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A fact from Majority judgment appeared on Wikipedia's Main Page in the Did you know column on 11 July 2011 (check views). The text of the entry was as follows:
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What is the conceptual model we should use to determine the ratings in the Tennessee example?
To be compatible with Independence of Irrelevant Alternatives, as claimed in the article, we would have to consider voters would calibrate their scale not just based on the alternatives available in the given election, but to any city in the state. For example, this would change whether or not Memphis voters would grade Chattanooga above Knoxville (or both above the lowest rating).
Balinski advocates using more ratings in his preferred embodiment. I believe we should consider adding "poorest" rating.
Regarding IIA, I don't understand the following, perhaps we can clarify, from the article,
"By assuming that ratings are given independently of other candidates, it satisfies the independence of clones criterion and the independence of irrelevant alternatives criterion, but the latter criterion is incompatible with the majority criterion if voters shift their judgments in order to express their preferences between the available candidates."
I think the problem may be that the reason given for the incompatibility of the two criteria is confused with the manner in which MJ fails the IIA criterion (or rather the condition required to uphold its passage). Filingpro (talk) 16:02, 18 March 2016 (UTC)[reply]
Majority judgment voting satisfies the majority criterion for rated ballots, the mutual majority criterion [...] It also fails the ranked or preferential majority criterion
This is a contradiction, because the mutual majority criterion implies the majority criterion, therefore failure of the majority criterion implies failure of the mutual majority criterion. So I have removed the part saying that it passes the mutual majority criterion for now.
I suspect what was meant by "mutual majority criterion" in this context was something like "MJ always elects a candidate from a set of candidates that a majority prefers above all others, so long as the majority gives every candidate in the set a perfect grade and every candidate not in the set a less-than-perfect grade". This is actually true, since any candidate preferred by the majority will have a perfect median rating, while any candidate not preferred by the majority is guaranteed to have a less-than-perfect grade, since the median voter (someone in the majority) gave them a less-than-perfect rating. So I have added this part in instead. GreekApple123 (talk) 06:30, 1 April 2020 (UTC)[reply]
It doesn't have to be a perfect rating. MJ elects a candidate from the set of those with the highest median rating. If some candidates are Acceptable and all the others are Poor or lower, the winner will be in the Acceptable group. - Frankie1969 (talk) 11:46, 1 April 2020 (UTC)[reply]
A "perfect grade" has no meaning in the context of counting MJ's grade. Each grade given by each voter aims simply to express that voter's subjective judgment about the suitability for office of that candidate. This means that each MJ post-election report provides more valuable information for helping to educate the electorate, including the numbers of each grade received by each candidate from all voters. These reports would also enable analysts most comprehensively and reliably be able to report the number and ordinal intensity with which the different agendas in the society are being pursued by their fellow citizens.
The Majority Judgment and Usual judgment articles restate much of the info presented in the Highest median voting rules article and the two voting systems differ only in their tiebreaker rules, with the main difference in each being "advantages" sections, which can probably be summarized in a more general comparison section. Anecdotally, I was rather confused about the systems until I read this article and understood they differ only in tie-breaking methods. Putnam3145 (talk) 02:13, 16 September 2022 (UTC)[reply]
I agree in principle, but this should imply a bit of re-writing. On the one hand the Highest median and Usual judgement pieces are written in a technical style that is only suitable in separate sections of a main article; on the other hand the current writing of the Majority Jugement page is by places clearly propaganda in favor of MJ rather than encyclopedia stlyle. SoldierJo (talk) 16:18, 15 November 2022 (UTC)[reply]
@Putnam3145 You're correct that they only differ in "tie-breaking methods", but I'm not sure whether the term "Majority Judgment" is used to describe highest medians with a different tiebreaker. It's worth noting that despite being called a tiebreaker, breaking ties in Majority Judgment is quite common (maybe ~5% of the time), so it's not like ties in plurality. Many close elections (i.e. in swing districts/states) would be determined by the tiebreaker. –Maximum Limelihood Estimator16:41, 14 April 2024 (UTC)[reply]