<div dir="ltr"><div class="gmail_quote"><div dir="ltr">May I repeat the request to put terms like <a href="http://wiki.electorama.com/wiki/MAM" target="_blank">MAM</a> in electorama before you use them here? For now, that link goes to an empty page.<div>
<br></div><div>(Even CD... I understand that term, and I even think I might have invented it, but these conversations should be at least theoretically readable to somebody who doesn't already know all the acronyms.)</div>
</div><div class="gmail_extra"><br><br><div class="gmail_quote">2014-05-20 19:42 GMT-04:00 Forest Simmons <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu" target="_blank" onclick="window.open('https://mail.google.com/mail/?view=cm&tf=1&to=fsimmons@pcc.edu&cc=&bcc=&su=&body=','_blank');return false;">fsimmons@pcc.edu</a>></span>:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div><div class="h5">
<div dir="ltr"><div><div><div><div>Chris,<br><br></div>for Benham, what if we count fractional (for equal rank top) as you suggest when doing the IRV eliminations, but check at each step for a pairwise beats all candidate in the usual way?<br>
<br></div>In your example below, since B beats A pairwise 31 to zero and B beats C 65 to 35, no IRV elimination step is required, so how equal rank top is counted in this example does not seem to matter.<br><br></div>Or is there some reason for doing a "symmetric completion" of equal rankings for the pairwise contests as well?<br>
<br></div>Forest<br><div><div><div><div><div><div><div class="gmail_extra"><br><br><div class="gmail_quote"><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<br>
Date: Wed, 21 May 2014 03:53:38 +0930<div><br>
From: "C.Benham" <<a href="mailto:cbenham@adam.com.au" target="_blank" onclick="window.open('https://mail.google.com/mail/?view=cm&tf=1&to=cbenham@adam.com.au&cc=&bcc=&su=&body=','_blank');return false;">cbenham@adam.com.au</a>><br>
To: <a href="mailto:election-methods@lists.electorama.com" target="_blank" onclick="window.open('https://mail.google.com/mail/?view=cm&tf=1&to=election-methods@lists.electorama.com&cc=&bcc=&su=&body=','_blank');return false;">election-methods@lists.electorama.com</a><br>
</div><div>
Subject: Re: [EM] New Criterion<br></div>
Message-ID: <<a href="mailto:537B9DAA.4030406@adam.com.au" target="_blank" onclick="window.open('https://mail.google.com/mail/?view=cm&tf=1&to=537B9DAA.4030406@adam.com.au&cc=&bcc=&su=&body=','_blank');return false;">537B9DAA.4030406@adam.com.au</a>><div>
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Forest,<br>
<br>
I've been meaning to remind you: for IRV and Benham (and Woodall and<br>
similar) I'm strongly opposed to allowing voters to do any equal-ranking<br>
apart from truncating because it makes Push-over strategizing much less<br>
risky and more likely to succeed.<br>
<br>
Two versions of ER-IRV have been discussed, one where an A=B ballot<br>
gives a "whole vote" to each and one where it gives half a vote to each,<br>
i.e,<br>
ER-IRV(whole) and ER-IRV(fractional). The problem I referred to is<br>
much worse for the former and so I consider the latter to less bad.<br>
<br>
But if we insist on allowing above-bottom equal-ranking and don't mind a<br>
lot of extra complexity, I have this suggestion:<br>
<br>
*Before each elimination, order the candidates according to their<br>
ER-IRV(fractional), (so that among continuing candidates a ballot that<br>
equal-top<br>
ranks n candidates give 1/n of a vote to each).<br>
<br>
Then assign each of the ballots that equal-top rank more than one<br>
candidate to whichever of them is highest in that order.<br>
<br>
Then eliminate the candidate with the fewest ballots assigned to hir.*<br>
<br></div><div>
34 A=B<br>
31 B<br>
35 C<br>
<br></div><div>
So in this example of Forest's, to create the initial order the 34 A=B<br>
ballots give half a vote each to A and B, to give the scores<br>
B (31+17=48) > C35 > A17.<br>
<br>
B is above A in this order, so all of the A=B ballots are assigned to B.<br>
This gives the scores B65 > C35 > A0. A has the lowest score so<br>
A is eliminated and B wins.<br>
<br>
Chris Benham<br>
<br>
<br>
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