<div dir="ltr">Smith's <a href="http://rangevoting.org/PuzzIgnoredInfo.html">http://rangevoting.org/PuzzIgnoredInfo.html</a><br><br>needs to be taken w. a grain of salt.<br><br>The short-comings of IRV depend on the likely number of serious candidates whose a priori odds of winning, before one assigns voter-utilities, are strong. If real life important single-winner political elections have economies of scale in running a serious election then it's reasonable to expect only 1, 2 or 3 (maybe 4 once in a blue moon) candidates to have a priori, no matter what election rule gets used, serious chance to win, while the others are at best trying to move the center on their key issues and at worse potential spoilers in a fptp election.<br>
<br>So it seems disengaged from reality to let C, the number of candidates, go to infinity... and if a lot of candidates are not going to get elected then to disregard voter info/preference over them is of much less consequence.<br>
<div class="gmail_extra"><br clear="all"><div><div dir="ltr">dlw</div></div>
<br><br><div class="gmail_quote">On Mon, May 27, 2013 at 2:02 PM, <span dir="ltr"><<a href="mailto:election-methods-request@lists.electorama.com" target="_blank">election-methods-request@lists.electorama.com</a>></span> wrote:<br>
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Today's Topics:<br>
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1. "true expressivities" of voting methods (Warren D Smith)<br>
2. Re: [CES #8439] "true expressivities" of voting methods<br>
(Jameson Quinn)<br>
3. Re: "true expressivities" of voting methods (Richard Fobes)<br>
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----------------------------------------------------------------------<br>
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Message: 1<br>
Date: Mon, 27 May 2013 11:52:09 -0400<br>
From: Warren D Smith <<a href="mailto:warren.wds@gmail.com">warren.wds@gmail.com</a>><br>
To: electionscience <<a href="mailto:electionscience@googlegroups.com">electionscience@googlegroups.com</a>>,<br>
election-methods <<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: [EM] "true expressivities" of voting methods<br>
Message-ID:<br>
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<a href="http://rangevoting.org/PuzzIgnoredInfo.html" target="_blank">http://rangevoting.org/PuzzIgnoredInfo.html</a><br>
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------------------------------<br>
<br>
Message: 2<br>
Date: Mon, 27 May 2013 10:53:53 -0600<br>
From: Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</a>><br>
To: <a href="mailto:electionscience@googlegroups.com">electionscience@googlegroups.com</a><br>
Cc: election-methods <<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: Re: [EM] [CES #8439] "true expressivities" of voting methods<br>
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Interesting, that you can usually calculate the median using 1.5 bits per<br>
grade. That would seem to indicate that a 3-level Bucklin system such as<br>
MCA uses approximately all the info on the ballot. I've also noticed before<br>
that 3-level ballots have another interesting property: the differences<br>
between the Score, MJ, and Condorcet orders are all sharply limited, and<br>
it's impossible to construct pathological MJ examples like the one in the<br>
other thread where nearly all voters prefer X to Y but MJ chooses Y.<br>
<br>
2013/5/27 Warren D Smith <<a href="mailto:warren.wds@gmail.com">warren.wds@gmail.com</a>><br>
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Message: 3<br>
Date: Mon, 27 May 2013 11:48:05 -0700<br>
From: Richard Fobes <ElectionMethods@VoteFair.org><br>
To: <a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a><br>
Subject: Re: [EM] "true expressivities" of voting methods<br>
Message-ID: <51A3AA65.2010208@VoteFair.org><br>
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On 5/27/2013 8:52 AM, Warren D Smith wrote:<br>
> <a href="http://rangevoting.org/PuzzIgnoredInfo.html" target="_blank">http://rangevoting.org/PuzzIgnoredInfo.html</a><br>
<br>
Interesting.<br>
<br>
Plurality and Approval collect so much less information that they do not<br>
noticeably ignore any information.<br>
<br>
Instant-runoff voting obviously ignores information because it only<br>
considers preference information that "floats to the top".<br>
<br>
Borda clearly does not ignore information, but it yields the wrong<br>
results -- unless somehow every voter separately ranks every choice.<br>
<br>
When I was developing VoteFair ranking -- a.k.a. the Condorcet-Kemeny<br>
method -- I considered and then rejected the beatpath-like approach of<br>
looking at the biggest and smallest pairwise counts. I rejected it<br>
partly because (similar to IRV) it ignores lots of the numbers (the ones<br>
that are not big or small). (I also rejected it because it does not<br>
identify the second-most popular choice, the least-popular choice, etc.)<br>
This concept of ignoring information is part of why I claim that the<br>
Condorcet-Kemeny method is better than the Condorcet-Schulze method.<br>
The opposite claim (that Schulze is better than Kemeny) tends to be<br>
based on counting the number (or importance) of fairness criteria that<br>
are met or failed. When we finally measure how often those failures<br>
occur, the "information loss" of the Condorcet-Schulze method will<br>
become clear. In contrast, the Condorcet-Kemeny method considers every<br>
pairwise count, not just the biggest and/or smallest pairwise counts.<br>
<br>
Richard Fobes<br>
<br>
<br>
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End of Election-Methods Digest, Vol 107, Issue 13<br>
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</blockquote></div><br></div></div>