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Mike,<br>
<br>
A voting method algorithm stands or falls by its properties, i.e. its
criterion compliances and failures. Another school of thought is less
concerned about strict pass/fails of criteria and stresses how well the
method does in computer simulations at maximising "social utility"
and/or minimising negative emotions like "regret". <br>
<br>
<blockquote type="cite">Before continuing, though, I should clarify
that “middle”<br>
isn’t the best descriptive name for what a middle rating means or is
used for.<br>
Instead of calling it a middle rating, let’s call it (on the ballot)
an “accept coalition” rating. Let’s call the<br>
ratings on the ballot “top” and “accept coalition”. If you don’t give
a rating to a candidate, we<br>
can call that a “bottom rating”. A voter “accepts” a candidate if s/he
votes<br>
hir top or merely gives to hir an “accept coalition” rating.</blockquote>
<br>
Ballots are simply for voters to register their (hopefully and
"officially" presumably sincere) preferences among the candidates, not
to formally issue open invitations to the voters to play sordid
strategy games.<br>
<br>
<blockquote type="cite">For the method to wrong someone, it has to act
wrongly or wrongfully. <br>
</blockquote>
That is nicely circular...granted.<br>
<br>
<blockquote type="cite">But let’s consider
what MMT does, to judge whether what it does is wrong:</blockquote>
<br>
You then go on to more-or-less explain the details of MMT's algorithm,
putting a big positive spin on each of its components.<br>
<br>
<blockquote type="cite">Now,
please note that I’m not using MMT’s rule to justify MMT’s rule. </blockquote>
<br>
I'd like to "note" that, but I can't see what else you are doing. <br>
<br>
<blockquote type="cite">Among the candidates in those mutual majority
sets, MMT elects the most popular one (the one with
the most top-ratings).</blockquote>
<br>
Defining "popular" that way instead of say "fewest bottom-ratings" or
"best top-ratings minus bottom-ratings score" (or perhaps even by some
non-positional measure) looks quite arbitrary and uncompelling<br>
<br>
<blockquote type="cite">How wrong is it to elect the most popular
candidate among those among whom
majority has determined that the winner must be chosen?</blockquote>
<br>
It's "wrong" because it's an algorithm that needlessly fails some
desirable criteria. There are other methods (and there need only be
one) that don't fail those criteria while sharing all of MMT's
desirable criterion compliances. <br>
<br>
<blockquote type="cite">MMT’s rules were chosen to achieve FBC
compliance, avoid the
co-operation/defection problem, and enforce majority rule in some way.<br>
</blockquote>
<br>
That is fine and admirable, but there are much better methods that do
the same thing.<br>
<br>
<blockquote type="cite">Sincere preferences:<br>
<br>
49: C<br>
27: A>B<br>
24: B>A<br>
20: A<br>
<br>
<br>
The A>B and B>A voters should obviously coalition-accept
each other’s candidates. What should the 20 A voters do, who are
indifferent between
B and C?<br>
Well, they should know that A probably doesn’t have top ratings from a
majority of the voters. And they should know that A probably is not
even the Plurality winner. <br>
<br>
</blockquote>
Err... why should they "know" that? A's top-ratings score is 47, not
far behind C's top-ratings score of 49.<br>
<br>
If all the voters have very good information about each others'
preferences and are aware of and happy to use the best strategy (no
matter how insincere or weird) then all deterministic methods<br>
are about as good as each other at picking the right winner.<br>
<br>
<blockquote type="cite">And how does Chris justify saying that the
result is
“wrong”? He says that it shouldn’t be possible for voters to foul up
their voted-favorite’s chance of winning.</blockquote>
No, that would refer to Mono-add-Top. I said that methods must meet
Mono-add-Plump (compared to which Mono-add-Top is a bit arbitrary and
"expensive").<br>
Also the result gives bad failures of other criteria, like the
tied-at-the-top rule modified pairwise beats-all criterion (compatible
with FBC etc.) and my new "Add-Top Proofed Solid-Coalition Majority"<br>
criterion (doubtless also compatible with FBC, ABE etc.) and Condorcet
Loser.<br>
<br>
<br>
<blockquote type="cite">Could there be a method that would protect the
A-plumpers from their own stupidity? Sure.<br>
Is the voting system obligated to do that? No. The voters are adults,
responsible for their own actions.<br>
</blockquote>
<br>
If the "stupidity" is just honest voting, then the voting system is
obligated to protect those voters if it can (without giving up some
other desirable property). If the honest voting is just plumping, I say
that the voting system can do that easily.<br>
<br>
<blockquote type="cite">And notice that though Chris is affronted by
noncompliance with
Mono-Add-Plump, by an FBC/ABE method, Chris isn’t bothered by IRV’s
particularly flagrant
form of nonmonotonicity. Why the inconsistency and self-contradiction,
Chris?<br>
<br>
</blockquote>
You might have got a clue from what I wrote in an earlier post:<br>
<br>
"...if failure of Mono-add-Plump isn't self-evidently <b
class="moz-txt-star"><span class="moz-txt-tag">*</span>completely
ridiculous<span class="moz-txt-tag">*</span></b> (and so much so that
anything not compatible with Mono-add-Plump compliance is thereby made
a complete nonsense of), then I have no idea what is.
