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<p style="margin: 0in 0in 8pt;"><font face="Calibri">To Kristofer,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Thank you for your earlier than expected response and especially for putting me onto Majority Judgment (MJ).</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">MJ seems to be even a better system for electing a single-winner than my IRVa.<span style="mso-spacerun: yes;">
</span>In different ways, each allows each citizen to express the intensity with which she supports or opposes each candidate and guarantees the election of a winner who is supported by an absolute majority.<span style="mso-spacerun: yes;">
</span>However, in contrast to IRVa, MJ enables each citizen within the MJ winner’s majority to be a part of that majority purely as a result of her own judgments.<span style="mso-spacerun: yes;">
</span>She would never have to rely on her IRVa first choice but eliminated candidate sequentially to transfer her ‘default vote’ to the remaining candidate he currently sees as the one mostly likely to represent him and her most faithfully, i.e. until a majority
candidate is discovered.<span style="mso-spacerun: yes;"> </span>Also, while both IRVa and MJ would seems to offer no practical opportunity for anyone to manipulate an election with many voters and candidates, theoretically MJ would seems to be even more
resistant to strategic voting.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Do you agree?<span style="mso-spacerun: yes;">
</span>Is MJ currently your own preferred method for electing a single-winner?</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Your answers to these questions may help further to clarify any later discussion we may have both about IRVa and MAM.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">________________________________________</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">From: Kristofer Munsterhjelm <km_elmet@t-online.de></font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Sent: Wednesday, June 1, 2016 9:14 PM</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">To: steve bosworth; election-methods@lists.electorama.com</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Subject: Re: [EM] Kristofer and Steve on IRVa vs. MAM</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">On 05/30/2016 04:53 PM, steve bosworth wrote:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> This reply to Kristofer's post is strengthened by the attachments it mentions and which Steve will also sent to you by email if you wish (stevebosworth@hotmail.com).</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="mso-spacerun: yes;"> </span>________________________________________</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> From: steve bosworth <stevebosworth@hotmail.com></font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> Sent: Sunday, May 29, 2016 7:54 PM</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> To: Kristofer Munsterhjelm</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> Subject: Re: Your 5th APR dialogue with Steve</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> To Kristofer,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> Thank you for your response. In one sense, I accept that if</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> truncated ballots are not permitted, Condorcet will also support the winner with</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> at least by 50% + 1, e.g. the MAM winner will be supported by at least</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> 50%+1 of all the voters. However, this ‘support’ will usually be</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> composed mainly of indirect or ‘transitive’ support. In contrast to</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> IRVa, the percentage of voters who have expressly preferred the winner</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> over each of the other candidates can easily be much less than 50%. This</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> is illustrated by the example discussed in the Endnote to the attached</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> newly drafted Appendix 4 to my article (Super Equality for Each</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> Citizen’s Vote in the Legislature’).</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> In that extreme example, ‘as a result of using IRV, candidate F is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> elected with a 61% majority and with an average intensity of preference</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> of 9.62 out of 10. In contrast, by counting the same 100 ballots using</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> MAM, candidate E is elected with the explicit support of only 39% and</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> with an average intensity of preference of 9.28.’</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K: What is the definition of "average intensity of preference"?</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">I tend to think that it's generally impossible to directly infer</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">enthusiasm from a ranked ballot, since we're dealing with ordinal data.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">All you can say is whether "X likes Y more than X likes Z".</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">S: Yes and I accept that ‘likes more’ does not always amount to ‘enthusiasm’.<span style="mso-spacerun: yes;">
</span>However, it is always a ‘preference’.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K: You can't know whether a ballot like</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A>B>C>D>E>F</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">"I really like A, B, and C; I think D and E are so-so, and I loathe F"</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">S: No, if this is what the voter feels, this is better expressed as</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A=B=C>D=E</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">And leave F to be counted equal as ranked bottom with any other candidate not ‘expressly’ preferred.<span style="mso-spacerun: yes;">
</span></font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K: or if it is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">"I really like A, I think B is so-so, and I hate everybody else, but I'd</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">rather have C than D, D than E, E than F".</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>Again, if ‘hate’ means ‘I do not want to support their election in any way, I see these feelings as more clearly expressed as follows:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A>B</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">However, if, in this case, ‘hate’ includes degrees of dislike, and the fear that F might only be prevented from being elected by the election of C, D, or E; this would be best expressed as:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A>B>C>D>E</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K: In other words, the rankings themselves can't tell you whether</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A>B>C>D</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Washington > Lincoln > Bush > Khrushchev</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">or if it is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Lincoln > Khrushchev > Lenin > Stalin,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>A given voter herself knows.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K: … and how much weight you should put on first place compared with second</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">place is obviously different for these two scenarios, as far as</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">intensity is concerned.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">S:<span style="mso-spacerun: yes;">
