<div dir="ltr">I'm sorry the results I copied didn't get transferred well.<br><br>1. We need to keep in mind that the number of competitive candidates and the number of candidates in a political election will never be the same and that for rule evaluation by simulation this distinction matters.<br>
<div class="gmail_extra"><br>2. Expressivity arguably has diminishing returns when there are many low-info voters or also due to the complexity of political issues and pervasiveness of misinformation in coampaigns, etc. GIGO. <br>
<br>3. Ordinality vs Cardinality or something in-between in voter utilities matters as well. If one can transform ordinal prefs without changing the order then one can create an indeterminancy in voting choices that then adds to indeterminancy in election outcomes that may prove undesirable. <br clear="all">
<div><div dir="ltr">dlw</div></div>
<br><br><div class="gmail_quote">On Mon, May 27, 2013 at 4:55 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>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Send Election-Methods mailing list submissions to<br>
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<br>
Today's Topics:<br>
<br>
1. In political elections C (in terms of serious candidates w.<br>
an a priori strong chance of election) will never get large!<br>
(David L Wetzell)<br>
2. Does IRV pass strategic condorcet? (Jameson Quinn)<br>
3. A Table to look at small C props of Change in Expressivity<br>
for Change in C. (David L Wetzell)<br>
<br>
<br>
----------------------------------------------------------------------<br>
<br>
Message: 1<br>
Date: Mon, 27 May 2013 14:19:42 -0500<br>
From: David L Wetzell <<a href="mailto:wetzelld@gmail.com">wetzelld@gmail.com</a>><br>
To: EM <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a>><br>
Subject: [EM] In political elections C (in terms of serious candidates<br>
w. an a priori strong chance of election) will never get large!<br>
Message-ID:<br>
<<a href="mailto:CAMyHmnfQ0Q31a9o6X--ik7-YmCgqZv3OJbTe6GvMfO0ZsaZwcQ@mail.gmail.com">CAMyHmnfQ0Q31a9o6X--ik7-YmCgqZv3OJbTe6GvMfO0ZsaZwcQ@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="iso-8859-1"<br>
<br>
Smith's <a href="http://rangevoting.org/PuzzIgnoredInfo.html" target="_blank">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<br>
whose a priori odds of winning, before one assigns voter-utilities, are<br>
strong. If real life important single-winner political elections have<br>
economies of scale in running a serious election then it's reasonable to<br>
expect only 1, 2 or 3 (maybe 4 once in a blue moon) candidates to have a<br>
priori, no matter what election rule gets used, serious chance to win,<br>
while the others are at best trying to move the center on their key issues<br>
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<br>
to infinity... and if a lot of candidates are not going to get elected then<br>
to disregard voter info/preference over them is of much less consequence.<br>
<br>
dlw<br>
<br>
<br>
On Mon, May 27, 2013 at 2:02 PM, <<br>
<a href="mailto:election-methods-request@lists.electorama.com">election-methods-request@lists.electorama.com</a>> wrote:<br>
<br>
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> Today's Topics:<br>
><br>
> 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>
> <<br>
> <a href="mailto:CAAJP7Y2xCc91B0BXW8xXLhQFb6jXDK-hhbUKwceSvpMHP1Z5%2BQ@mail.gmail.com">CAAJP7Y2xCc91B0BXW8xXLhQFb6jXDK-hhbUKwceSvpMHP1Z5+Q@mail.gmail.com</a>><br>
> Content-Type: text/plain; charset=ISO-8859-1<br>
><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>
> Message-ID:<br>
> <<br>
> <a href="mailto:CAO82iZyWv9%2B700MR1q6GODYX1UQdMr64v718WKG-MX9gsMvo7A@mail.gmail.com">CAO82iZyWv9+700MR1q6GODYX1UQdMr64v718WKG-MX9gsMvo7A@mail.gmail.com</a>><br>
> Content-Type: text/plain; charset="iso-8859-1"<br>
><br>
> 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>
><br>
