<div dir="ltr"><div><div><div><div><div><div><div><div><div><div><div><div><div>Thanks to Juho and Toby for their insights.<br><br></div>It is true, as they suggest, that question 2 is the harder one.<br><br></div>The simplest answer to question one that I know of is based on an idea that Martin Harper came up with 12 years ago as a way of showing that ordinary Approval satisfies "one voter one vote" in the same strict sense that IRV does (through vote transfer):<br>
<br></div>First list the candidates in order of most approval to least approval. Then on each ballot transfer the entire support of the voter to the highest candidate on the list that is approved on the ballot. In other words, the voter's one and only vote is for the candidate she approves that is most approved by other voters. As Martin pointed out, this assignment of votes still elects the ordinary Approval winner in the single winner case. (Half a dozen years later Jobst pointed out that this same idea can be used to assign probabilities in a single winner lottery method.)<br>
<br></div>I am now pointing out that Martin Harper's vote transfer scheme is a simple way of designing a PR method (based on approval ballots) that solves problem one. In the given example let us assume that the truncations are reliable indicators of disapproval. Then the approval ballots are<br>
<br></div>10 A<br></div>30 A, M<br></div>45 B, M<br></div>15 B<br><br></div>The approval order is M>B>A<br><br></div>The first faction ballots all count for A. The last faction ballots all count for B, and the other 75 ballots all count for M, yielding the desired quotas of 10, 15, and 75 respectively.<br>
<br></div>Toby asks the question of why this M heavy proportion is so desirable. <br><br></div>One answer is that in these polarized countries (the ones that inspired this thread in the first place) the fewer extremists in power the better. But in my next post, the one addressing question two, I will give a more dispassionate answer to that question.<br>
<br></div>Forest<br><div><div><div><div><div><div><div><div><div><br></div></div></div></div></div></div></div></div></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Wed, Jun 25, 2014 at 12:23 PM, Toby Pereira <span dir="ltr"><<a href="mailto:tdp201b@yahoo.co.uk" target="_blank">tdp201b@yahoo.co.uk</a>></span> wrote:<br>
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<div><span>At first glance it seems that 10, 15 and 75 for A, B, M respectively seems a little optimistic from a voting system. It's not just that party list PR would shut out M - I can't see any system calling itself PR could award the seats in those proportions. Something like reweighted range voting or the score PR system I detailed a couple of weeks ago would stop M being shut out with honest voting, but they would go nowhere near as far as you are suggesting.</span></div>
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<span>Regarding voter honesty, it may be difficult to ensure it anyway with a normal score-based PR method, but I can't see how you could get it to work given that you would want the middle two factions' support for A and B to be effectively ignored. To be clear, 10, 15, 75 are the proportions you'd expect if the 75 people who gave a positive score to M completely lost all their support for A/B and raised M to from 80 to 100.</span></div>
<div><br><blockquote style="padding-left:5px;margin-top:5px;margin-left:5px;border-left-color:rgb(16,16,255);border-left-width:2px;border-left-style:solid"> <div style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,Sans-Serif;font-size:10pt">
<div style="font-family:HelveticaNeue,Helvetica Neue,Helvetica,Arial,Lucida Grande,Sans-Serif;font-size:12pt"> <div dir="ltr">
<div style="margin:5px 0px;padding:0px;border:1px solid rgb(204,204,204);min-height:0px;line-height:0;font-size:0px" readonly></div> <font face="Arial"> <b><span style="font-weight:bold">From:</span></b> Forest Simmons <<a href="mailto:fsimmons@pcc.edu" target="_blank">fsimmons@pcc.edu</a>><br>
<b><span style="font-weight:bold">To:</span></b> EM <<a href="mailto:election-methods@lists.electorama.com" target="_blank">election-methods@lists.electorama.com</a>> <br> <b><span style="font-weight:bold">Sent:</span></b> Wednesday, 25 June 2014, 1:21<br>
<b><span style="font-weight:bold">Subject:</span></b> [EM] PR for ethnically polarized electorates<br> </font> </div> <div><div><div class="h5"><br><div><div dir="ltr"><div><div><div><div><div><div>In Rwanda it was the Hutu and the Tutsi tribal division. In Iraq the Sunni, Shia, and Kurds. In the former Yugoslavia it was the Serbs Croats and Bosnians. There are similar divisions today in the Ukraine, Israel, Syria, Bolivia, etc.<br>
<br></div>What do they have in common? A need for electing a representative body that has as many moderates and as much consensus as possible so that minorities are not so desperate for separation, i.e. to prevent the scourge of Balkanization that seems to be spreading like a plague.<br>
<br></div>Suppose that there are two extreme groups A and B supported by two individual ethnicities, as well as a more moderate group M with preferences like<br><br></div><div>10 A(100)<br></div>30 A(100)>M(80)<br></div>
45 B(100)>M(80)<br></div></div><div><div><div><div><div><div><div><div><div><div>15 B(100)<br></div><div><br></div><div>(The numbers in parentheses represent voter expectations of relative benefits.)<br>
<br></div><div>In ordinary party list PR methods the parliament would be formed by 40 representatives from A and 60 representatives from B. The moderate party would be shut out entirely.<br><br></div>
<div>Here are my questions:<br></div><div><br></div><div>1. What method(s) would take this information and elect a parliament with respective party strengths of 10, 15, and 75 for A, B, and M?<br>
<br></div><div>2. What election method could possibly get the two middle factions to honestly convey this information via their ballots? In other words, how to keep the two middle factions from defecting from their common interest?<br>
<br></div><div>Forest<br></div><div><br></div></div></div></div></div></div></div></div></div></div></div></div><br></div></div>----<br>Election-Methods mailing list - see <a href="http://electorama.com/em" target="_blank">http://electorama.com/em</a>for list info<br>
<br><br></div> </div> </div> </blockquote><div></div> </div></div></div></blockquote></div><br></div>