</span>Nevertheless, each voter must decide.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K: The general approach for dealing with intensity of ranking is to use</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">ratings instead, or use something like Majority Judgement where you're</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">permitted to skip ranks and each rank has a name ("Excellent", "Good", etc).</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">As for the MAM example, it seems that F wins in MAM as well.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">If I'm not mistaken, your vote set is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">38: F</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">23: G>F</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">25: E</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">9: M>N>E</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">5: K>P>E</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">candidates: E F G K M N P</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">The Condorcet matrix (row beats column) is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Option<span style="mso-spacerun: yes;">
</span>E<span style="mso-spacerun: yes;"> </span>F<span style="mso-spacerun: yes;">
</span>G<span style="mso-spacerun: yes;"> </span>K<span style="mso-spacerun: yes;">
</span>M<span style="mso-spacerun: yes;"> </span>N<span style="mso-spacerun: yes;">
</span>P</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">E<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>39<span style="mso-spacerun: yes;">
</span>39<span style="mso-spacerun: yes;"> </span>34<span style="mso-spacerun: yes;">
</span>30<span style="mso-spacerun: yes;"> </span>30<span style="mso-spacerun: yes;">
</span>34</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">F<span style="mso-spacerun: yes;">
</span>61<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>38<span style="mso-spacerun: yes;"> </span>61<span style="mso-spacerun: yes;">
</span>61<span style="mso-spacerun: yes;"> </span>61<span style="mso-spacerun: yes;">
</span>61</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">G<span style="mso-spacerun: yes;">
</span>23<span style="mso-spacerun: yes;"> </span>23<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>23<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span>23<span style="mso-spacerun: yes;">
</span>23<span style="mso-spacerun: yes;"> </span>23</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K<span style="mso-spacerun: yes;">
</span>5<span style="mso-spacerun: yes;"> </span>5<span style="mso-spacerun: yes;">
</span>5<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>5<span style="mso-spacerun: yes;"> </span>5<span style="mso-spacerun: yes;">
</span>5</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">M<span style="mso-spacerun: yes;">
</span>9<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>9<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>9</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">N<span style="mso-spacerun: yes;">
</span>9<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>9<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>9</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">P<span style="mso-spacerun: yes;">
</span>5<span style="mso-spacerun: yes;"> </span>5<span style="mso-spacerun: yes;">
</span>5<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>5<span style="mso-spacerun: yes;"> </span>5<span style="mso-spacerun: yes;">
</span>0</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">The wv matrix is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Option<span style="mso-spacerun: yes;">
</span>E<span style="mso-spacerun: yes;"> </span>F<span style="mso-spacerun: yes;">
</span>G<span style="mso-spacerun: yes;"> </span>K<span style="mso-spacerun: yes;">
</span>M<span style="mso-spacerun: yes;"> </span>N<span style="mso-spacerun: yes;">
</span>P</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">E<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>39<span style="mso-spacerun: yes;"> </span>34<span style="mso-spacerun: yes;">
</span>30<span style="mso-spacerun: yes;"> </span>30<span style="mso-spacerun: yes;">
</span>34</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">F<span style="mso-spacerun: yes;">
</span>61<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>38<span style="mso-spacerun: yes;"> </span>61<span style="mso-spacerun: yes;">
</span>61<span style="mso-spacerun: yes;"> </span>61<span style="mso-spacerun: yes;">
</span>61</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">G<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>23<span style="mso-spacerun: yes;">
</span>23<span style="mso-spacerun: yes;"> </span>23<span style="mso-spacerun: yes;">
</span>23</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">K<span style="mso-spacerun: yes;">
</span><span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>5</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">M<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>9</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">N<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>9<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>9</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">P<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0<span style="mso-spacerun: yes;"> </span>0<span style="mso-spacerun: yes;">
</span>0</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">So the first few lock-ins go (equal strength defeats broken in</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">alphabetical order for simplicity):</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">1. F>E with 61 votes</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">2. F>K with 61 votes</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">3. F>M with 61 votes</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">4. F>P with 61 votes</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Clearly, E can't possibly beat F since F is locked ahead of E on the</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">very first step. You must have calculated the Condorcet or wv matrix</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">incorrectly. In fact, regardless of whether you use wv or margins, F</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">becomes the CW: he beats everybody else pairwise.