> > <a href="http://rangevoting.org/PuzzIgnoredInfo.html" target="_blank">http://rangevoting.org/PuzzIgnoredInfo.html</a><br>
> ><br>
> > --<br>
> > You received this message because you are subscribed to the Google Groups<br>
> > "The Center for Election Science" group.<br>
> > To unsubscribe from this group and stop receiving emails from it, send an<br>
> > email to <a href="mailto:electionscience%2Bunsubscribe@googlegroups.com">electionscience+unsubscribe@googlegroups.com</a>.<br>
> > For more options, visit <a href="https://groups.google.com/groups/opt_out" target="_blank">https://groups.google.com/groups/opt_out</a>.<br>
> ><br>
> ><br>
> ><br>
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> ><br>
><br>
> ------------------------------<br>
><br>
> 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>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed<br>
><br>
> 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>
><br>
> ------------------------------<br>
><br>
> _______________________________________________<br>
> Election-Methods mailing list<br>
> <a href="mailto:Election-Methods@lists.electorama.com">Election-Methods@lists.electorama.com</a><br>
> <a href="http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com" target="_blank">http://lists.electorama.com/listinfo.cgi/election-methods-electorama.com</a><br>
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><br>
> End of Election-Methods Digest, Vol 107, Issue 13<br>
> *************************************************<br>
><br>
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------------------------------<br>
<br>
Message: 2<br>
Date: Mon, 27 May 2013 14:50:58 -0600<br>
From: Jameson Quinn <<a href="mailto:jameson.quinn@gmail.com">jameson.quinn@gmail.com</a>><br>
To: election-methods <<a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a>><br>
Subject: [EM] Does IRV pass strategic condorcet?<br>
Message-ID:<br>
<<a href="mailto:CAO82iZzh5FVrxG7btfKHTjQjW4DKit0%2BKBRbFdHgmsJhkG2Y0w@mail.gmail.com">CAO82iZzh5FVrxG7btfKHTjQjW4DKit0+KBRbFdHgmsJhkG2Y0w@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="iso-8859-1"<br>
<br>
If there is a majority Condorcet winner, any voting system that passes the<br>
majority criterion will elect that candidate in a unique strong Nash<br>
equilibrium. But the standard version of chicken dilemma involves a<br>
non-majority Condorcet winner:<br>
40: X<br>
35: Y>Z<br>
25: Z>Y<br>
<br>
Y is the CW, but the victory over Z is non-majority, only 35 to 25, because<br>
the X voters are indifferent.<br>
<br>
In that case, and (I believe but haven't proven) all other cases with a CW,<br>
rated systems like Approval, Score or (Graduated?) Majority Judgment still<br>
have a strong Nash equilibrium for the CW: Y voters top-rate only Y, while<br>
Z voters top-rate both Y and Z. The problem is that this is no longer<br>
unique; there's another strong Nash equilibrium where Y voters bullet and Z<br>
voters compromise, and if both groups shoot for the equilibrium they<br>
prefer, the result is a non-equilibrium where the Condorcet loser Z wins.<br>
<br>
(SODA mostly solves this problem by forcing candidate X to pre-declare a<br>
preference between Y and Z; but that's not the point of this message.)<br>
<br>
My question for the list is: can anyone prove, or give a counterexample<br>
for, the proposition that, in IRV, there always strong Nash equilibrium in<br>
which the CW wins? My suspicion is that it's not true, and I'll be looking<br>
at scenarios myself to see if I can prove it either way, but I thought I'd<br>
open up this interesting puzzle to the list as well.<br>
<br>
(This message was inspired by comments on the wikipedia talk page for<br>
Voting system.)<br>
<br>
Jameson<br>
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------------------------------<br>
<br>
Message: 3<br>
Date: Mon, 27 May 2013 16:55:00 -0500<br>
