User:BetterVotingAdvocacy/Big page of ideas: Difference between revisions
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Revision as of 01:06, 6 July 2020
, 3 years ago→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 ===
This section is for things that I'm still working on; they may not be totally correct, but hopefully they have various insights in them.
(Work in progress, calculations and reasoning are off) Expressiveness of rated pairwise vs. other ballot types:
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** 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.
I'm trying to evaluate whether is a way to essentially "track" a voter if voters are allowed to weaken their votes in Condorcet. By track I mean that you could figure out some voter's preferences by looking at the election result data; here is one example<ref>http://www.votingmatters.org.uk/ISSUE30/I30P2.pdf</ref>. My guess for how you could create an example where such a thing is possible is to have an election with few voters, where only 1 of the voters weakens their vote at all. Keep in mind that this may be somewhat realistic when considering that each precinct releases its own vote totals, such that a very small precinct may be vulnerable to this type of thing, if it exists.
== Condorcet ==
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