<!DOCTYPE html>
<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
</head>
<body>
<p><br>
<blockquote type="cite">
<pre
style="white-space: pre-wrap; color: rgb(0, 0, 0); font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial;">I would like to nominate Double Defeat, Hare.
*Voters strictly rank from the top however many candidates they wish and
also may specify an approval cutoff.
Default approval is only goes to top-ranked candidates.
All candidates that are pairwise beaten by a more approved candidate are
disqualified.
If that leaves more than one qualified (i.e. not disqualified)
candidate, commence eliminations according to Hare
rules until only one qualified candidate remains.*
This is a compromise between Hare and Condorcet which will probably not
please the fundamentalist supporters of either,
because it doesn't meet the Condorcet criterion and is more complicated
than Hare and fails Later-no-Harm and Later-no-Help.
But it addresses the concern some have about electing a weak low social
utility Condorcet winner, and I think it might simulate
well.</pre>
</blockquote>
<br>
I think that methods that allow voters to both rank the candidates
and specify an approval threshold/cutoff<br>
should never elect a candidate that is pairwise beaten by a more
approved candidate. <br>
<br>
I coined this criterion as "Double Defeat" and it occurred to me
that it could be a disqualification device that<br>
is part of a method.<br>
<br>
Some people are wary of Condorcet electing a "weak centrist"
candidate, for example<br>
<br>
49 A>>>C>B<br>
48 B>>>C>A<br>
03 C>A>>>B<br>
<br>
Assuming all voters get the same utility from electing their
favourites, the Hare (and FPP and presumably Approval)<br>
winner is the highest Social Utility candidate A.<br>
<br>
With those sincere preferences, the
ranking-with-specified-approval ballots would be<br>
<br>
49 A|>C<br>
48 B|>C<br>
03 C>A|<br>
<br>
Here the Double Defeat rule doesn't interfere with Hare. B is
disqualified because B is pairwise beaten by the more approved A.<br>
<br>
So then, following Hare rules C is eliminated leaving A as the
only qualified candidate and so winner.<br>
<br>
The C>A voters have no real complaint other than "The method
should meet the Condorcet criterion" and any complaint from<br>
the B>C voters is answered by "To get a result you prefer you
didn't have to order-reverse, you could have had A disqualified by<br>
approving C".<br>
<br>
The method is similar in spirit to an "Approval-enhanced Hare"
that arose from discussion I had here a few months ago with
Forest,<br>
but which I forgot about and didn't rediscover until after
nominations for the poll had closed:<br>
<br>
*Elect the most approved member of the set comprising the Hare
winner and all the candidates with a beat-path to the Hare
winner.*<br>
<br>
49 A (sincere might be A>B)<br>
24 B (sincere might be B>C)<br>
27 C>B<br>
<br>
A classic example that has been interpreted as Hare and Margins by
electing A failing Minimal Defense and avoidably causing the C
voters to regret<br>
not Compromising, and alternatively by electing B the C>B
voters having been taken advantage of by the B voters using a
Defection strategy, a failure<br>
of the Chicken Dilemma criterion.<br>
<br>
In this example it is true that in all the methods that meet
Double Defeat it is up to the C>B voters to decide which is
more important for them:<br>
preventing the election of their greater evil A, or preventing
being taken advantage of by Defecting B voters.<br>
<br>
Chris B.<br>
<br>
<br>
<br>
</p>
</body>
</html>