<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type">
<title></title>
</head>
<body bgcolor="#ffffff" text="#000000">
Warren Smith (Wed.Oct.5):<br>
<br>
<blockquote type="cite">
<pre wrap="">wds:
<span class="moz-txt-citetags">>> </span>Robla failed to mention that range voting <b
class="moz-txt-star"><span class="moz-txt-tag">*</span>does<span
class="moz-txt-tag">*</span></b> obey a weakened form of
<span class="moz-txt-citetags">>></span>the majority-winner criterion (call it "WMW"). Specifically:
<span class="moz-txt-citetags">>> </span> "If a strict majority of the voters regard X as their unique favorite, then
<span class="moz-txt-citetags">>> </span> they, acting alone without regard to what the other voters do, can force his election."
<span class="moz-txt-citetags">>></span>I don't know about you, but I personally regard WMW as a more-desirable critrion for
<span class="moz-txt-citetags">>></span>a voting system to obey, than Anderson 1994's MW criterion.
</pre>
<pre wrap=""><!---->
</pre>
<blockquote type="cite">
<pre wrap=""><span class="moz-txt-citetags">></span>Chris Benham:
<span class="moz-txt-citetags">></span>Are there any methods actually <b
class="moz-txt-star"><span class="moz-txt-tag">*</span>fail<span
class="moz-txt-tag">*</span></b> this criterion? Borda perhaps?
</pre>
</blockquote>
<pre wrap=""><!---->
--response by wds:
yes, Borda fails it. So does the somewhat Borda-like method used
on the Island of Nauru. So does Coombs' IRV-like voting method.
Also Ken Arrow's favorite voting method (or so I heard) the Arrow-Raynaud method,
fails this test.
Range voting, however, passes this test.
wds</pre>
</blockquote>
<br>
Warren,<br>
I've seen Coombs defined with and without a majority-stopping rule.
(To me not having it seems worse and odd). I assume you are referring
to the version without:<br>
<a class="moz-txt-link-freetext" href="http://cec.wustl.edu/~rhl1/rbvote/desc.html">http://cec.wustl.edu/~rhl1/rbvote/desc.html</a><br>
<blockquote type="cite">The candidate with the largest last-rank total
is eliminated. The last-rank totals are recalculated and the step
repeated until only one remains. <br>
</blockquote>
The other version seems more common:<br>
<a class="moz-txt-link-freetext" href="http://wiki.electorama.com/wiki/Coombs%27_method">http://wiki.electorama.com/wiki/Coombs%27_method</a><br>
<blockquote type="cite">
<p>Each voter rank-orders all of the candidates on their ballot. If
at any time one candidate is ranked first (among non-eliminated
candidates) by an absolute majority of the voters, then this is the
winner. As long as this is not the case, the candidate which is ranked
last (again among non-eliminated candidates) by the most (or a <a
title="Plurality" href="/wiki/Plurality">plurality</a> of) voters is
eliminated. </p>
</blockquote>
BTW, do you know for sure that one of these definitions is incorrect?
Obviously the version with the stopping-rule meets your WMW criterion.<br>
<br>
I am sure that "Arrow-Raynaud" is the same as plain "Raynaud"
(sometimes spelt "Reynaud") which is a method that meets the Condorcet
criterion.<br>
What according to you is its definition, and can you give an example of
it failing your WMW criterion?<br>
<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
<br>
<br>
<br>
</body>
</html>