<br>
<br>
The only way this view of mine could be dented (and I made a bit wiser
and sadder) is if it was proved to me that compliance with
Mono-add-Plump isn't compatible with some other clearly desirable (IMO)
property or set of properties."<br>
<br>
There is no "inconsistency and contradiction" on my part. IRV meets
Mono-add-Plump (and Mono-Append and Mono-add-Top) but fails Mono-raise
(aka normal "monotonicity"). I agree that that failure<br>
(and for that matter its failure of Participation) isn't (focussed on
in isolation) a great look, but IRV has a long list of positive
criterion compliances: Mutual Majority, Mutual Dominant Third,
Condorcet Loser,<br>
the Plurality criterion, Clone-Winner and Clone-Loser (together make
Clone Independence), Later-no-Help (and so Invulnerability to Burial)
and Later-no-Harm, and no strategy better than sincere ranking<br>
in the zero-info case.<br>
<br>
There is no other method that shares those good properties and also
meets Mono-Raise.<br>
<br>
Chris Benham<br>
<br>
<br>
<br>
Mike Ossipoff wrote (19 Dec 2011):<br>
<br>
Chris:<br>
<br>
<br>
<br>
Ok, you said who’s wronged. Before commenting on your<br>
explanation of how they were wronged, let’s consider what that implies:
For the<br>
method to wrong someone, it has to act wrongly or wrongfully. Now,
please note<br>
that I’m not using MMT’s rule to justify MMT’s rule. But let’s consider
what<br>
MMT does, to judge whether what it does is wrong:<br>
<br>
<br>
<br>
Before continuing, though, I should clarify that “middle”<br>
isn’t the best descriptive name for what a middle rating means or is
used for.<br>
Instead of calling it a middle rating, let’s call it (on the ballot)
an “accept coalition” rating. Let’s call the<br>
ratings on the ballot “top” and “accept coalition”. If you don’t give
a rating to a candidate, we<br>
can call that a “bottom rating”. A voter “accepts” a candidate if s/he
votes<br>
hir top or merely gives to hir an “accept coalition” rating.<br>
<br>
<br>
<br>
Since I’ve written MMT’s definition elsewhere, I won’t<br>
repeat it here, but will summarize what MMT does:<br>
<br>
<br>
<br>
It finds sets of candidates who are accepted by the same<br>
majority of the voters, where that set contains at least one top-rated<br>
candidate on each of those accepting ballots. Before the comma, that
sentence<br>
refers to majority support for the set of candidates. After the comma,
it<br>
refers to the mutuality of that support.<br>
<br>
<br>
<br>
A majority of the voters is a group who can get their<br>
way A good method lets them do that<br>
easily, without favorite-burial. MMT lets them ensure that the winner
will be<br>
someone accepted for coalition by all of the voters in such a mutual
majority.<br>
It should be clear why I call that a mutual majority coalition.<br>
<br>
<br>
<br>
Letting a voter-majority determine a set from which the<br>
winner will be chosen—Are you sure that you want to say that that is
wrong?<br>
<br>
<br>
<br>
Ok, if that isn’t what MMT does wrong, then is it<br>
this?: Among the candidates in those<br>
mutual majority sets, MMT elects the most popular one (the one with
the most top-ratings). How<br>
wrong is it to elect the most popular candidate among those among whom
majority has determined that the winner must<br>
be chosen?<br>
<br>
<br>
<br>
If there are no mutual majority sets, then MMT elects the<br>
most popular candidate. How wrong is that?<br>
<br>
<br>
<br>
Note that I’m not saying that what MMT does is the only<br>
right thing to do. I’m asking if you can find something wrong about it.<br>
<br>
No, don’t quote Woodall’s monotonicity requirements. I’m<br>
asking what’s wrong with MMT’s rules, themselves.<br>
<br>
<br>
<br>
Ok, now that we agree that MMT’s rules aren’t, of<br>
themselves, wrong:<br>
<br>
<br>
<br>
MMT’s rules were chosen to achieve FBC compliance, avoid the<br>
co-operation/defection problem, and enforce majority rule in some way.<br>
Different methods do that in different ways. MMT’s mutuality
requirement is a<br>
precaution that makes it possible to entirely eliminate the<br>
co-operation/defection dilemma. <br>
<br>
<br>
<br>
As I said, MMT is a new kind of method, with a new kind of<br>
strategy—a milder, less confrontive, more dilemma-free strategy. Not
only does it eliminate favorite-burial incentive and the
co-operation/defection dilemma, but Chris's terms like "burial
