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<font face="Helvetica, Arial, sans-serif">Thanks to Kevin and
Michael for pointing out a feature of minimax I was unaware of. I
had however seen Richard Darlington's paper [1] in which he
referred to 'several studies' comparing margins with winning
votes. He reports that margins 'was the big winner in all of
them'. I suppose I'll have to look deeper.<br>
Colin<br>
[1]. <a class="moz-txt-link-freetext" href="https://arxiv.org/abs/1807.01366">https://arxiv.org/abs/1807.01366</a><br>
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<div class="moz-cite-prefix">On 18/09/2023 07:57, Michael Ossipoff
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAOKDY5DNcvimxv+r6wOgfcViHsWyCG8kt0zUZgVddmd=Be34Hg@mail.gmail.com">
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<div class="gmail_quote" dir="auto">
<div dir="ltr" class="gmail_attr">---------- Forwarded message
---------<br>
From: <strong class="gmail_sendername" dir="auto">Michael
Ossipoff</strong> <span dir="auto"><<a
href="mailto:email9648742@gmail.com"
moz-do-not-send="true">email9648742@gmail.com</a>></span><br>
Date: Sun, Sep 17, 2023 at 22:54<br>
Subject: Re: [EM] Ranked Pairs<br>
To: Forest Simmons <<a
href="mailto:forest.simmons21@gmail.com"
moz-do-not-send="true">forest.simmons21@gmail.com</a>><br>
</div>
<div class="gmail_quote" dir="auto"><br>
</div>
This was meant to be sent by “Reply All”, in order to post it.
So now I’m forwarding it to EM.<br>
<br>
<div dir="auto">Forest—</div>
<div dir="auto"><br>
</div>
<div dir="auto">But wv prevents truncation (strategic or
otherwise) from taking the win from a CW.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&, with, wv, refusing to rank anymore you
don’t approve will cause offensive order-reversal by their
preferrers to backfire.</div>
<div dir="auto"><br>
</div>
<div dir="auto">I’d always take that precaution, & would
advise others to.</div>
<div dir="auto"><br>
</div>
<div dir="auto">When we discussed these guarantees years ago
they seemed absolute, & we still have the
guarantee-criteria based on them…met by wv versions of
MinMax, RP, CSSD, & Smith//MinMax.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&, with MinMax, whose winner can come
from anywhere, not just from the top-cycle, & so,
offensive order-reversal, when there are a fair number of
candidates, is unpredictable & risky for its
perpetrators, even if the precaution of deterrent-truncation
isn’t taken.</div>
<div><br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sun, Sep 17, 2023 at
21:17 Forest Simmons <<a
href="mailto:forest.simmons21@gmail.com"
target="_blank" moz-do-not-send="true">forest.simmons21@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div dir="auto">
<div><br>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">On Sat, Sep 16,
2023, 9:42 PM Michael Ossipoff <<a
href="mailto:email9648742@gmail.com"
target="_blank" moz-do-not-send="true">email9648742@gmail.com</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px
0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">
<div dir="auto">Is that RP(wv), or RP(margins) ?</div>
<div dir="auto"><br>
</div>
<div dir="auto">RP(wv) would thwart & deter
offensive strategy, an important property in
public elections.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…&, actually, it seems to me
that MinMax(wv) would do that better.</div>
<div dir="auto"><br>
</div>
<div dir="auto">That’s because, choosing only
from the Smith Set RP, limits it’s choice to
the strategic top-cycle that created by the
offensive strategists.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Suppose that the CW’s preferrers
don’t do defensive truncation (never rank
anyone you wouldn’t approve in Approval, or
whose preferrers you regard as likely to
offensively order-reverse) ?</div>
<div dir="auto"><br>
</div>
<div dir="auto">Knowing that RP will limit its
choice to their small strategic top-cycle, it
would be easier for the strategists to be
fairly sur that their candidate would win in
that top-cycle.</div>
<div dir="auto"><br>
</div>
