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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Thanks for your reply, let’s see what I can grasp on this pass, shall we? ;)<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal style='margin-left:.5in'><b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif"'> Jameson Quinn [mailto:jameson.quinn@gmail.com] <br><b>Sent:</b> Sunday, June 16, 2013 10:36 PM<br><b>Subject:</b> Re: [EM] Voting Criteria 101, Four Criteria<o:p></o:p></span></p><div><p class=MsoNormal style='margin-left:.5in'><span style='color:#1F497D'><br></span>2013/6/16 Benjamin Grant <<a href="mailto:benn@4efix.com" target="_blank">benn@4efix.com</a>><o:p></o:p></p><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p style='margin-left:.5in'>Re: Majority Criteria:<o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>To be honest, I am worried that some (or all) of your history lesson regarding Arrow might not have landed as well as it should in my brain.</span><o:p></o:p></p></div></div></blockquote><div><p class=MsoNormal style='margin-left:.5in'>Sorry. Sometimes I tend to try to say things too succinctly, and end up leaving my meaning a bit locked up in jargon or terminology. If you have any specific questions about the "history lesson" I'd be happy to expand.<o:p></o:p></p></div><div><p class=MsoNormal style='margin-left:.5in'><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>No problem, I may return to that.</span><o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>freely assign a score of 0 to the maximum amount to each candidate (say 100), the candidate with the greatest aggregate score wins) let me see how this might fail. Let’s say out of 1000 people 550 give candidate A scores of “100”. Then let’s say that 700 people give candidate B scores of “80” each. Let’s also say that everyone else falls short of either of those totals. A gets 55,000 total, B gets 56,000. B wins.</span><o:p></o:p></p></div></div></blockquote><div><p class=MsoNormal style='margin-left:.5in'>Right. <o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-right:0in'><div><div><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>On the one hand, one could say in one sense this violates Majority, but in another sense one could perhaps with even more justification claim that B actually has the larger majority. Or maybe to put another way, Majority criteria only applies to voters when the system is one person, 1 vote – others perhaps Majority criteria applies to *<b>votes</b>*, not voters.</span><o:p></o:p></p><p class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;margin-left:.5in'><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>In other words, maybe Majority criteria should be worded thusly: <b>If one candidate is preferred by an absolute majority of *votes*, then that candidate must win.</b></span><o:p></o:p></p></div></div></blockquote><div><p class=MsoNormal style='margin-left:.5in'><o:p> </o:p></p></div><div><p class=MsoNormal style='margin-left:.5in'>That would be stretching the criterion to the point of meaninglessness. The majority criterion speaks of voters, and Range doesn't pass, but Bucklin systems do.<o:p></o:p></p></div><div><p class=MsoNormal style='margin-left:.5in'><o:p> </o:p></p></div><div><p class=MsoNormal style='margin-left:.5in'>The more controversial case for this criterion is approval. Some try to define the criterion so that an internal preference which doesn't fit on the ballot is enough to constitute a "majority"; others prefer to define it so that a "majority" only means anything in terms of the ballots themselves. I tend to side with the latter as a matter of definition, but I certainly understand that as a practical matter approval's passing of the majority criterion leaves much to be desired.<o:p></o:p></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>So my takeaway I think is that vis-à-vis voting systems, there are 3 kinds of voting systems with regard to the Majority criterion: systems that fulfil the criterion, systems that fail it, and systems in which “majority” makes no sense.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>I would say that First Past the Post would be an example of the 1st – it is easy to see that FPTP fulfils Majority, as if over 50% of the votes cast are for A, then A wins, always. An (admittedly lame) example of the 2<sup>nd</sup> – a system that fails the Majority Criterion, is the following: Of all candidates on the ballot, the one that gets the least votes, wins. Call this LPTP (Last Past the Post)<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>However, let’s look at Score Voting again – which I *<b>think</b>* can work like this: each voter gives each candidate a score from 0 to 9 on their ballot, with empty spots being treated as 0. Then add up all the scores for each candidate, the one with the highest total score wins.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Now let’s look at the following election being run that way:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>45 votes give Candidate A a score of 9, Candidate B a score of 6, Candidate C a score of 0, and Candidate D a score of 3<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>20 votes give A:0, B:6, C:9, and D:3<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>20 votes give A:0 B:6 C:3 D:9<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>15 votes give A:6 B:9 C:3 D:0<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>The totals are A:495 B:645 C:285 D:375 – so B wins.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>My thought is that perhaps in the context of this vote, the concept of majority as applied in the first two example (FPTP and LPTP) doesn’t work here. I also think that changing the definition of “majority” so that it is intelligible here will make it less understandable in the context of FPTP/LPTP.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Maybe what I am wondering is, is the context of some of these voting system so different that *<b>some</b>* concepts – like “majority” do not make sense in all contexts, and that trying to alter the definition to make it fit better in one context makes it fit worse in others?