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">If you'd like to check the calculation for other ballot sets,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">http://www.ericgorr.net/condorcet/ will give both the Condorcet matrix</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">and the wv matrix when verbosity is set to "Tell me some things" or</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">"Tell me everything".</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">It'll also show what pairs MAM locks if you set it to "Tell me</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">everything", although it may not show them in order of defeat strength;</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">it locks large numbers of pairs at once when it knows that it can do so</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">without causing a cycle.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">I'll further comment on a few others, as much as I have time to at least:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> As a result, the attached appendix also claims that only ‘IRVa</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> allows</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> each citizen to guarantee:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> 1)<span style="mso-spacerun: yes;">
</span>that her vote will continue quantitatively to count equally,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">- As do all -a methods.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> 2) that the winner will be elected by a majority of all the voters</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">><span style="mso-spacerun: yes;">
</span>who have not deliberately cancelled the possibility of their otherwise</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">><span style="mso-spacerun: yes;">
</span>wasted ‘default vote’ being counted until the majority winner is</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">><span style="mso-spacerun: yes;">
</span>discovered, and</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">I'm not sure what that means.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> 3)<span style="mso-spacerun: yes;">
</span>that the winner will be supported more enthusiastically than any other candidate.’</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Consider this example from rangevoting.org:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">10:<span style="mso-spacerun: yes;">
</span>G > C > P > M</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">3:<span style="mso-spacerun: yes;">
</span>C > G > P > M</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">5:<span style="mso-spacerun: yes;">
</span>C > P > M > G</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">6:<span style="mso-spacerun: yes;">
</span>M > P > C > G</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">4:<span style="mso-spacerun: yes;">
</span>P > M > C > G</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">IRV elects M. But M only has 6 first preferences whereas C, the</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Condorcet winner, has 8. Since C is the Condorcet winner, it's also</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">supported by a majority, so majority support can't be the reason C</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">doesn't win in IRV.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">So if first preferences is the metric of enthusiasm, IRV fails.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">And if it isn't, then it's possible to construct examples where:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="mso-spacerun: yes;">
</span>- some candidate A has one more first preference vote than some other</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">candidate W,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="mso-spacerun: yes;">
</span>- A has no second place preferences,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="mso-spacerun: yes;">
</span>- W has some constant c number of second place preferences,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="mso-spacerun: yes;">
</span>- A wins in IRV,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"><span style="mso-spacerun: yes;">
</span>- W is the Condorcet winner,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">meaning that if one first place vote is worth x second place votes, then</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">you can make IRV choose wrong no matter what x is.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">E.g. for x=14:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">4:<span style="mso-spacerun: yes;">
</span>W>B>A>C>D</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">5:<span style="mso-spacerun: yes;">
</span>A>W>B>C>D</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">5:<span style="mso-spacerun: yes;">
</span>C>W>A>B>D</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">5:<span style="mso-spacerun: yes;">
</span>D>W>A>B>C</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">W has 4 first preferences and A has 5. W has 15 second preferences (A</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">has none) and A has 14 third preferences.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">So either enthusiasm is only based on first preferences, in which case</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">the first example shows that IRV gets it wrong, or it's based on first</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">*and* second preferences, in which case the second example would make</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">IRV get it wrong.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">There's a continuum argument hiding in here, though I don't have time to</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">go into it in detail. Briefly: IRV is more Plurality-like than Condorcet</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">and more Condorcetian than Plurality. So any argument that favors IRV</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">has to show that the argument can't be taken to its logical conclusion</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">to favor either Condorcet or Plurality just as strongly.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> S: Yes, if I understand you, this ‘incrementation’ can cause each</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> citizen’s vote to have a different value in the whole process. If so,</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> the principle of ‘one-citizen-one-vote’ is violated.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Suppose we conduct a presidential election by Approval ("thumbs up" or</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">"like") voting, and there are 5 candidates. That is, each voter gets a</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">list of the 5 presidential candidates and is told to place a mark by</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">each candidate he likes. The candidate with the most likes/approvals wins.