Re: Best Single- Winner Method
...
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.

To appreciate how easy it is to understand, here’s a full description
of the IPE method:

“Voters rank the candidates using as many ranking levels as there are
candidates, or at least 5 ranking levels if ovals are marked on a
paper ballot and space is limited and lots of the candidates are
unlikely to win. During counting, each elimination round eliminates
the candidate who loses every pairwise contest against every other
remaining candidate. If an elimination round has no pairwise-losing
candidate then, for that round, each ballot gives one count to the
lowest-ranked remaining candidate on that ballot, and the candidate
with the highest such count is eliminated. The last remaining
candidate wins.”

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

Election-Methods mailing list - see https://electorama.com/em for list info

... I suppose you could have a bottom cycle and a
CW who is ranked bottom on the highest number of ballots.

That combination would be very very unlikely, but why allow it?
Why not use my version?

(If you are referring to something other than MJ, please specify what
it is.)

On 22/05/2019 3:15 pm, C.Benham wrote:

Richard,

Can you please explain, perhaps with an example, how your "Instant
Pairwise Elimination" method can possibly "elect a non-Condorcet winner"?

Steve,

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

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
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.

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, 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.

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]
<#m_-2981034959420349233__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] <#m_-2981034959420349233__msoanchor_1>Numerical scores

Election-Methods mailing list - see https://electorama.com/em for list info

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