<html><head></head><body><div class="ydpbbc70114yahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:13px;"><div></div>
<div dir="ltr" data-setdir="false">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><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Toby</div><div><br></div><div><br></div>
</div><div id="ydpfb885ae5yahoo_quoted_2472273349" class="ydpfb885ae5yahoo_quoted">
<div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;">
<div>
On Thursday, 17 August 2023 at 05:43:00 BST, C.Benham <cbenham@adam.com.au> wrote:
</div>
<div><br></div>
<div><br></div>
<div><div id="ydpfb885ae5yiv4142299930"><div>
<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.)
<div dir="ltr"><br clear="none">
</div>
</blockquote>
<p>Toby,<br clear="none">
<br clear="none">
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">
</p>
<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">
<br clear="none">
</p>
<div id="ydpfb885ae5yiv4142299930yqt30400" class="ydpfb885ae5yiv4142299930yqt4135720190"><div class="ydpfb885ae5yiv4142299930moz-cite-prefix">O</div></div></div></div></div>
</div>
</div></body></html>