<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>Do you know remember their arguments, or your own, on why centrists are not good? I think methods that elect centrists (like CW) are quite good general purpose single-winner methods. But on the other hand there are many kind of single-winner elections, and in many cases the targets may well be very different.</div><div><br></div><div>Some thoughts on why we might not recommend not always electing a "centrist" candidate:</div><div>- we want to alternate between different parties, not to elect from the "centrist" party every time</div><div>- we want to have proportional representation of all parties in time (based on lottery or credit votes)</div><div>- we want to elect from major parties (not from _small_ centrist parties)</div><div>- we want to have a system that exaggerates small changes in balance so that the policy will always reflect the current needs and tendencies (electing centrists may lead to having no changes in the policy and voters having no influence on the policy)</div><div><br></div><div>We could also have different definitions of what "centrist" means. Maybe the second option below is the default value.</div><div>- no extreme opinions in any questions (close to median opinion in all questions) (= "median opinions")</div><div>- second preference of many voters, or typically in the first half of the individual rankings, close to being a Condorcet winner (= "good in pairwise comparisons")</div><div>- accepted or ranked quite high by many voters in all parties / segments of the society (= "wide support")</div><div><br></div><div>Juho</div><div><br></div><div><br></div><br><div><div>On 11.7.2011, at 13.06, Jameson Quinn wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite">This system seems explicitly designed to elect a centrist. In <a href="https://sites.google.com/site/ridalaraki/xfiles/BalinskiLarakiExperiEvid%28LastVersion%29.pdf?attredirects=0">their experimental paper</a> on Majority Judgment, system inventors Badinski and Laraki run a simulation to see how often different systems elect a centrist. Most systems they test either elect the centrist almost always (ie, condorcet systems) or almost never (plurality, IRV, runoffs), but their MJ system does about half the time. They argue that this "lack of bias" either towards or away from centrists is best, because a system which is too skewed to the middle or to the extremes will distort the political dialogue in corresponding ways. Though I think their simulation is just a rudimentary first step, I find their normative argument convincing; and so I don't really like this "distance" method.<div>
<br></div><div>JQ<br><br><div class="gmail_quote">2011/7/10 <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
First find a clone consistent way of defining distance between candidates.<br>
<br>
Then while two or more candidates remain<br>
of the two with the greatest distance from each other<br>
eliminate the one with the greatest pairwise defeat<br>
EndWhile.<br>
<br>
Various variants are possble. For example, you could count defeats only from the remaining<br>
candidates. Also there are various possible measures of defeat strength. In that regard, if you say that<br>
any defeat by covering is stronger than every non-covering defeat, then the method will always elect a<br>
covered candidate.<br>
<br>
To get a distance estimate in a large election you could just ask each voter to list the pair of candidates<br>
that seem the most different on the issue or combination of issues of most concern (to that voter). The<br>
pair submitted by the greatest number of voters would be the first pair considered, etc.<br>
<br>
What potential for manipulation does this direct approach introduce?<br>
<br>
Perhaps voters would try to pit their favorites' rivals against each other. Would that be insincere? Not if<br>
they consider their favorite to have a reasonable middle of the road position, while viewing the rivals as<br>
being at opposite unreasonable extremes.<br>
<br>
What indirect measure of distance could be used?<br>
<br>
If we count the number of ballots on which candidates X and Y are ranked at opposite extremes (top<br>
rank for one versus unranked for the other), the monotonicity of the method would probably be<br>
destroyed. Is there a more subtle way of inferring the distance that wouldn't destroy the monotonicity?<br>
<br>
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</blockquote></div><br></div>
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