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<p>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?"<br>
</p>
<p>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.<br>
</p>
<p>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: <i>A majority must not rank over the winner the candidate
who would win if the winner were deleted from the votes</i>.)
MAM is both a singlewinner and multiwinner method; in either case
the winner(s) is(are) determined by its order of finish.</p>
<p>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:</p>
<blockquote>
<p><u>MAM</u><br>
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).</p>
<p>Count all the head-to-head majorities.<br>
</p>
<p>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).</p>
</blockquote>
Voting for a Published Ranking (VPR) is as simple as possible for
voters:
<blockquote>
<p><u>VPR</u><br>
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.</p>
<p>Each voter votes by selecting one candidate. <u>Each vote is
treated as if it were the ranking published by its selected
candidate</u>.</p>
<p>The tallying of the voters' rankings is the same as in MAM.<br>
</p>
</blockquote>
<p>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."<br>
</p>
<p>Assuming adequate technology in all the voting booths, a hybrid
of VPR & MAM seems better than either VPR or MAM:</p>
<blockquote>
<p><u>VPR/MAM Hybrid</u><br>
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.</p>
<p>Each voter begins by selecting one candidate. <u>That
candidate's published ranking is displayed to the voter, who
may rearrange it as desired</u> (perhaps by drag&drop on a
touchscreen) before submitting it as his/her vote.</p>
<p>The tallying of the voters' rankings is the same as in MAM.</p>
</blockquote>
<p>Note 1: Tiebreaking in MAM differs from tiebreaking in Ranked
Pairs in three ways:<br>
(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.<br>
(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.<br>
(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.<br>
</p>
<p>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.)<br>
</p>
<p>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.</p>
<p>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.<br>
</p>
<p></p>
<p>--Steve<br>
</p>
<div class="moz-cite-prefix">On 10/12/2024 2:56 PM, Kristofer
Munsterhjelm wrote:<br>
</div>
<blockquote type="cite" cite="mid:e7a9f58e-c7e6-85fd-3d8a-09ab565c3677@munsterhjelm.no">Lately,
I've been updating my Electowiki page,
<a class="moz-txt-link-freetext" href="https://electowiki.org/wiki/User:Kristomun/Proposed_voting_methods">https://electowiki.org/wiki/User:Kristomun/Proposed_voting_methods</a>.
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.
<br>
<br>
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: <b><font color="#0000ff">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</font></b>?
<br>
<br>
-km<br>
</blockquote>
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