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>As originally written, I think, the Majority criterion states that: “</span><span style='font-size:10.0pt;font-family:"Arial","sans-serif";color:black;background:white'>if one candidate is preferred by a majority (more than 50%) of voters, then that candidate must win</span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>”<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Well, in the above Score Voting system context, the concept of preference as an all or nothing trait makes no sense. You could has scores of A:9 B:6 C:3 D:1 and be said to in some sense express some amount of preference for each of them. The only way in which the criterion would make sense is if we mutated the criterion somewhat like this: “</span><span style='font-size:10.0pt;font-family:"Arial","sans-serif";color:black;background:white'>if one candidate is preferred (at the highest score or ranking, where such exists) by a majority (more than 50%) of voters, then that candidate must win</span><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>”<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>OK, let’s create a new Score Voting election, four candidates, 100 voters, 0-9 scores:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>51 votes: A:9 B:7 C:4 D:0<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>29 votes: A:0 B:5 C:6 D:9<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>11 votes: A:1 B:7 C:4 D:0<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>9 votes: A:2 B:0 C:9 D:2<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Results: A:488 B:555 C:515 D:255<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Well, in this case over half of the group ranked A the highest, but ranked B just a little lower. I guess we could say that in one sense A did not win even though he got the highest vote from over half. And yet I don’t feel bad about B winning – since the 51 percent likes B almost as much, and B had much more support than A with both the 29% and the 11%. It seems intuitive to say that B had more support than A in that election. And yet, it also seems intuitive to me to say that the Last Past the Post (LPTP) election system is a bad one. What’s bad about LPTP that is simultaneously not bad about B winning the above election?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Maybe we ought to toss out the Majority criterion altogether, and replace it with something more on point? (I know, who the heck am I to suggest such a thing, I am not sure I am suggesting it seriously as much as following the thought process to its conclusion.) <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Maybe the underlying idea is behind the desire for the Majority Criterion is two-fold:<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>1)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>We don’t want to see losers win. We don’t want someone winning who is obviously (in some sense) received less support than someone they beat. For example, LPTP: in a single vote system, where each person votes for only a single candidate on the ballot, and then all votes are added, and the one with the least votes wins – we do not want to see that outcome, assuming that the intent of the ballot is presented as voting for your favorite candidate.<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>2)<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>We also don’t want to see a FPTP election where five people run for office, one candidate gets 26 percent of the vote and wins, but 74% of the voters got their preferences overruled by the 26% - minority rule. So perhaps that’s another criteria dealing with something like “the greatest good for the greatest number” or something?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>The first one can probably be worded something like “A more preferred candidate should not lose to a less preferred candidate”, and then if needed people can argue over what it means to be more preferred or less preferred in different contexts. However, in the ones where it matters, ie, LPTP it should be obvious.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>As to the second – I think that is what the Majority criterion is trying to encapsulate. At any rate, it is the only piece that I *<b>personally</b>* need from a system. I am not sure how to word it it. Perhaps something like this: “If, as quantified by the voting system, the preference that a candidate be elected is less than the preference that they NOT be elected, then they must not win.” <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Or more strongly, perhaps, “If, as quantified by the voting system, a candidate cannot muster more support for their election than against it, they must not win.”<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>OK, so now we have two criterion:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Losers Can’t Win</span></b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>: A more preferred candidate must not lose to a less preferred candidate. (This one may be so trivially obvious that no one ever bothered to name it or worry about it.)<o:p></o:p></span></p><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>No Minority Rule</span></b><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>: If, as quantified by the voting system, a candidate cannot muster more support for their election than against it, they must not win.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Now for all I know, either or both of the above already exist as a criterion that I just haven’t bumped into yet – if so, please tell me what their proper name is so I can use it. Here’s my main question though:<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>As understood, under what circumstances can a voting system FAIL the Majority Criterion, but NOT fail either Losers Can’t Win or No Minority Rule, as defined above?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Or to put another way, if we retain LCW and NMR, do we really need the seemingly more vague Majority Criterion?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Thoughts? Anyone? Beuler?<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Will respond to points on the other Criteria in a following post, this is I am sure quite long enough on it’s own.</span><o:p></o:p></p></div></div><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D;mso-ligatures:standard'>-Benn Grant<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D;mso-ligatures:standard'>eFix Computer Consulting<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D;mso-ligatures:standard'><a href="mailto:benn@4efix.com"><span style='color:#0563C1'>benn@4efix.com</span></a><o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D;mso-ligatures:standard'>603.283.6601<o:p></o:p></span></p></div></body></html>