<div dir="ltr">I used Excel to evaluate the true expressivity of the different systems w. low numbers of candidates. <br><br><br><table border="0" cellpadding="0" cellspacing="0" width="394" style="border-collapse:collapse;width:295pt">
<colgroup><col width="64" style="width:48pt">
<col width="74" style="width:55pt">
<col width="64" span="4" style="width:48pt">
</colgroup><tbody><tr height="19" style="height:14.4pt">
<td height="19" class="" width="64" style="height:14.4pt;width:48pt">Type/C</td>
<td class="" align="right" width="74" style="width:55pt">1</td>
<td class="" align="right" width="64" style="width:48pt">2</td>
<td class="" align="right" width="64" style="width:48pt">3</td>
<td class="" align="right" width="64" style="width:48pt">4</td>
<td class="" align="right" width="64" style="width:48pt">5</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt">RV 5 levels</td>
<td class="" align="right">2.3</td>
<td class="" align="right">4.6</td>
<td class="" align="right">7.0</td>
<td class="" align="right">9.3</td>
<td class="" align="right">11.6</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt">B&C</td>
<td class="" align="right">0.0</td>
<td class="" align="right">2.0</td>
<td class="" align="right">4.8</td>
<td class="" align="right">8.0</td>
<td class="" align="right">11.6</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt">MJ</td>
<td class="" align="right">1.5</td>
<td class="" align="right">3.0</td>
<td class="" align="right">4.5</td>
<td class="" align="right">6.0</td>
<td class="" align="right">7.5</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt">AV</td>
<td class="" align="right">1.0</td>
<td class="" align="right">2.0</td>
<td class="" align="right">3.0</td>
<td class="" align="right">4.0</td>
<td class="" align="right">5.0</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt">IR</td>
<td class="" align="right">0.0</td>
<td class="" align="right">1.0</td>
<td class="" align="right">2.1</td>
<td class="" align="right">3.2</td>
<td class="" align="right">4.2</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt">P</td>
<td class="" align="right">0.0</td>
<td class="" align="right">1.0</td>
<td class="" align="right">1.6</td>
<td class="" align="right">2.0</td>
<td class="" align="right">2.3</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt"></td>
<td class="">Stdev NonP</td>
<td class="">Stdev NonP</td>
<td class="">Stdev NonP</td>
<td class="">Stdev NonP</td>
<td class="">Stdev NonP</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt"></td>
<td class="" align="right">1.0</td>
<td class="" align="right">1.4</td>
<td class="" align="right">1.9</td>
<td class="" align="right">2.6</td>
<td class="" align="right">3.5</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt"></td>
<td class=""></td>
<td class="">% Change</td>
<td class="">% Change</td>
<td class="">% Change</td>
<td class="">% Change</td>
</tr>
<tr height="19" style="height:14.4pt">
<td height="19" class="" style="height:14.4pt"></td>
<td class=""></td>
<td class="" align="right">37%</td>
<td class="" align="right">35%</td>
<td class="" align="right">39%</td>
<td class="" align="right">37%</td>
</tr></tbody></table><br>My thoughts, yes, there is consistently more expressivity of the other alternatives to P than IRV and the amount of diffs in expressiveness tends to grow exponentially with the number of candidates, thereby justifying my contention that the expected number of serious candidates matters. But there also is a clear high increase in expressiveness of IR over P for the lower levels of C greater than 2. <br>
<div class="gmail_extra"><br>If we throw the real world effects of a significant portion of low-info voters into the mix and I expect declining returns to expressiveness...<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>
<br>
<br>
----------------------------------------------------------------------<br>
<br>
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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<br>
<a href="http://rangevoting.org/PuzzIgnoredInfo.html" target="_blank">http://rangevoting.org/PuzzIgnoredInfo.html</a><br>
<br>
<br>
------------------------------<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>
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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>