(2) Best Single-Winner Method-IBIFA vs. MJ
Steve,
On 14/06/2019 6:18 am, steve bosworth wrote:
S: By saying, "of course not", I understanding that you instead
mean that your concept of an ideal democracy only guarantees that the
winner will be support by a plurality of voting citizens who Top-rated
them, I.e. like FPTP in this respect. Correct me if I'm mistaken.
C: You asked me a simple yes-no question and I answered it. If you are
not sincerely very stupid, please stop pretending to be.
S: What other appropriate reason can a citizen have for supporting a
candidate to win other than they "trust" them to represent their own
scale of political values and concerns?
C: That is entirely their business.
C: MJ elects B. Obviously MJ punished the A>B voters ….
S: I think you already know that to "punish" means to treat someone
differently while MJ treats every grade given by every citizen in
exactly the same way.
C: To "punish" a subset of voters in this context means to give them
cause to regret the way they voted. How do you justify not attempting to
minimise
the proportion of voters in that category, while pretending to be in
favour of minimising "opportunities for tactical voting" (as I think you
put it).
To the extent that you give voters incentive to vote insincerely you
tend to have a "garbage in, garbage out" problem.
S: Please study Balinski's reasons for concluding ...
C: No thanks, I'm not interested in joining your Bible-study group.
S: Also, I think you can already see that IBIFA's promise to give
Top-rating more weight than Middle-ratings creates an incentive to
give their first preference candidate a Top-rating..
C: Shock! Horror! MJ and also all sane methods that use ratings
ballots (except those that use them only to infer ranking and perhaps
also approval)
have the same incentive. Generally speaking the incentive the to give a
one's favourite a top-rating (or to rank no lower than equal-first) is
not regarded as a
problem in single-winner methods that we should be concerned about.
(Why on earth do you think it does? Obviously there can only be "no
incentive"
if it can't make a difference whether they do or not.)
Rather what is of greater concern is the incentive in most methods for
the voter to not do that. Fortunately neither IBIFA or MJ (or Relevant
Ratings or Approval)
have that problem.
S: Also, IBIFA gives more of an incentive dishonestly to Bottom all of
their less preferred candidates.
C: No it doesn't, as illustrated by the example in my last post.
45: A>B
30: B
25: C
IBIFA elects A (the CW: A>B 45-30, A>C 45-25).
IBIFA (like all Condorcet methods and IRV) elects A whether or not the A
supporters "dishonestly Bottom all their less preferred candidates"
but MJ (and all other versions of Median Ratings, such as Bucklin) only
elects A if they do just that.
I look forward to seeing your counter-example.
Chris Benham
Hi Chris,
I'll respond inline below. I look forward to our next exchange.
Steve
*From:*C.Benham cbenham@adam.com.au
Sent: Wednesday, June 12, 2019 2:40 AM
To: steve bosworth; cbenham@adam.com.au; EM list
Cc: John M
Subject: Re: Best Single-Winner Method-IBIFA vs. MJ
Chris Benham wrote:
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.
On 12/06/2019 6:34 am, steve bosworth wrote:
S: 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?
C: Of course not. ….
S: Please remember that my claim is that "in a workable and ideal
democracy, [MJ makes it possible for] each citizen’s vote [to] count
equally – one-person-one-vote. No citizen’s vote would be needlessly
wasted either quantitatively or qualitatively. This also means that
the… single-winner in an election will have received at least 50%
plus one of all the citizens’ votes cast.".
S: By saying, "of course not", I understanding that you instead
mean that your concept of an ideal democracy only guarantees that the
winner will be support by a plurality of voting citizens who Top-rated
them, I.e. like FPTP in this respect. Correct me if I'm mistaken.
S: In any case, the plain fact is the MJ guarantees all the above
benefits while IBIFA does not.
C: …. 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.
S: It seems to me that we can only reliably talk about the recorded
votes that citizens have actually made. The citizens who could or
would have stayed at home are unknowable. We only know who in fact
voted and those citizens who did not vote. Of course, the results of
any particular election would be different in almost any way we might
choose by hypothetically removing any key votes relevant to our purpose.