incentive", "random-fill", etc.lose their meaning when one tries to
apply them to MMT. There, they don't point to an actual problem. <br>
<br>
Generalities can be useful, but we must remember that they are
generalities. There can be instances where they aren't useful
ormeaningful. <br>
<br>
<br>
<br>
<br>
Yes, MMT's strategy will be unfamiliar to you, Chris. <br>
<br>
<br>
<br>
I’ll just say a few brief things about that strategy. Unless<br>
you’re sure that your candidate has a top-ratings majority, you should<br>
coalition-accept other candidates. You could do so sincerely, accepting<br>
candidates who are the best ones with whom you could put together a
majority.<br>
Your candidate will be accepted by their voters if they regard your
candidate<br>
similiarly. <br>
<br>
<br>
<br>
If you’re only interested in electing your favorite, then you<br>
should accept a set of less popular candidates (so that your favorite
will be<br>
the winner within that coalition), and, of course, the set’s support
should add<br>
up to at least a majority of the voters.<br>
<br>
<br>
<br>
Those candidates’ supporters will coalition-accept your<br>
favorite if they want to elect hir as a more popular compromise. Note
that,<br>
because the coalition-acceptance must be mutual, the coalition is in
the best interest of<br>
all concerned. You don’t coalition-accept a more popular candidate
unless you<br>
really want to elect hir as a compromise.<br>
<br>
<br>
<br>
Looking at your example, then, what should the A voters do?<br>
<br>
<br>
<br>
I’ll copy your example here:<br>
<br>
<br>
<br>
Sincere preferences:<br>
<br>
<br>
<br>
49: C<br>
<br>
27: A>B<br>
<br>
24: B>A<br>
<br>
20: A<br>
<br>
<br>
<br>
The A>B and B>A voters should obviously coalition-accept
eachother’s<br>
candidates. What should the 20 A voters do, who are indifferent between
B and C?<br>
<br>
<br>
<br>
Well, they should know that A probably doesn’t have top<br>
ratings from a majority of the voters. And they should know that<br>
<br>
A probably is not even the Plurality winner. They need a<br>
coalition. They probably know that A has roughly the same popularity as
B. <br>
<br>
<br>
<br>
But even if they didn’t know those things, there are still<br>
things that could be said: If A is<br>
strong in top ratings, enough to win without a coalition, then A must
have more<br>
top ratings than B. If so, then A would be the winning candidate in an
{A. B}<br>
coalition. If A doesn’t have as many top-ratings as B, and would
therefore not<br>
be the winning candidate in that coalition, then obviously A couldn’t
be a<br>
winner without the coalition either. So, at least A has a chance in the<br>
coalition, since A might have more top-ratings than B. <br>
<br>
<br>
<br>
So, obviously, the 20 voters should should<br>
coalition-accept B. Should they<br>
coalition-accept C, whom they like as much as B? The only difference is
that,<br>
if they know anything about the numbers, they know that C is much more
likely<br>
to dominate a coalition than B is. Maybe they have a 50:50 chance of<br>
top-ratings-beating B. They probably don’t know for sure if A and B
voters add<br>
up to a majority, but it’s a hope. <br>
<br>
But it doesn't matter whether they<br>
include C, because of course it turns out that C voters don’t accept
anyone<br>
else, and none of the A>B and B>A voters accept C. So C won’t be
in the coalition anyway.<br>
<br>
<br>
<br>
Are the A-plumpers wronged? Yes. They’re wronged by Chris, when<br>
he makes them vote as foolishly as they did.<br>
<br>
<br>
<br>
Are the A>B voters wronged? Yes. They’re wronged by the<br>
stupid voting of the A-plumpers.<br>
<br>
<br>
<br>
Now, what about Chris’s claim about how the A-plumpers were<br>
wronged?<br>
<br>
<br>
<br>
He says that their ballots were given negative weight. That<br>
statement is incorrect. The A-plumpers were positively counted toward
A’s<br>
top-ratings total. The only kind of mark<br>
that the A-plumpers made was fully and positively counted. Chris, read
that<br>
sentence again.<br>
<br>
<br>
<br>
Though we looked closely at each part of MMT’s rule, and I’m<br>
guessing that Chris isn’t going to be able to find anything wrong with
MMT’s<br>
rules, themselves, Chris is still objecting because, by refusing to
accept a<br>
mutual-support coalition, the A-plumpers made there not be one. Well,
where I<br>
come from, a majority coalition doesn’t exist if it isn’t accepted by a<br>
majority.<br>
<br>
