[EM] Request for proposed methods

[Steve Eppley]

Kristofer Munsterhjelm asked us yesterday, "do you know any methods that have been proposed or discussed but that neither have their own Electowiki articles nor are listed on my page?"

The three voting methods discussed below -- Maximize Affirmed Majorities (MAM), Voting for a Published Ranking (VPR), and a hybrid of VPR & MAM -- aren't listed on Kristofer's Electowiki page nor do they have their own Electowiki articles.

MAM differs from Ranked Pairs in several ways and satisfies additional criteria.  It's the only voting method that satisfies the Immunity from Majority Complaints criterion, IMC. (That implies MAM also satisfies Immunity from Second-Place Complaints, I2C: /A majority must not rank over the winner the candidate who would win if the winner were deleted from the votes/.)  MAM is both a singlewinner and multiwinner method; in either case the winner(s) is(are) determined by its order of finish.

When it's reasonable to neglect tiebreaking details -- as in public elections, where it would be very rare that two majorities are the same size or a head-to-head pairing is tied -- MAM can be briefly defined as follows:

    _MAM_
    Allow each voter to rank the candidates.  Expressing indifference between candidates is allowed (unlike Tideman's Ranked Pairs).  As a time-saving shortcut, any candidate(s) that a voter doesn't explicitly rank is(are) treated as if the voter had ranked it(them) at the bottom (below the explicitly-ranked candidates).

    Count all the head-to-head majorities.

    Construct the order of finish by processing the head-to-head majorities one at a time from largest majority to smallest majority, placing each majority's higher-ranked candidate ahead of their lower-ranked candidate in the order of finish (except when their lower-ranked candidate has already been placed ahead of their higher-ranked candidate).

Voting for a Published Ranking (VPR) is as simple as possible for voters:

    _VPR_
    In advance of the election, each candidate publishes a ranking of all the candidates.  Any candidate who doesn't publish a ranking is treated as if s/he'd published the ranking that has him/her on top and all the other candidates tied at the bottom.

    Each voter votes by selecting one candidate.  _Each vote is treated as if it were the ranking published by its selected candidate_.

    The tallying of the voters' rankings is the same as in MAM.

VPR is useful in societies where some voters will have trouble ranking candidates and in societies where the technology available for voting booths isn't advanced enough to support voters expressing rankings on machine-readable ballots.  VPR also ought to reduce the amount of campaign money needed by "good compromise" candidates, because they can win by persuading other candidates to rank them higher than worse candidates.  An important advantage of VPR over voting methods that require voters to explicitly express rankings is that "low information" voters, who don't know as much about some of the "good compromise" candidates as their favorite candidate knows, can vote "better" rankings... voters won't fail to rank compromises over "greater evils."

Assuming adequate technology in all the voting booths, a hybrid of VPR & MAM seems better than either VPR or MAM:

    _VPR/MAM Hybrid_
    In advance of the election, each candidate publishes a ranking of all the candidates.  Any candidate who doesn't publish a ranking is treated as if s/he'd published the ranking that has him/her on top and all the other candidates tied at the bottom.

    Each voter begins by selecting one candidate.  _That candidate's published ranking is displayed to the voter, who may rearrange it as desired_ (perhaps by drag&drop on a touchscreen) before submitting it as his/her vote.

    The tallying of the voters' rankings is the same as in MAM.

Note 1: Tiebreaking in MAM differs from tiebreaking in Ranked Pairs in three ways:
(1.1)  MAM uses Random Voter Hierarchy (not Random Dictator) when it's necessary to construct a tiebreak ordering of the candidates, because allowing voters to express indifference means Random Dictator might not suffice to construct a tiebreak ordering that's strict.
(1.2)  When majorities are the same size, MAM uses the tiebreak ordering in a way that differs from how Zavist-Tideman's 1989 uses it to resolve same-size margins.  Zavist's algorithm is less robust, and if it were used with MAM then MAM would fail the Strong Pareto criterion.  MAM's algorithm seems more natural than Zavist's algorithm, and Ranked Pairs could be amended to use it without breaking any criteria.
(1.3)  If a pairwise tie causes the order of finish to remain non-strict (has one or more ties) after all the majorities have been processed, the tiebreak ordering breaks the remaining ties.  This step is never needed by Ranked Pairs because Ranked Pairs resolves each tied pairing as two same-size margins... both margins of a tied pairing equal zero.

Note 2: The Electowiki article for Ranked Pairs includes an external link to MAM but that webpage no longer exists.  It was at a free webhost that deleted the webpages.  I still have copies, but to improve compatibility it would be best to export them from html to pdf (and change the filenames in their internal links from .html to .pdf).  Also, the online MAM tallying engine software requires the host to support PHP 5 because the source code uses a couple of functions not supported by more recent versions of PHP. (Alternatively, the software could be migrated to a more recent PHP, or to a different language such as JavaScript running in the user's web browser.)

Note 3: Schultz's method is listed on Kristofer's page as multiwinner.  But it fails the Resolvability criterion when more than one winner is to be elected, so it's not as deterministic as most voting methods.

Note 4:  In Electowiki, the language describing Ranked Pairs seems needlessly complicated, as if the author either had a lot of mental baggage or was intentionally trying to make it hard to understand.  At any rate, the language describing MAM can be even simpler and more familiar than for Ranked Pairs, because a head-to-head majority is a coalition of people, which naturally has properties relevant to MAM: their size (the number of people in the coalition), their higher-ranked candidate, and their lower-ranked candidate.

--Steve

On 10/12/2024 2:56 PM, Kristofer Munsterhjelm wrote:
> Lately, I've been updating my Electowiki page, https://electowiki.org/wiki/User:Kristomun/Proposed_voting_methods. This page lists various voting methods that aren't described in detail on the wiki, but have been proposed in either literature or on EM.
>
> Though I've managed to find a number of methods (including one that might provide a divisor PR analog of the DPC), I imagine there are still lots out there that I haven't happened across. So I'd like to ask the list: *do you know any methods that have been proposed or discussed but that neither have their own Electowiki articles nor are listed on my page*?
>
> -km
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