S: In your above example, the 3 citizens who voted for E also
Bottomed (Rejected) all the other candidates. Why do you think that
the 51 citizens who gave B their 2nd preference (and who thereby would
elect B by an absolute majority (if MJ were used) are a less important
than the group of 49 citizens who gave their 1st preference to A?
S: No citizen’s vote would be needlessly wasted either quantitatively
or qualitatively.
C: Refreshing our memories on what you mean by that:
S:I see a citizen’s vote as being wasted quantitatively to the degree
when 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.
C: If we cross out "most trusted" and replace it with 'preferred (for
whatever reason)', that is fine.
S: What other appropriate reason can a citizen have for supporting a
candidate to win other than they "trust" them to represent their own
scale of political values and concerns?
S: 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.
C: 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)?
S: The discovery of MJ means that it is always possible for the
winner to have this majority, and that is currently a necessary
element in my concept of "workable and ideal democracy". It is
because the candidate from the "Smith set", etc. may still not be
supported by such a majority that they are less attractive winner than
one who this majority support.
S: 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.
C: Yes, I can imagine the voters would hate that.
S: This leads to the demeaning identification of some citizens votes
as being “irrelevant”.
C: 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.
S: Contrary to what you may be implying, MJ does not count "those
ballots [intending] to change" the winner. MJ counts all the grades
given to all the candidates by all the voters equally in order to fine
the absolute majority winner, the one with the highest median-grade.
The grade of Reject given both to A and B by the 3 citizens who only
preferred E simply caused a new highest median-grade to exist. The
new median-grade for A became Bottom (Reject) while B's became 2nd
preference.
S: IBIFA also prompts dishonest voting (tactical voting) because it
gives more weight to a Top-rating than a Middle-rating.
C: I've already explained, and gave an example, that MJ has a much
stronger truncation incentive than does IBIFA.
S:: As far as I can see, truncation is not a problem for MJ. It
automatically counts a grade of Reject for each candidate not
explicitly give one of its other grades by a citizen: Excellent, Very
Good, Good, Acceptable, or Poor.This both gives the count as much
relevant information as possible and makes it as easy as possible for
each citizen to vote.In your view, please explain the nature of the
problem thattruncation can sometimes pose.
C: 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."
S: Please again note that 49 of the IBIFA voter are "happy" with their
winner, while 51 of the MJ voters would be happy with their
winner.Again, how do you justify IBIFA’s needlessly giving fewer
citizen satisfaction with the result of the election?
C: MJ elects B. Obviously MJ punished the A>B voters ….
S: I think you already know that to "punish" means to treat someone
differently while MJ treats every grade given by every citizen in
exactly the same way.
[….]
C: I think you'll find that Balinski’s 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).
C: MJ just gives voters a weaker (but still quite strong) incentive
to do that.
S: Please study Balinski's reasons for concluding that MJ reduces
both the incentives and opportunities for successful dishonest voting
by almost "half" (Majority Judgment, pp. 14, 15, 19, 187-198, 374).
Also, I think you can already see that IBIFA's promise to give
Top-rating more weight than Middle-ratings creates an incentive to
give their first preference candidate a Top-rating, even if they would
have honestly graded that candidate as only Acceptable if using MJ
rather than IBIAF for that elections.Also, IBIFA gives more of an
incentive dishonestly to Bottom all of their less preferred
candidates.With MJ you cannot give any extra help to the candidate you
most favor, no matter which grade you give them provide it is one of
the grades above that candidate's median-grade. Nor can you give
extra damage to the candidate who do not want to win provided you
award them a grade lower than his median-grade.
[….]
Chris Benham
Steve
From: C.Benham cbenham@adam.com.au
Sent: Wednesday, June 12, 2019 2:40 AM
To: steve bosworth; cbenham@adam.com.au; EM list
Cc: John M
Subject: Re: Best Single-Winner Method-IBIFA vs. MJ
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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