[EM] Best Single-Winner Method

C.Benham cbenham at adam.com.au
Wed May 22 05:12:05 PDT 2019


Earlier I responded briefly to your 4-point list: yes, yes, not 

To expand a bit, MJ is a Median Ratings method with a relatively 
complicated tie-breaker, justified by I've no idea what.

Bucklin is likewise a Median Ratings method and will usually give the 
same winner, but the "tie breaker" is simple.

An example I recently came up with to critique another Bucklin-like 

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.

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.

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.

To expand a bit my earlier response to your point 4, I think it's highly 
desirable for a method to meet FBC (the Favorite Betrayal
Criterion), especially in the current US situation.

Potentially popular candidates the mainstream media and political 
establishment doesn't like can be sunk by fake polls and
the voters' fear of some perceived Greater Evil.

They can say "Forget candidate X!  X is only polling at 1 or 2%. That 
justifies us ignoring X. If you vote for X you'll just be helping
Greater Evil win!".  And their prophesy that X won't be a viable 
candidate tends to be self-fulfilling.

But if the used voting method meets FBC, the voter can in response reply 
(or at least think) "Ok, maybe I have to top-rate some
'realistic' Compromise candidate to maximise  the chance of beating 
Greater Evil, but I like X and I know that it can't possibly hurt
me to also top-rate X so I will."

If the method meets FBC no voter who knows and understands that can be 
cowed into not voting their sincere favorite at least
equal-top.  FBC is met by Approval, MJ and the currently proposed 
version of Bucklin, and IBIFA.

Of those I judge IBIFA to be by far the best.  IRV and all Condorcet 
methods unfortunately fail FBC.

For a method that doesn't meet FBC, I consider meeting the Condorcet 
criterion to be desirable. Unfortunately all Condorcet
methods are (to greatly varying degrees) vulnerable to Burial strategy, 
i.e. insincerely down-ranking to make a higher (usually
top) ranked candidate win.

In my humble opinion the best of the methods that are invulnerable to 
Burial is IRV.

Chris Benham

On 21/05/2019 5:16 am, steve bosworth wrote:
> Re: Best Single- Winner Method
> Sennet Williams,Forest Simmons, Robert Bristow-Johnson, Abd dul Raman 
> Lomax, and Chris Benham have recently addressed each others’ claims 
> about IRV, 3-slot Methods, IBIFA, and Asset.This discussion prompts me 
> to request some help later after I have clarified several issues.
> Firstly, please correct me if I am mistaken but currently I am 
> assuming that we all would ideally want the Best Single-Winner Method:
>  1. To be simple enough so voters can both use it and understand how
>     it is counted;
>  2. To minimize the wasting of citizens’ votes (see below),and
>  3. To guarantee that the winner among 3 or more candidates is the
>     candidate most supported by at least 50% plus one (an absolute
>     majority) of all the citizens voting, and
>  4. To offer as few incentives and possibilities for voting tactical.
> Given these desires, currently I see Majority Judgment (MJ) as 
> superior to all of the above methods on each of these counts.However, 
> since the above discussions have not mentioned MJ, I assume that many 
> contributors would reject this claim for MJ. This is why I would very 
> much appreciate receiving any of your clarifications or explanations 
> of how my claim for MJ cannot be sustained.What important flaws to you 
> see in MJ?
> To help you to marshal your criticisms of MJ, please let me explain 
> more full my own understandings and reasons for favoring MJ.Firstly, 
> Isee a citizen’s vote as being wasted /quantitatively/ to the degree 
> that it fails equally to help one of their most trusted candidates to 
> win.  A citizen’s vote is wasted /qualitatively/ to the degree that it 
> instead helps to elect a candidate whom they judge less /fit/ for 
> office, rather than an available candidate judged to be more fit.
> Other than in MJ, such waste is present in all the existing methods, 
> whether they ask voters to rank, score, or approve as many of the 
> candidates as they might wish.Of course, most dramatic is the waste 
> provided by plurality or First-Past-The-Post voting.
> To counter qualitative waste, Balinski and Laraki (/Majority Judgment, 
> /2010 MIT) argue that our capacity for judging qualities of human 
> behavior can be most meaningfully expressed in an election by each 
> voter grading each candidate’s suitability for office as either 
> Excellent (/ideal/), Very Good, Good, Acceptable, Poor, or “Reject” 
> (/entirely unsuitable/).These grades are more discerning, meaningful, 
> and informative than merely expressing preferences or using numeric 
> scores[MOU1] <#_msocom_1>, X’s or ticks.Such grading makes it more 
> likely that the highest quality candidate will be elected in the eyes 
> of the electorate.
> Each candidate who is not explicitly graded is counted as ”Reject” by 
> that voter.  As a result, all the candidates will receiv the same 
> number of evaluations, but a different set of grades from the 
> voters.The Majority Judgment (MJ) winner is the one who has received 
> grades from an absolute majority of all the voters that are equal to, 
> or higher than, the highest /median-grade/ given to any candidate. 
> This median-grade is found as follows:
>   * Place all the grades, high to low, top to bottom, in side-by-side
>     columns, the name of each candidate at the top of each of these
>     columns.
>   * The median-grade for each candidate is the grade located half way
>     down each column, i.e. in the middle if there is an odd number of
>     voters, the lower middle if the number is even.
> If more than one candidate has the same highest median-grade, the MJ 
> winner is discovered by removing (one-by-one) any grades equal in 
> value to the current highest median grade from each tied candidate’s 
> total until only one of the previously tied candidates currently has 
> the highest remaining median-grade.
> Also, in contrast to the alternatives, Balinski explains how MJ 
> reduces by almost half, both the incentives and opportunities for 
> effective tactical voting.Thus, each voter has every appropriate 
> incentive, not only to vote but to reveal their honest evaluations of 
> each candidate.
> Thus, to me, using MJ should be simpler and more satisfying because 
> grading many candidates is both easier and more meaningful than 
> ranking or scoring them.Also, finding and comparing the median-grades 
> of all the candidate is quite simple.Unlike MJ, IRV, Condorcet 
> methods, and Scoring do not guarantee the election of the candidate 
> most preferred by at least 50% plus one of all the citizens 
> voting.Unlike IRV but like Condorcet methods and Score, MJ does not 
> eliminate any candidate until the winner is discovered.
> Finally, I would favor the following Asset option to be added at the 
> bottom of each MJ ballot:  Any citizen who currently feels that they 
> do not yet know enough about any of the candidates to grade them, can 
> instead give their proxy vote to the Register Elector who will do this 
> for them.  They could do this  by WRITING-IN the published code of 
> that Registered Elector.
> I look forward to your comments.
> Steve
> ------------------------------------------------------------------------
> [MOU1] <#_msoanchor_1>Numerical scores
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