B>C, A=C>B, B=C>A, A=B=C, A>B=C, B>A=C, C>A=B), with each of these also allowing for an additional number of possible votes.
* There are two variations of rated pairwise to consider here: one where the voter can only indicate their score for their more-preferred candidate in the matchup (i.e. they can only indicate marginal preference), and one where they can indicate their scores for both the candidates. The figures computed above are for the former variation, but the latter variation greatly increases the level of expressiveness, since, for example, a voter wishing to indicate they prefer A 1 point more than B can cast that as A:4 B:3, A:3 B:2, A:2 B:1, or A:1 B:0, while there is only one way to cast that preference using the margins-based variation.
== Condorcet ==
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