[EM] Best Single-Winner Method-IBIFA vs. MJ

[C.Benham]

> 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. 

Steve,

On 12/06/2019 6:34 am, steve bosworth wrote:
> Your concept of “irrelevant ballots” seems to be central to your IBIFA 
> method of counting.Do you also see this concept as conflicting with my 
> own assumption that in a workable and ideal democracy, each citizen’s 
> vote would count equally – one-person-one-vote?

Of course not.  But "count" only has some positive sensible meaning if 
we are talking about counting towards a result that the voter prefers
(as expressed on the voter's ballot) over what would have resulted if 
the voter had stayed home.

> No citizen’s vote would be needlessly wasted either quantitatively or 
> qualitatively.
Refreshing our memories on what you mean by that:
> I see 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. 

If we cross out "most trusted" and replace it with 'preferred (for 
whatever reason)', that is fine.

> This also means that whenever possible, the single-winner in an 
> election will have received at least 50% plus one of all the citizens’ 
> votes cast.

No it doesn't.  Why doesn't it mean that the winner should preferably 
come from the Smith set (be the Condorcet winner or come from the smallest
set S of candidates that pairwise beat all the outside-S candidates)?

> In contrast to MJ, the trouble in my view with IBIFA is that it gives 
> more weight to higher preferences than lower preferences, e.g. a 
> citizen’s Top-rated vote for a candidate is given more weight than a 
> citizen’s Middle-rated vote for a different candidate.

Yes, I can imagine the voters would hate that.

> This leads to the demeaning identification of some citizens votes as 
> being “irrelevant”. 

MJ brilliantly avoids that by "counting" those ballots so that they 
cause the winner to change from A (perhaps a Condorcet winner) to B,
when those ballots express indifference between A and B.

> It also prompts dishonest voting (tactical voting) because a 
> Top-rating counts more than a Middle-rating when using IBIFA. 

I've already explained, and gave an example, that MJ has a much stronger 
truncation incentive than does IBIFA.

45: A>B
30: B
25: C

IBIFA elects  A  (the CW:  A>B 45-30,  A>C 45-25).

Imagine how happy the A>B voters are that MJ doesn't "give more weight 
to higher preferences than lower preferences" and
ensures that "whenever possible, the single-winner in an election will 
have received at least 50% plus one of all the citizens’ votes cast."

MJ elects B.  Obviously MJ punished the A>B voters for not "dishonestly" 
simply voting A, and IBIFA didn't.

IBIFA is much more Condorcet-ish than MJ.  In the example no Condorcet 
method would punish those A>B voters like MJ does.

That is one of the reasons that "some people" continue to propose the 
"less than satisfactory Condorcet methods."

I think you'll find that the Balinski claim that MJ is so wonderful at 
resisting tactical voting is mainly based on the comparison with
Average Rating (now aka Score Voting) which gives voters a very strong 
incentive to just submit approval ballots (i.e. only use the
top and bottom grades).

MJ just gives voters a weaker (but still quite strong) incentive to do 
that.  I would say that in general the best Condorcet
methods plus IRV plus IBIFA  are all somewhat better than MJ at not 
penalising voters for voting sincerely.

Chris Benham




On 12/06/2019 6:34 am, steve bosworth wrote:
>
> Hi Chris,
>
> Your concept of “irrelevant ballots” seems to be central to your IBIFA 
> method of counting.Do you also see this concept as conflicting with my 
> own assumption that in a workable and ideal democracy, each citizen’s 
> vote would count equally – one-person-one-vote?No citizen’s vote would 
> be needlessly wasted either quantitatively or qualitatively. This also 
> means that whenever possible, the single-winner in an election will 
> have received at least 50% plus one of all the citizens’ votes cast.
>
> If we do disagree, how to you justify IBIFA’s violations of the above 
> democratic principles, especially when MJ provides a simpler and more 
> meaningful method which guarantees that its elections conform to the 
> above democratic principles?
>
> In contrast to MJ, the trouble in my view with IBIFA is that it gives 
> more weight to higher preferences than lower preferences, e.g. a 
> citizen’s Top-rated vote for a candidate is given more weight than a 
> citizen’s Middle-rated vote for a different candidate. This leads to 
> the demeaning identification of some citizens votes as being 
> “irrelevant”. It also prompts dishonest voting (tactical voting) 
> because a Top-rating counts more than a Middle-rating when using IBIFA.
>
> In contrast to IBIFA, please note that MJ gives the same weight to 
> each of the different grades that might be given to the its winner. 
> Only one of the grades given by a voter can be added to the total 
> which defines the winner’s majority.An Excellent only has the priority 
> of being looked for first.
>
> What do you think of the following possible explanation of how you 
> have been needlessly lead to adopt your idea of “irrelevant 
> ballots”.As I see it, perhaps this flaw in IBIFA stems from a 
> Condorcet habit of minds which mistakenly assumes that the primary 
> electoral concern is to find the candidate who is preferred, head to 
> head, over each of the other candidates.The voter is only to focus on 
> comparing and ranking the particular candidates in the race.These 
> comparisons and rankings presumably proceed upon the qualities 
> intuitively identified by the voter as needed for an ideal candidate 
> for the office being sought.Alternatively, it would proceed most 
> rationally after the voter analyzes and clarifies the hierarchy of 
> such ideal qualities.
>
> In contrast, Balinski suggests that each candidate should, in the 
> light of these qualities, be given one of the 6 grades regarding their 
> suitability for office (Excellent, Very Good, Good, Acceptable, Poor, 
> or Reject).However, a follower of Condorcet does not grade the 
> candidates but simply proceeds to ranking them.Next he uses a 
> Condorcet method to see if a Condorcet winner exists.However, this is 
> less than satisfactory because we all know that each Condorcet method 
> sometimes fails to find such a winner, let alone a winner who has 
> received an absolute majority of the preferences.
>
> Given that MJ guarantees the election of the candidate who is judged 
> to be most fit for the office by an absolute majority of the grades 
> given to this winner, (i.e. grades equal to or higher than the highest 
> median-grade given to any of the candidate), why does anyone continues 
> to propose the less than satisfactory Condorcet methods?
>
> Finally, you have also said that you do not understand MJ's procedure 
> for breaking ties. Please let me try to clarify this again:
>
> In a single-office election, 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 temporarily 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.
>
>     What do you think?What telling criticism of MJ can be made?
>
>     I look forward to the next step in our dialogue.
>
>     Steve
>
>


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