[EM] (6) To Kristofer and everyone: MJ best to ‘tolerate’
stevebosworth at hotmail.com
Thu Sep 15 11:52:54 PDT 2016
From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Sent: Wednesday, June 1, 2016 9:14 PM
To: steve bosworth; election-methods at lists.electorama.com
Subject: Re: [EM](6) To Kristofer and everyone: MJ best to ‘tolerate’
To Kristofer and everyone:
Kristofer, while our most recent exchange was on June 31st, I want to thank you for forcing me to think more carefully and completely. As a result of the clarifications you offered me, when combined with my recent EM discussions with Kevin and Jameson, I am currently favoring MJ over all other methods for electing a president.
MJ simply asks each voter to grade each candidate when judged against each voter’s own criteria of what an EXCELLENT candidate would look like. Any candidate judged to be less than EXCELLENT must be graded either as VERRY GOOD, GOOD, ACCEPTABLE, POOR, or REJECTED. Balinski and Laraki refer to each voters own criteria for grading candidates as being ‘absolute’ (but this is only in the sense that these criteria should be independent of any one set of candidates that might be seeking election). These criteria are not rankings but they can be used to make rankings. MJ’s winner is the candidate whose majority ‘median-grade’ is higher than any other candidate.
For example, I see MJ as both better than IRV and MJ because:
1. I believe that ordinary citizens would more easily understand both how to mark MJ’s ballot and how the winner is discovered using its count. They would find it even more difficulty in understanding how MAM’s ballots are counted.
2. At the same time, both MJ and MAM have the following similar advantage over IRV: All MAM voters’ ‘rankings’ and MJ voters’ ‘gradings’ of all candidates continue to count until their respective winners are discovered. Some of the IRV voters’ ‘rankings’ are not counted after any of its candidates are eliminated and before IRV’s winner is discovered.
3. However, MJ has another advantage over MAM: because ‘grades’ are more evaluatively clear than are ‘ranks’, MJ’s ‘‘majorities of grades are … considerably more discerning decisions than are [MAM’s] majorities of preferences’ (Belinski & Laraki, Majority Judgment, p.283)?
4. Moreover, unlike the different intensities of each MJ voter’s ‘grades’ (evaluations) for each candidate, the different intensities of each MAM voter’s ‘rankings’ recorded on her ballot are not directly counted. For example, an MAM voter’s different intensities of preference for A over B and A over G in the following list of preferences are not differently counted: A>B>C>D>E>F>G. In contrast, all the ‘grades’ given to all candidates by all MJ voters continue fully to count until the highest ‘majority-grade’ winner is discovered. Thus, I see MJ as the most democratic method because it both wastes no citizen’s vote and is most likely to elect the candidate who is supported as enthusiastically as possible by the larges majority of citizens.
5. Also, MJ seems to offer less scope for manipulative voting than any other method. B&L argue that MJ is entirely strategy-proof with regard to grades. At the same time, if B&L’s mathematical proofs are correct, even when and if voters might instead use MJ’s ‘gradings’ as ‘rankings’, MJ structurally cuts by almost ‘half’ all the opportunities for all the manipulative strategies that are offered by all the methods other than MJ (Belinski & Laraki, Majority Judgment, pp.14, 15, 189-198, 212, 245, 282-292). (I assume that your mathematical knowledge is currently much superior to mine. Consequently, I’m hoping that you will be able to tell me whether the above B&L claim of ‘almost half’ is fully justified by B&L’s mathematical proofs.)
If it is fully justified, MJ would have this advantage over IRV and MAM. I say this even though it still seems to me that, in any case, it would also be extremely unlikely that strategic voting would be successful when using IRV or MAM to elect one winner by millions of voters.
6. I still favor MJ even though it is theoretically vulnerable to ‘Later-no-harm’ (LNH). I am currently persuaded by B&L that this could occur in practice only in an election composed of voters and candidates whose numbers could be counted on one person’s hands. This is confirmed by Jameson in his 1st informative and recent EM posts: 1): ‘there is the failure of the later-no-harm (LNH) criterion. But note: MJ actually does pass a weaker version of LNH: rating additional candidates at above bottom will not harm the winner as long as those candidates are ranked below the winning median. My claim is that over time, the winning median grade will mostly fall in a given band of grades; for instance, using letter grades, between B- and D+. In that case, making distinctions between A and B at the top or D and F at the bottom are strategically safe.’
7. Similarly, I am aware that MJ fails the strong Independence of Irrelevant Alternative (IIA) candidates test. However, B&L explain how MJ does at least pass a weaker IIA test. As Jameson put in his 2nd recent and informative EM contribution: ‘Note that this strategy will almost certainly not affect the medians, and thus will not change the winner. Though technically it breaks IIA, it only does so in bizarre cases where both voter and candidate distributions differ severely from historical norms.’
S: I would very much appreciate anyone explaining why you think any of the above views are mistaken. Please try to correct any mistakes you have noticed in the above.
I look forward to hearing from you,
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