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<div dir="ltr" data-setdir="false">Chris</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">It's not that I disagree with your views of STAR's behaviour as a method. And there are changes that could be made that would improve STAR, as you say. However, I just don't think that STAR's failure here can reasonably be called a monotonicity failure.</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div>
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On Saturday, 19 August 2023 at 04:10:32 BST, C.Benham <cbenham@adam.com.au> wrote:
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<p>Toby,<br clear="none">
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</p><blockquote type="cite">I wouldn't count this as a monotonicity
failure because it involves decreasing Y's score as well as
increasing X's.</blockquote>
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This is like a sophist's technical loophole. Why do we
particularly care about "monotonicity failure"? To avoid some
hypothetical mild embarrassment? <br clear="none">
For the sake of marketing bragging rights? <br clear="none">
<br clear="none">
Or because it is related to Push-over strategy
incentive/vulnerability? STAR is much worse in that respect than
IRV because there the strategists are entirely<br clear="none">
relying on other voters to both get their favourite into the final
two and to there win the pairwise contest, so if too many of X's
supporters try the strategy it<br clear="none">
could backfire. <br clear="none">
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Whereas with STAR the strategists could be a bit cautious and give
the weak candidate they are trying to promote into the final a
score of max. minus one<br clear="none">
while also giving their favourite X max. points.<br clear="none">
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That way all of X's supporters could use the strategy and it could
still succeed. <br clear="none">
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The 0-5 score ballot is too restrictive (certainly for STAR) Say,
as I earlier advocated, the voters rank however many candidates
they want to and give an approval cutoff wherever<br clear="none">
they want, and we elect the pairwise winner between the two most
approved candidates.<br clear="none">
<br clear="none">
That would be very similar to STAR (0-5 score ballots) but
wouldn't it be better? And also a method that fails mono-raise
and Condorcet and many other criteria <br clear="none">
and is obviously terrible?<br clear="none">
<br clear="none">
Chris<br clear="none">
<div id="ydp8a4fb1aayiv4453078911yqt02508" class="ydp8a4fb1aayiv4453078911yqt7085660008"><div class="ydp8a4fb1aayiv4453078911moz-cite-prefix">On 17/08/2023 9:47 pm, Toby Pereira
wrote:<br clear="none">
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<div dir="ltr">I wouldn't count this as a
monotonicity failure because it involves decreasing Y's score
as well as increasing X's. Mono-raise may have been defined
specifically for ordinal ballots where raising a candidate
inevitably pushes others down. Whereas with a rated ballot, I
think one would be more likely to define monotonicity criteria
in terms of increasing a candidate's score while leaving all
others the same.</div>
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<div dir="ltr">Toby</div>
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<div> On Thursday, 17 August 2023 at 05:43:00 BST, C.Benham
<a shape="rect" href="mailto:cbenham@adam.com.au" class="ydp8a4fb1aayiv4453078911moz-txt-link-rfc2396E" rel="nofollow" target="_blank"><cbenham@adam.com.au></a> wrote: </div>
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<p>Toby Pereira wrote: </p>
<blockquote type="cite">I'm not a fan of STAR, but I am
still interested in seeing how it stands up to
scrutiny given that it has a following. (Actually I'm
not aware of how STAR fails monotonicity. I was under
the impression that it passed.)
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<p>Toby,<br clear="none">
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To give you a bit of a preview before I get around to
cooking up all the examples, nothing with such obvious
Push-over incentive can meet mono-raise (aka
"monotonicty")<br clear="none">
<br clear="none">
Suppose X beats Y in the final. Now suppose on some
ballots with Y above X, we raise X so it is now above
Y. That could reduce Y's score enough for it to be
replaced in the final<br clear="none">
by Z, a candidate that pairwise beats X.<br clear="none">
<br clear="none">
Voters who are mainly concerned to have their
favourite X win and are fairly certain that X will
reach the final will have a strong incentive to give X
max points (5) and then also<br clear="none">
give a 4 (or even a 5) to all those candidates that
they think X can beat pairwise.<br clear="none">
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<p>If enough voters use that strategy and it fails, both
the finalists could be candidates with little sincere
support.<br clear="none">
<br clear="none">
Chris Benham<br clear="none">
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<div class="ydp8a4fb1aayiv4453078911ydpfb885ae5yiv4142299930moz-cite-prefix">O</div>
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