<html>
<head>
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
</head>
<body text="#000000" bgcolor="#FFFFFF">
<p>John,<br>
<blockquote type="cite">
<pre>It seems to me the Condorcet Loser criterion is incomplete and inexact: a
single Condorcet Loser is meaningless.</pre>
</blockquote>
The Condorcet Loser criterion is "incomplete and inexact" for what
purpose? The criterion just<br>
refers to one desirable property that IRV (and of course some
other methods) have that not all<br>
other (used or proposed or plausible) methods have.<br>
<br>
Isn't the pairwise winner out of two random candidates clearly a
bit better than simply Random Candidate?<br>
<br>
</p>
<blockquote type="cite">
<pre>The proper criterion should be ALL Condorcet Losers, such that eliminating the single Condorcet Loser
leaves you with exactly one Condorcet Loser, thus both of them are the least-optimal set.</pre>
<p><br>
</p>
</blockquote>
As someone else pointed out, what if there is no single Condorcet
loser but rather a bottom cycle (an upside-down<br>
"Smith set")? Saying that it shouldn't be eliminated but a single
Condorcet loser should implies violating Clone Independence.<br>
<br>
And if you say that we should keep eliminating the CL or the bottom
cycle candidates I don't see how that is different from<br>
saying that the winner has to be from the top cycle (Smith set).<br>
<br>
But yes, just as Smith implies Condorcet but (because not vice
versa) they are still two separate criteria, I suppose you<br>
could have a bottom version of "Smith" to go along with CL but not
to replace it.<br>
<br>
Chris Benham<br>
<p><br>
<br>
<br>
<blockquote type="cite"><b>John</b> <a title="[EM] Condorcet
Loser, and equivalents"
href="mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20Condorcet%20Loser%2C%20and%20equivalents&In-Reply-To=%3CCAKYQpdvUv1iq%3DJRsd-vtKfN9%3Db3OJxTm5aV7ryb99GGoqtE2nA%40mail.gmail.com%3E">john.r.moser
at gmail.com </a><br>
<i>Tue Jun 4 11:50:48 PDT 2019</i></blockquote>
<blockquote type="cite">
<ul>
<li><b>Messages sorted by:</b> <a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-June/date.html#2172">[
date ]</a> <a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-June/thread.html#2172">[
thread ]</a> <a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-June/subject.html#2172">[
subject ]</a> <a
href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2019-June/author.html#2172">[
author ]</a> </li>
</ul>
<hr>
<pre>[Not subscribed, please CC me]
Andy Montroll beats Bob Kiss.
Andy Montroll beats Kurt Wright.
Bob Kiss beats Kurt Wright.
Montroll, Kiss, and Wright beat Dan Smith.
Montroll, Kiss, Wright, and Smith beat James Simpson.
James Simpson is the Condorcet Loser.
…is that right?
In the race {Montroll, Kiss, Wright}, Kurt Wright is the Condorcet Loser.
Let's say candidate D appears. D signs up, becomes a candidate, is on the
ballot, and never campaigns.
D loses horribly, of course.
D is now the Condorcet Loser. Kurt Wright isn't.
Does this change the nature of the candidate, Kurt Wright, or the social
choice made?
Think about it. Without Simpson, Smith is the Condorcet Loser. Without
Smith, Wright is the Condorcet Loser. You have a chain of absolute
Condorcet Loser until you have a tie or a strongly connected component
containing more than one candidate which is not part of the Smith or
Schwartz set.
This is important.
We say Instant Runoff Voting passes the Condorcet Loser criterion, but can
elect the second-place Condorcet Loser. That means Kurt Wright is the
Condorcet Loser and IRV can't elect Wright; but in theory, you can add
Candidate D and get Kurt Wright elected.
In practice, between two candidates, the loser is the Condorcet loser.
Montroll beats Kiss, so Kiss is the Condorcet Loser. By adding Kurt
Wright, you have a new Condorcet Loser. This eliminates Montroll and,
being that Kurt Wright is now the Condorcet Loser and is one-on-one with
another candidate, Bob Kiss wins.
It seems to me the Condorcet Loser criterion is incomplete and inexact: a
single Condorcet Loser is meaningless. The proper criterion should be ALL
Condorcet Losers, such that eliminating the single Condorcet Loser leaves
you with exactly one Condorcet Loser, thus both of them are the
least-optimal set.
I suppose we can call this the Generalized Least-Optimal Alternative
Theorem, unless somebody else (probably Markus Schulze) came up with it
before I did. It's the property I systematically manipulate when breaking
IRV.
Thoughts? Has this been done before? Does this generalize not just to
IRV, but to all systems which specifically pass the Condorcet Loser
criterion proper (i.e. they have no special property like Smith-efficiency
that implies Condorcet Loser criterion, but CAN elect the second-place
Condorcet loser)? That last one seems like it must be true.
</pre>
</blockquote>
<br>
</p>
<div id="DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2"><br />
<table style="border-top: 1px solid #D3D4DE;">
<tr>
<td style="width: 55px; padding-top: 13px;"><a href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" target="_blank"><img src="https://ipmcdn.avast.com/images/icons/icon-envelope-tick-green-avg-v1.png" alt="" width="46" height="29" style="width: 46px; height: 29px;" /></a></td>
<td style="width: 470px; padding-top: 12px; color: #41424e; font-size: 13px; font-family: Arial, Helvetica, sans-serif; line-height: 18px;">Virus-free. <a href="http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient" target="_blank" style="color: #4453ea;">www.avg.com</a>
</td>
</tr>
</table><a href="#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2" width="1" height="1"> </a></div></body>
</html>