From: David L Wetzell <<a href="mailto:wetzelld@gmail.com">wetzelld@gmail.com</a>><br>
To: EM <<a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a>><br>
Subject: [EM] A Table to look at small C props of Change in<br>
Expressivity for Change in C.<br>
Message-ID:<br>
<CAMyHmnfvNUf8gaS2gZ0TV3YHkO+x1UPXr=<a href="mailto:e8Zp6JneNV1Rrr1g@mail.gmail.com">e8Zp6JneNV1Rrr1g@mail.gmail.com</a>><br>
Content-Type: text/plain; charset="iso-8859-1"<br>
<br>
I used Excel to evaluate the true expressivity of the different systems w.<br>
low numbers of candidates.<br>
<br>
<br>
Type/C 1 2 3 4 5 RV 5 levels 2.3 4.6 7.0 9.3 11.6 B&C 0.0 2.0 4.8 8.0<br>
11.6 MJ 1.5 3.0 4.5 6.0 7.5 AV 1.0 2.0 3.0 4.0 5.0 IR 0.0 1.0 2.1 3.2 4.2<br>
P 0.0 1.0 1.6 2.0 2.3 Stdev NonP Stdev NonP Stdev NonP Stdev NonP Stdev<br>
NonP 1.0 1.4 1.9 2.6 3.5 % Change % Change % Change % Change 37% 35%<br>
39% 37%<br>
My thoughts, yes, there is consistently more expressivity of the other<br>
alternatives to P than IRV and the amount of diffs in expressiveness tends<br>
to grow exponentially with the number of candidates, thereby justifying my<br>
contention that the expected number of serious candidates matters. But<br>
there also is a clear high increase in expressiveness of IR over P for the<br>
lower levels of C greater than 2.<br>
<br>
If we throw the real world effects of a significant portion of low-info<br>
voters into the mix and I expect declining returns to expressiveness...<br>
dlw<br>
<br>
<br>
On Mon, May 27, 2013 at 2:02 PM, <<br>
<a href="mailto:election-methods-request@lists.electorama.com">election-methods-request@lists.electorama.com</a>> wrote:<br>
<br>
> Send Election-Methods mailing list submissions to<br>
> <a href="mailto:election-methods@lists.electorama.com">election-methods@lists.electorama.com</a><br>
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><br>
> or, via email, send a message with subject or body 'help' to<br>
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><br>
> When replying, please edit your Subject line so it is more specific<br>
> than "Re: Contents of Election-Methods digest..."<br>
><br>
><br>
> Today's Topics:<br>
><br>
> 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>
> <<br>
> <a href="mailto:CAAJP7Y2xCc91B0BXW8xXLhQFb6jXDK-hhbUKwceSvpMHP1Z5%2BQ@mail.gmail.com">CAAJP7Y2xCc91B0BXW8xXLhQFb6jXDK-hhbUKwceSvpMHP1Z5+Q@mail.gmail.com</a>><br>
> Content-Type: text/plain; charset=ISO-8859-1<br>
><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>
> Message-ID:<br>
> <<br>
> <a href="mailto:CAO82iZyWv9%2B700MR1q6GODYX1UQdMr64v718WKG-MX9gsMvo7A@mail.gmail.com">CAO82iZyWv9+700MR1q6GODYX1UQdMr64v718WKG-MX9gsMvo7A@mail.gmail.com</a>><br>
> Content-Type: text/plain; charset="iso-8859-1"<br>
><br>
> 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>
><br>
> > <a href="http://rangevoting.org/PuzzIgnoredInfo.html" target="_blank">http://rangevoting.org/PuzzIgnoredInfo.html</a><br>
> ><br>
> > --<br>
> > You received this message because you are subscribed to the Google Groups<br>
> > "The Center for Election Science" group.<br>
> > To unsubscribe from this group and stop receiving emails from it, send an<br>
> > email to <a href="mailto:electionscience%2Bunsubscribe@googlegroups.com">electionscience+unsubscribe@googlegroups.com</a>.<br>
> > For more options, visit <a href="https://groups.google.com/groups/opt_out" target="_blank">https://groups.google.com/groups/opt_out</a>.<br>
> ><br>
> ><br>
> ><br>
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> ><br>
><br>
> ------------------------------<br>
><br>
> 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>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed<br>
><br>
> 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>
><br>
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> End of Election-Methods Digest, Vol 107, Issue 13<br>
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