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Now suppose that voter A chooses to approve of two candidates, while</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">voter B chooses to approve of three. Does that violate one citizen one</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">vote? After all, voter A "spent" two points (gave points to two</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">candidates) while B "spent" three.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">I'd say no, because each ballot has one state for each candidate: either</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">liked or unliked. Each ballot adds the same information to the voting</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">pool: whether the candidate chose to strengthen candidate X, candidate</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Y, candidate Z, etc... So if there are 5 candidates, each ballot has 5</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">aye/nay votes, and each voter spends 5 such votes. The voter who liked</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">two candidates used 2 ayes and 3 nays, and the other voter used 3 ayes</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">and 2 nays.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Analogously, a Condorcet election could be conducted by asking the voter</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">"in which of these runoffs would you support the first candidate on the</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">ballot?". There are n^2 hypothetical runoffs for n candidates, so that</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">kind of ballot would have n^2 aye/nay votes.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">In a three candidate election, someone who votes</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A>B>C</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">would say aye to "would you support the first candidate on the ballot in</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">an A vs B runoff?", "in an A vs C runoff?" and "in a B vs C runoff?",</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">and nay to all the others. It's just that, to spare the voter from</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">having to fill out a bunch of tedious yes/no questions, the method</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">infers the answer to these aye/nay questions from a ranked ballot.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">And if the Approval ballot doesn't violate one man one vote, then</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">neither does the Condorcet ballot. Yes, some voters increment more</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">runoffs than others (if there's equal rank and truncation), but deciding</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">to *not* increment someone's runoff is also a vote.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>he helps C more by protecting C from A and B, i.e. by increasing A>C and</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>> A>B.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> I do not understand your phrase:<span style="mso-spacerun: yes;">
</span>‘i.e. by increasing A>C and A>B’.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> This is because C>A>B>D favors C over A.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Either I meant that he helps C by protecting C from an increase of A>C</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">and from an increase of A>B, or that was a typo. In either case, what I</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">meant was that if someone raises C, the number of votes it takes to make</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">A beat C is also increased.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">I could probably have made that clearer.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> S: Using IRVa in the example in the attached Endnote, and when also</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> used in your following example, each vote continues to count (directly</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> or indirectly) as one until a majority winner is discovered.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Monotonicity failures require multiple ballot sets. See</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">http://www.rangevoting.org/Monotone.html. My point is that the voter's</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">power is an unpredictable function of his ranking. If he moves a</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">candidate higher on his ranking, he may cause the candidate to lose and</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">vice versa. That's not something that says "equal power" to me.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Under no method (except possibly Random Pair, Random Dictator, and</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">combinations of them) are votes completely equal in power anyway. It</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">depends on what they vote and when they do it. Suppose you have a</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">majority election:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">51: A</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">50: B</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">and two voters show up, and they're the last two voters of the election.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">If they vote for B, they change the outcome (great power); if they vote</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">for A, nothing happens (not so much).</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>> K: * That is, unless there are truncated ballots, but then IRV doesn't give</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>> a majority either.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">> This is why I added ‘Asset Voting’ to IRV, to produce IRVa.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">Yes, but we were initially talking about IRV without -a:</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri"> </font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> However, before I do that, I want to claim that in comparison to all</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> other electoral system not using the above asset voting, APR (also</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> without this asset addition) still does all it could do to allow each</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> citizen to guarantee that her one vote will be added to the weighted</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> vote of the one elected candidate of all the pre-established number of</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> the assembly’s members whom she most trusts to speak, work, and vote</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> faithfully on her behalf. Do you agree? Also in this case, this</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">>>> simplified APR might waste some votes.</font></p>
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<p style="margin: 0in 0in 8pt;"><font face="Calibri">That's what I was responding to.</font></p>
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