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<div>One problem with using the winner of the single biggest defeat is that it could just be a candidate dominating a clone, saying little about their performance overall. And if you're not confining it to e.g. the Smith Set, it could possibly even be the second weakest candidate of many.</div><div><br></div><div>Toby</div><div><br></div>
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On Monday, 20 February 2023 at 01:28:18 GMT, Forest Simmons <forest.simmons21@gmail.com> wrote:
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<div><div id="ydpcc00f14byiv5274668252"><div><div>I have learned a lot from the "hay guys" thread that spontaneously upgraded into this "hey guys" thread.<div><br clear="none"></div><div>Colin Champion made some very helpful points and pointers about the psychology of what we are involved in. Many similar practical considerations contributed by all participants.</div><div><br clear="none"></div><div>Several suggestions have been made about how to complete this sentence:</div><div><br clear="none"></div><div>"Lacking a candidate that defeats every other candidate in pairwise head-to-head comparisons, elect the candidate that ..."</div><div><br clear="none"></div><div>I can live with most of those suggestions ... which is neither here nor there in the grand scheme of things ... but I hope haven't offended anybody or discouraged anybody's contributions to these explorations.</div><div><br clear="none"></div><div>Several people have said, "Why not just ...?"</div><div><br clear="none"></div><div>And I thought, "Why didn't I think of that?"</div><div><br clear="none"></div><div>The most promising idea I am currently thinking along these lines goes like this:</div><div><br clear="none"></div><div>Elect the pairwise undefeated champion ... or lacking such a champion, elect the winner of the strongest pairwise defeat ... meaning the pairwise contest with the greatest sum of winner approval and loser disapproval ... winner approval measured by winning votes ... the number of ballots on which the winner outranks the loser... loser disapproval measured by loser abstentions ... the number of ballots on which the pairwise loser is unranked.</div><div><br clear="none"></div><div>So winning votes plus loser abstentions is my proposal for defeat strength ... not to be used in Rsnked Pairs ... but just in the first and strongest step of RP ... and then only in the absence of a Condorcet Winner.</div><div><br clear="none"></div><div>For now it's just an idea needing an experimental shake down beyond my meager manual tests.</div><div><br clear="none"></div><div>But who knows?</div><div><br clear="none"></div><div>-Forest </div></div><br clear="none"><div class="ydpcc00f14byiv5274668252gmail_quote"><div id="ydpcc00f14byiv5274668252yqt49262" class="ydpcc00f14byiv5274668252yqt5956133618"><div dir="ltr" class="ydpcc00f14byiv5274668252gmail_attr">On Sun, Feb 19, 2023, 10:47 AM Colin Champion <<a shape="rect" href="mailto:colin.champion@routemaster.app" rel="nofollow" target="_blank">colin.champion@routemaster.app</a>> wrote:<br clear="none"></div><blockquote style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;" class="ydpcc00f14byiv5274668252gmail_quote">
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<font face="Helvetica, Arial, sans-serif">I asked Kristofer whether
Condorcet+FPTP complied with the Condorcet Loser criterion. He
replied "probably not" with a sketch proof, and then gave the
following example.<br clear="none">
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[preliminary election]<br clear="none">
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40: L>C>R <br clear="none">
42: R>C>L <br clear="none">
10: C>L>R <br clear="none">
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R is the Condorcet loser and Plurality winner. (L is the IRV
winner.) <br clear="none">
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Now clone C, the CW: <br clear="none">
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40: L>Ca>Cb>Cc>R <br clear="none">
42: R>Cb>Cc>Ca>L <br clear="none">
10: Cc>Ca>Cb>L>R <br clear="none">
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There's no CW, so Plurality elects R, the Condorcet loser.
(Incidentally, R ties for first in minmax.) <br clear="none">
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Seems OK. Verified with <a shape="rect" href="https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html" rel="nofollow" target="_blank">https://web.archive.org/web/20220403135047/http://www.cs.angelo.edu/~rlegrand/rbvote/calc.html</a>.
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I'd wondered whether Robert didn't have any intellectual commitent
to the criterion, but had used it in argument against IRV and
therefore found his options limited. <br clear="none">
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CJC<br clear="none">
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<div>On 19/02/2023 17:31, Kristofer
Munsterhjelm wrote:<br clear="none">
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<blockquote type="cite">On
2/19/23 16:36, Colin Champion wrote:
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<blockquote type="cite">"Politicians and the voting public would
not accept anything more complicated than X" is my own favourite
line of argument - but I substitute my own value for X(minimax).
I know that my judgement is coloured by my preferences. There's
a surprising degree of dissent over which methods are simpler
than which, and where the boundary should be drawn. People who
deal directly with politicians and the voting public can no
doubt get closer to the truth than people whose interest is
predominantly theoretical, but I wish there was an authoritative
and objective source of information. If only some behavioural
psychologist was funded to investigate the question...
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To be finicky, the issue isn't exactly one of simplicity but
rather one of psychological acceptability, which includes the
notions of whether a method "makes sense" to the average
onlooker, and whether it is seen as conferring legitimacy on its
winner rather than being an unmotivated piece of jiggery pokery.
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Notwithstanding all this... you and Robert may well be right.
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FWIW, I suspect the complexity people are willing to accept
depends on their trust in the political process in general. For
instance, some local New Zealand elections use Meek's method,
which is complex however you put it.[1] And I wouldn't be prepared
to explain the pretty messy greedy algorithm used to allocate
party list top-up seats here (in Norway), but people seem to
accept it.[2]
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I don't think Robert could use minmax because the criterion he's
using is "if more people prefer X to Y than vice versa, then Y is
not elected". That seems to imply at least Condorcet loser. I'm
not sure, though -- if you're particularly critical, you could
even say it implies Smith, but I don't think Robert had that in
mind.
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-km
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[1] I wonder what the legal language for *that* is... it's
basically impossible to do by hand.
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[2] IMHO, biproportional apportionment is *much* simpler. I
suspect what's keeping it from being changed is mostl inertia.
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