<br>
<br>
You don’t accept a majority coalition. Therefore there isn’t<br>
a majority coalition. Therefore your candidate doesn’t benefit from one,<br>
because there isn’t one.<br>
<br>
<br>
<br>
We can make A win if we pick and choose among the voters,<br>
removing some, to reduce the total number of voters, to manufacture a
majority<br>
coalition via that tinkering.<br>
<br>
<br>
<br>
Chris’s objection isn’t justified by, and shouldn’t be based on, a
claim that<br>
MMT’s rules, of themselves, are wrong. He’s unlikely to find anything
wrong<br>
with them. It’s the _result_ that Chris doesn’t like. He’s saying that
the<br>
result had a kind of nonmonotonicity: Selective removal of some voters
who top-rated A could make A win.<br>
<br>
<br>
<br>
It’s that the rule did something that Chris doesn’t like. It<br>
isn’t that he finds something wrong with the rule itself, or any
particular<br>
part of it. And how does Chris justify saying that the result is
“wrong”? He says that it shouldn’t be possible for<br>
voters to foul up their voted-favorite’s chance of winning. Excuse me,
Chris, but<br>
where does it say that?<br>
<br>
<br>
<br>
In Woodall? :-)<br>
<br>
<br>
<br>
<br>
<br>
<br>
<br>
“The Truth according to Woodall”?<br>
<br>
<br>
<br>
Note that, though Chris doesn’t like that result, he can’t<br>
say that it is wrong, other than according to his own taste. Or only
according<br>
to Woodall. So let’s distinguish between “That’s wrong” versus “I
personally<br>
don’t like that, and Woodall says it’s bad.”<br>
<br>
<br>
<br>
Aside from that, is such nonmonotonicity impossible or never<br>
found in everyday life? No. It isn’t<br>
even anything new to our everyday experience:<br>
<br>
<br>
<br>
Dennis’s mother says to Dennis:<br>
<br>
<br>
<br>
Dennis, Mr. Wilson here says that he isn’t going to make us<br>
pay for his living room picture window through which you hit a
baseball. That’s<br>
because I told him that you’re sorry, and you promise not to play
baseball in<br>
the street anymore.<br>
<br>
<br>
<br>
Dennis says:<br>
<br>
<br>
<br>
Mr. Wilson, kiss my<br>
a**. I’ll play baseball in the street<br>
anytime I want to. It wasn’t my fault that your picture window was in
the way<br>
of my baseball, and so go ahead and try to sue us.<br>
<br>
<br>
<br>
[end of Dennis story]<br>
<br>
<br>
<br>
Dennis and his mother both vote to not pay for the window.<br>
But even though Dennis arrives, and registers his wish to not pay for
the<br>
window, his arrival has made it so that his family will have to pay for
the<br>
window. Nonmonotonicity, just as in<br>
Chris’s example.<br>
<br>
<br>
<br>
It happens in everyday life.<br>
<br>
<br>
<br>
You can cry about it if you want to, Chris, but it’s a fact<br>
of life.<br>
<br>
<br>
<br>
And notice that though Chris is affronted by<br>
noncompliance with Mono-Add-Plump, by an<br>
FBC/ABE method, Chris isn’t bothered by IRV’s particularly flagrant
form of<br>
nonmonotonicity. Why the inconsistency and self-contradiction, Chris?<br>
<br>
<br>
<br>
Could there be a method that would protect the A-plumpers<br>
from their own stupidity? Sure.<br>
<br>
<br>
<br>
Is the voting system obligated to do that? No. The voters<br>
are adults, responsible for their own actions.<br>
<br>
<br>
<br>
But don’t get me wrong. It would be nice to afford that<br>
deluxe, extra, foolproofness protection, for such as the A-plumpers.<br>
<br>
<br>
<br>
There are some FBC/ABE methods that do that:<br>
<br>
<br>
<br>
GMAT, MTAOC, and MMPO.<br>
<br>
<br>
<br>
But I’ve been told that GMAT and MTAOC don’t have the<br>
simplicity and brevity of definition needed for a successful public
proposal.<br>
<br>
<br>
<br>
And an MMPO public proposal could be vulnerable to the<br>
distraction that could be achieved by a criticism based on Kevin’s MMPO<br>
bad-example. I’ve told why that criticism isn’t valid, because no one is<br>
significantly wronged by the election of someone to whom no one prefers<br>
anyone other than their favorite.<br>
Nevertheless, the opposition using that criticism could make a
distraction from<br>
the more relevant issues of the proposal. As I said, the opposition
will have<br>
more media money to broadcast the criticism than the proponents will
have to<br>
answer it.<br>
<br>
<br>
<br>
So that leaves MMT as the feasible FBC/ABE proposal.<br>
<br>
<br>
<br>
Mike Ossipoff<br>
<br>
<br>
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