<div dir="auto">But, with MinMax, the winner is
chosen more broadly, & could be anywhere
in the candidate-set. …making it more
difficult & risky to confidently do
offensive order/reversal.</div>
<div dir="auto"><br>
</div>
<div dir="auto">RP(margins) might the best
choice for a completely honest electorate, but
MinMax(wv) seems better for public elections,
due to its better thwarting & deterrence
of offensive strategy.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Yes, MinMax doesn’t meet the
luxury cosmetic look-good criteria that RP
meets. </div>
<div dir="auto"><br>
</div>
<div dir="auto">But for one thing, I remind you
that natural ( sincere) top-cycles are
vanishingly-rare.</div>
</blockquote>
</div>
</div>
<div dir="auto"><br>
</div>
<div dir="auto">This is the same conclusión I have
come around to. </div>
<div dir="auto"><br>
</div>
<div dir="auto">And methods that break a three member
top cycle at the weakest link tend to reward the
burier faction.</div>
</div>
<div dir="auto">
<div dir="auto">
<div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0px
0px 0px
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<div dir="auto"><br>
</div>
<div dir="auto">So do you want to have less
strategy-protection, in order for the result
to maybe look better in a vanishingly rare
natural top/cycle?</div>
<div dir="auto"><br>
</div>
<div dir="auto">…& how bad is a violation of
Condorcet-Loser anyway. “Beaten by all the
other alternatives” sounds like some kind of
unanimity, but of course it isn’t. It isn’t
like a Pareto-violation. I remind you that the
MinMax winner has fewer voters preferring some
particular candidate over him than anyone else
does.</div>
<div dir="auto"><br>
</div>
<div dir="auto">Clone-Criterion violation? How
bad that really in MinMax, especially when
we’re talking about a vanishingly rare natural
top-cycle?</div>
<div dir="auto"><br>
</div>
<div dir="auto">RP(margins) for a completely
honest electorate.</div>
<div dir="auto"><br>
</div>
<div dir="auto">MinMax(wv) for public elections.</div>
<div dir="auto"><br>
</div>
<div dir="auto">..& about a primary to
reduce the candidates to 5: Forget the
primary. If you think people will have trouble
rank-ordering lots of candidates, I remind you
that, to vote among them in a primary, they’d
still have to examine & choose among the
initial many candidates.</div>
<div dir="auto"><br>
</div>
<div dir="auto">…harder than ranking only the
ones you know & regard as deserving &
definitely in your accepts& preferred set.</div>
<div dir="auto"><br>
<div class="gmail_quote" dir="auto">
<div dir="ltr" class="gmail_attr">On Wed,
Sep 13, 2023 at 00:18 Colin Champion <<a
href="mailto:colin.champion@routemaster.app" rel="noreferrer"
target="_blank" moz-do-not-send="true">colin.champion@routemaster.app</a>>
wrote:<br>
</div>
<blockquote class="gmail_quote"
style="margin:0px 0px 0px
0.8ex;border-left-width:1px;border-left-style:solid;padding-left:1ex;border-left-color:rgb(204,204,204)">I
notice that RP is the only election method
mentioned by name in the <br>
Virginia agenda.<br>
<br>
A while ago I ran some simulations on
elections with truncated ballots. <br>
Something I noticed was that the presence
of RP in the list of methods <br>
made the software unacceptably slow. I
didn't look into the cause, but <br>
there's a natural explanation, which is
the fact that RP is known to be <br>
NP-complete when it deals correctly with
tied margins, i.e. by <br>
exhausting over all their permutations.
Presumably if some candidates <br>
are unpopular and ballots are extensively
truncated, then tied margins <br>
are much likelier than with complete
ballots.<br>
<br>
I gather that practical implementations of
RP choose a random <br>
permutation rather than exhausting. This
seems to me to bring a danger. <br>
The presence of a few vanity candidates
(truncated off almost all <br>
ballots) may lead to ties, and this may
lead to a comfortable winner <br>
looking as though he owes his victory to a
coin-toss. Obviously this <br>
undermines the legitimacy of his win.<br>
<br>
CJC<br>
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