[EM] Best Single-Winner Method--MJ

[C.Benham]

On 28/05/2019 8:06 am, steve bosworth wrote:
>
> Hi Cris,
>
> Thank you for commenting on my post asking for any criticisms of MJ.I 
> will respond inline to your two relevant posts and I look forward to 
> the next stage of our dialogue.
>
> Steve Bosworth
>
> Message: 3
> Date: Wed, 22 May 2019 01:24:41 +0930
> From: Chris Benham <cbenhamau at yahoo.com.au>
> To: election-methods at lists.electorama.com
> Subject: Re: [EM] Burlington and Condorce methods
> Message-ID: <5e95b93f-398e-c151-a448-6f2632c7ca76 at yahoo.com.au>
> Content-Type: text/plain; charset="windows-1252"; Format="flowed"
>
>
> C: An example I recently came up with to critique another Bucklin-like 
> proposal:
>
> 46: A
> 03: A>B
> 25: C>B
> 23: D>B
>
> 97 ballots  (majority threshold = 48)
>
> (If  you want MJ-style  multi-slot ratings ballots, assume that all 
> the voters have given their favourite the highest possible rating and 
> those that rated B above bottom all gave B the same middle rating and 
> that truncating here signifies giving the
> lowest possible rating).
>
> MJ and Bucklin  both rightly elect A.   IBIFA  and IRV also elect A.  
> A is the Condorcet winner: A>B 49-48, A>C 49-25, A>D 49-23,
> A>E 49>0.
>
> A is the most Top-rated candidate:  A49,  C25,  D23,  B0, E0.
>
> S:No, Balinski’s MJ not simply counts all the number of “Top-rated” 
> grades give to all the candidates, but all the grade above each of 
> their median-grade, plus the median-grade.
>
>
> C:So suppose the votes are counted and it is announced that A has won, 
> but just before this is officially and irrevocably confirmed
> someone pipes up, "Hang on a minute, we found a few more ballots!"  
> (Maybe they are late-arriving postal votes that had been
> thought lost.)
>
> These 3 new ballots are inspected and found that all they do is give 
> the highest possible rating to E, a candidate with no support on any 
> of the other 97 ballots. What do we do now?  Laugh and carry on with 
> confirming A as still the winner?  No.
>
>
> S: No, Balinski’s MJ proceeds to discover any new median-grades of any 
> of all the candidates running, including all of the candidates not 
> mentioned by these additional ballots, i.e. all the candidates at the 
> bottom (i.e. all the candidates counted as “Reject” by these 
> additional ballots).Please consider my translation below of your above 
> example election using the terminology and symbols used by Balinski.
>
> 46: A
> 03: A>B
> 25: C>B
> 23: D>B
> 03: E
>
> 100 ballots  (majority threshold = 51)
>
> Now MJ and Bucklin and any other Median Ratings method elects B.  All 
> methods that I find acceptable elect A both with and without those 3E 
> ballots.
>
>
>> S:And by doing so you count the value of each of these 3 votes as 0 
>> contained in these 3 additional ballots, needless waste each, 
>> needlessly elect a candidate rejected by an absolute majority of all 
>> the voters rather than the candidate who is at least Accepted by an 
>> absolute majority.You do not fulfill MJ’s promise to allow each 
>> citizen to help to determine the median-grade of all the candidates 
>> by explicitly expressing their judgment of the suitability for office 
>> of each of all the candidates, by grading at least one candidate as 
>> at least Acceptable.You deny the equality of each voting 
>> citizen.Would your currently preferred method (IBIBA) also waste 
>> votes?If so, how could this be justified?
>
>
>> And by doing so you count the value of each of these 3 votes as 0 
>> contained in these 3 additional ballots, needless waste each, 
>> needlessly elect a candidate rejected by an absolute majority of all 
>> the voters rather than the candidate who is at least Accepted by an 
>> absolute majority.
>
> C: To "waste" a vote is something done to deny the person who voted 
> some power on the result in the direction of the voter's expressed 
> preference. So in my example
> the three votes weren't "wasted". It wasn't possible for them to help 
> elect E, and according to their ballots they don't care which of the 
> candidates they "reject" is elected.
> To say that their votes were in some meaningful way "wasted" is nonsense.
>
> Why should I care more about your standard that we never elect a 
> candidate who has (as you and Balinski interpret the ballots) been 
> "rejected" by "an absolute majority
> of all the voters" more  than I care about meeting the Condorcet 
> criterion?  Because as the example demonstrates the two are not 
> compatible.
>
> Neither MJ or IBIFA can meet the Condorcet criterion because they are 
> FBC methods, but when MJ and IBIFA give different winners the IBIFA 
> winner will always pairwise
> beat the MJ winner.
>
>> You do not fulfill MJ’s promise to allow each citizen to help to 
>> determine the median-grade of all the candidates by explicitly 
>> expressing their judgment of the suitability for office of each of 
>> all the candidates, by grading at least one candidate as at least 
>> Acceptable.
>
> C: That's right. Why should I?   What makes you think that all (or 
> even some or any) of the citizens want to "help determine the 
> median-grade of all the candidates"?
>
>> You deny the equality of each voting citizen.
>
> By not "allowing" 3 voters to change the result from one candidate 
> they don't care about to another candidate they don't care about, in 
> order to elect a Condorcet
> winner?     Recall  A>B 49-48,   A>C 49-25,   A>D 49-23,  A>E 49-3.
>
> You claim to want to "offer as few incentives and possibilities for 
> voting tactical." Tell that to the three A>B voters, who could have 
> made A win by just voting A
> like A's other 46 supporters.
>
> MJ (like all Median Ratings methods) has a significantly stronger 
> truncation incentive than does IBIFA and this is an example of that.
>
>> S:Balinski’s recommended “grades” for voters to award to as many of 
>> the candidates as they wish with regard to their suitability for 
>> office:Excellent (e) [ideal], Very Good (vg), Good (g), Acceptable 
>> (a), Poor, or Reject (r) [entirely unsuitable].
>
> I find the names Balinski gives to the grades (or ratings) on the 
> ballot annoying and bullying.  I would want to give my favourite A the 
> highest possible
> grade even if I thought A was mediocre or the least bad of a bad 
> bunch, and I would not enjoy having to lyingly declare that really A 
> is "excellent" and
> that some compromise even worse candidate I gave a lower grade to is 
> actually "very good" or  "good".
>
> [….]
>
> Chris Benham
>
>
>



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