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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'>Let me put forth (better, I hope) a more complete thought (which is probably one of those Bucklin Variants, as it turns out.)<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 ballot has every candidate on it. In order to be considered valid, each voter must rank each and every one of them. So with five candidates, a valid ballot might look like: 1<sup>st</sup>:B/2<sup>nd</sup>:D/3<sup>rd</sup>:A/4<sup>th</sup>:E/5<sup>th</sup>:C No duplicates, no skipping.<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'>Then we create a threshold of just over 50% of the number of votes. If 100 people vote, then 51 is the threshold.<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'>We then look at only the 1<sup>st</sup> place votes. If anyone hit the threshold, they win if they are the only one. If more than one candidate hit the threshold, the one that surpasses the threshold by more 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'>If no one yet hits the threshold, add in all the 2<sup>nd</sup> place votes, and check again. If still no one hits the threshold, add in the 3<sup>rd</sup> place votes, and so on.<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'>It was a thought experiment I was doing, I’m not at all sure, for example, that it might not be better to permit duplicates or skipping. I obviously need to go deeper.<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 think my next task is to put a pause in the pursuit of different voting systems to focus on understanding better the various criteria (later no harm, Condorcet, etc), in much more depth, ie, what they are each about, what it means that a system fulfills of fails one, etc.<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 will post more about that shortly – let me know if I am dragging this group to far into “voting theory kindergarten”, but I really want to “get” all this.<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'>Thanks.<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;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><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"'>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 11:20 AM<br><b>To:</b> Kristofer Munsterhjelm<br><b>Cc:</b> Benjamin Grant; election-methods@lists.electorama.com<br><b>Subject:</b> Re: [EM] Absolutely new here<o:p></o:p></span></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>As one of the principal advocates for Bucklin systems on this list, I thought I'd expand a bit on Kristofer's excellent response.<o:p></o:p></p><div><p class=MsoNormal>2013/6/16 Kristofer Munsterhjelm <<a href="mailto:km_elmet@lavabit.com" target="_blank">km_elmet@lavabit.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><p class=MsoNormal>On 06/16/2013 05:26 AM, Benjamin Grant wrote:<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><p class=MsoNormal>[...IRV discussion...]<o:p></o:p></p></div></blockquote><p class=MsoNormal style='margin-bottom:12.0pt'><br>[...good response...]<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'><p class=MsoNormal>2)I haven’t seen a voting system like this – what are the issues with<br>it? Upsides and downsides?<br><br>A)Each voter ranks their choices on their ballots, first through last place.<br><br>B)If one candidate got a majority of 1^st place votes, they win. If not,<o:p></o:p></p><div><p class=MsoNormal><br>the second place votes are added. If still no majority he third place<br>votes are added, and so on, until one candidate has a majority.<br><br>Would the above system work?<o:p></o:p></p></div></blockquote><p class=MsoNormal><br>That's Bucklin. <a href="http://en.wikipedia.org/wiki/Bucklin_voting" target="_blank">http://en.wikipedia.org/wiki/Bucklin_voting</a> . It's one of the few ranked methods that have been used in political elections in the United States, and it has a connection to median rating (which elects the candidate with highest median rating or grade).<br><br>It would work, but the rating variant is better. In the context of ranking, Bucklin fails Condorcet, for instance.<o:p></o:p></p></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>In case it wasn't clear, by "rating", Kristofer means a system with a fixed number of levels of support/opposition (typically 3-7), where voters can any number (including 0) of candidates at a given level. Ranking means that voters must give a strict ordering of candidates, with no ties or skipped ranks.<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'><p class=MsoNormal><br>It also has some bullet-voting incentive. <o:p></o:p></p></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>In this case, "It" refers to the ranked version only.<o:p></o:p></p></div><div><p class=MsoNormal> <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'><p class=MsoNormal>Say that you support candidate A. You're reasonably sure it will get quite a number of second-place votes. Then even though you might prefer B to A, it's strategically an advantage to rank A first, because then the method will detect a majority for A sooner.<br><br>One of the points of the graded/rated variants is to encourage the voters to think in absolute terms ("is this candidate good enough to deserve an A") rather than relative terms ("is this candidate better than that candidate"). If they do, then the method becomes more robust.<o:p></o:p></p></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Thanks.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>One think Kristofer didn't mention is that your definition wasn't quite complete. What happens if two candidates attain a majority at the same rank, or (in rated versions or due to truncation) no candidate attains a majority without including the bottom support level? Resolving this issue requires a Bucklin completion method, just as resolving cyclical preferences in Condorcet requires a Condorcet completion method. Colloquially, Bucklin completion methods are often called "Bucklin tiebreakers".<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Thus, there are many possible Bucklin systems, including "ER-Bucklin" (which majority is highest?), "Majority Judgment" (remove an equal number of ballots at the pivotal/median rating for each candidate until one of them gets a majority at a higher or lower rating), "Graduated Majority Judgment" (find the candidate who needs the lowest percentage of their ballots at the pivotal/median rating to attain a majority; also expressable as a simple algebraic formula that gives a non-integer score to each candidate), and the as-yet-unnamed method currently being discussed (for instance) <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2013-June/031877.html">here</a> and <a href="http://lists.electorama.com/pipermail/election-methods-electorama.com/2013-June/031880.html">here</a> (find the candidate with the greatest number of above-median votes). I'd appreciate it if you read the posts linked above and responded with your own opinion as to naming.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal>Supporters of Bucklin methods (like me) typically speak of the following advantages:<o:p></o:p></p></div><div><ul type=disc><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'>Voters can express, and the system can respond to, varying levels of support. Score voting (aka Range voting) is even better in this regard, but Bucklin systems are still better than most others.<o:p></o:p></li><li class=MsoNormal style='mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;mso-list:l0 level1 lfo1'>In many cases, an "honest" (scaled utility) vote is strategically optimal. For instance, say the rating categories were the letter grades A-F, and the two frontrunner candidates both had a median of "C". A voter who had given one of those two a "B" and the other one a "D" would have cast a full-power vote, and would not need to regret not having given those candidates an "A" and an "F". This contrasts with Score Voting, where in general only approval-style votes (all top- and bottom-rating) are strategically optimal. The hope is that by leaving more room for honest voting, Bucklin systems will get better information from voters, allowing a better result.<o:p></o:p></li></ul><div><p class=MsoNormal>Welcome to the list, and we hope to hear more from you,<o:p></o:p></p></div><div><p class=MsoNormal>Jameson<o:p></o:p></p></div></div></div></div></body></html>