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<p><br>
On April 9 last year I suggested the "Double Defeat, Hare" method
(nominating it as an alternative in a poll).<br>
</p>
<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;"><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;">*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.*</pre>
</blockquote></pre>
<p><br>
I now withdraw that not-so-clever idea because of this scenario:<br>
<br>
43 A|<br>
03 A<B|<br>
44 B>C| (sincere is B| or B|>A or B>A|)<br>
10 C|>A<br>
<br>
A is both the normal Hare winner and the sincere Condorcet winner.<br>
<br>
Approvals: C 54 B 47 A 46.<br>
<br>
C>A 54-47, A>B 56-44, B>C 47-10. <br>
<br>
Only A is disqualified by Double Defeat and C is eliminated by
the Hare rule leaving B the winner, rewarding the outrageous
Burial strategists.<br>
<br>
My favourite Condorcet method, Margins-Sorted Approval(explicit)
would punish them by electing C (as would the not-too-bad
Smith//Approval).<br>
<br>
It would first look at the BA pair because they are adjacent to
each other in the approval order and have a smaller margin of
difference in their approval scores (47-46=1) than the CB adjacent
pair (54-47=7) and notice that they are pairwise (by the rankings)
out of order<br>
and so flip that order, making it C>A>B. Neither of the
two adjacent pairs are now pairwise out of order so that order is
final and C is on top of it so C wins.<br>
<br>
Smith//Approval(explicit) sees that all three candidates are in
the Smith set and so elects the one with the most approval.<br>
<br>
Hare, being completely immune to Burial strategy (because it meets
Later-no-Help) elects (in this example) the sincere Condorcet
Winner.<br>
<br>
Chris Benham<br>
</p>
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