[EM] [EM (1)] Tolerating: MJ, HMJ, GMJ, SARA, or MAJORITY SCORE

[steve bosworth]

To-KristoferHMJ-1

________________________________

To Kristofer and everyone,



Thank you for your quick response.  I would like better to understand why you say that ‘MJ … doesn't make any assumptions about how far away Excellent is from Very Good or Very Good from Poor’.



I read Balinski and Laraki as saying that these grades are elements of a ‘common language’ through which each voter can meaningfully express his or her evaluation of each candidate.  People who understand that language, in the light of their own concept of Excellence, can meaningfully also judge the differences between the remaining 5 grades of candidate.  They at least see that a candidate they judge to be Very Good as less worthy than their Excellent candidate, and Good less worthy than Very Good, etc.  Consequently, B&L and I would say, for example, when one candidate has received a majority judgment composed of some Excellents and/or Very Goods, as well as ‘median-grades’, and a 2nd candidate has received a majority judgment composed entirely of grades equal to the ‘median-grade’ of the 1st candidate, society has judged that the 1st candidate should win.  Society would be more ‘satisfied’ when the 1st candidate wins.



In this context, it seems to me that HMJ’s averaging of ordinal scores is meaningful.  It is meaningful without anyone claiming that the value ‘distance’ between each grade and the next one above it or below it is exactly equal.



At the same time, B&L would make the point that while your following 2 examples are in one sense mathematically similar, only the 1st one takes advantage of the findings of experience and empirical research that most people can meaningfully use no more than 7 grades:



‘… if you ran MJ with the following assignments:
Excellent = 5
Very Good = 4
Good = 3
Acceptable = 2
Poor = 1
Reject = 0

‘you'd get the same result as if you ran it with these:

Excellent = 1000
Very Good = 800
Good = 500
Acceptable = 100
Poor = 20
Reject = 0’



What do you think?

Steve







From: Kristofer Munsterhjelm <km_elmet at t-online.de>
Sent: Sunday, October 30, 2016 9:53 PM
To: steve bosworth; Jameson Quinn; election-methods at lists.electorama.com
Subject: Re: [EM] Tolerating: MJ, HMJ, GMJ, SARA, or MAJORITY SCORE



On 10/30/2016 04:00 PM, steve bosworth wrote:
> Tolerating: MJ, HMJ, GMJ, SARA, MAJORITY SCORE
>
> To Jameson and everyone,
>
> Highest Majority Judgment (HMJ)
>
> Jameson seems to suggest that his SARA or Majority Score methods
> guarantees the election of the candidate with the ‘deepest and widest’
> support from the voters.  I am not yet clear that this claim could be
> sustained when compared with my refined version of Balinski &Laraki’s MJ
> which I will call Highest Majority Judgment (HMJ).
>
> There is only one difference between HMJ and B&L’s MJ.  Both HMJ and MJ
> start by discovering all the candidates who have receive the highest
> median grade, i.e. ‘majority-grade’.  If only one candidate has received
> this grade, she wins.  If 2 or more candidates have received this grade,
> the winner in a large election will most probably be discovered simply
> by going on to compare their different ‘majority-guages’ (see below).
> However, if the winner is not obvious from these comparisons, HMJ next
> uses a different tie-breaker than used by B&L.  HMJ discovers which has
> received the highest average evaluative score.  For example, using
> Excellent (5), Very Good (4), Good (3), Acceptable (2), Poor (1), or
> Reject (0), it divides the sum of the score equivalents of all the
> median and higher grades received by each candidate by the total number
> of these supporting median and higher than median grades.
>
> In contrast, MJ’s most precise if laborious way of discovery the winner
> is to go on to calculate which candidate has received the highest
> ‘majority-value’.   B&L see the complete ‘majority-value’ of each
> candidate as expressed by ‘the sequence of his (first) majority-grade,
> his second majority-grade, his third majority-grade, down to his /n/th
> majority-grade (if there are/n/ [voters])’ (B&L, Majority Judgment,
> p.6).  Thus, the number expressing this value starts with the score
> equivalent to their common ‘majority-grade’, followed after the decimal
> point by the sequence of each of all the scores of all the remaining
> majority-grades that would result, one by one, by removing each new
> majority-grade once it is found.

I'd like to mention, from a theory purist's perspective, that one of the
good things about MJ is that it doesn't make any assumptions about how
far away Excellent is from Very Good or Very Good from Poor. That is, if
you ran MJ with the following assignments:

Excellent = 5
Very Good = 4
Good = 3
Acceptable = 2
Poor = 1
Reject = 0

you'd get the same result as if you ran it with these:

Excellent = 1000
Very Good = 800
Good = 500
Acceptable = 100
Poor = 20
Reject = 0

All that's required for MJ to work is that the grading standard is
reasonably close to the same for every voter.

If you introduce averaging into the mix, this property is (obviously) lost.

Since you only do that as a last tiebreaker, the compromise would
probably not be that great in practice, but in theory, it changes the
perspective of the method: no longer do only the grades matter, but it
also matters what relative levels of satisfaction each grade corresponds to.



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