[EM] Who wronged the A-plumpers

Sun Dec 25 10:54:44 PST 2011

Mike,

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". 

> Before continuing, though, I should clarify that "middle"
> isn't the best descriptive name for what a middle rating means or is 
> used for.
> Instead of calling it a middle rating, let's call it (on the ballot)  
> an "accept coalition" rating. Let's call the
> ratings on the ballot "top" and "accept coalition".  If you don't give 
> a rating to a candidate, we
> can call that a "bottom rating". A voter "accepts" a candidate if s/he 
> votes
> hir top or merely gives to hir an "accept coalition" rating.

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.

> For the method to wrong someone, it has to act wrongly or wrongfully.

That is nicely circular...granted.

> But let's consider what MMT does, to judge whether what it does is wrong:

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.

> Now, please note that I'm not using MMT's rule to justify MMT's rule. 

I'd like to "note" that, but I can't see what else you are doing. 

> Among the candidates in those mutual majority sets, MMT elects the 
> most popular  one (the one with the most top-ratings).

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

> How wrong is it to elect the most popular candidate among those among 
> whom  majority has determined that the winner must be chosen?

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.

> MMT's rules were chosen to achieve FBC compliance, avoid the 
> co-operation/defection problem, and enforce majority rule in some way.

That is fine and admirable, but there are much better methods that do 
the same thing.

> Sincere preferences:
>
>  49: C
>  27: A>B
>  24: B>A
>  20: A
>
>  
> 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?
> 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.
>
Err... why should they "know" that?  A's top-ratings score is 47, not 
far behind  C's top-ratings score of 49.

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
are about as good as each other at picking the right winner.

> 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.

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").
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"
criterion (doubtless also compatible with FBC, ABE etc.) and  Condorcet 
Loser.

> Could there be a method that would protect the A-plumpers from their 
> own stupidity? Sure.
> Is the voting system obligated to do that? No. The voters are adults, 
> responsible for their own actions.

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.

> 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?
>
You might have got a clue from what I wrote in an earlier post:

"...if failure of Mono-add-Plump isn't self-evidently *completely 
ridiculous* (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.

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."

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
(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,
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
in the zero-info case.

There is no other method that shares those good properties and also 
meets Mono-Raise.

Chris Benham

Mike Ossipoff wrote  (19 Dec 2011):

Chris:

Ok, you said who's wronged. Before commenting on your
explanation of how they were wronged, let's consider what that implies: 
For the
method to wrong someone, it has to act wrongly or wrongfully. Now, 
please note
that I'm not using MMT's rule to justify MMT's rule. But let's consider what
MMT does, to judge whether what it does is wrong:

Before continuing, though, I should clarify that "middle"
isn't the best descriptive name for what a middle rating means or is 
used for.
Instead of calling it a middle rating, let's call it (on the ballot)  an 
"accept coalition" rating. Let's call the
ratings on the ballot "top" and "accept coalition".  If you don't give a 
rating to a candidate, we
can call that a "bottom rating". A voter "accepts" a candidate if s/he votes
hir top or merely gives to hir an "accept coalition" rating.

Since I've written MMT's definition elsewhere, I won't
repeat it here, but will summarize what MMT does:

It finds sets of candidates who are accepted by the same
majority of the voters, where that set contains at least one top-rated
candidate on each of those accepting ballots. Before the comma, that 
sentence
refers to majority support for the set of candidates. After the comma, it
refers to the mutuality of that support.

A majority of the voters is a group who can get their
way  A good method lets them do that
easily, without favorite-burial. MMT lets them ensure that the winner 
will be
someone accepted for coalition by all of the voters in such a mutual 
majority.
It should be clear why I call that a mutual majority coalition.

Letting a voter-majority determine a set from which the
winner will be chosen--Are you sure that you want to say that that is wrong?

Ok, if that isn't what MMT does wrong, then is it
this?:  Among the candidates in those
mutual majority sets, MMT elects the most popular  one (the one with the 
most top-ratings). How
wrong is it to elect the most popular candidate among those among whom  
majority has determined that the winner must
be chosen?

If there are no mutual majority sets, then MMT elects the
most popular candidate. How wrong is that?

Note that I'm not saying that what MMT does is the only
right thing to do. I'm asking if you can find something wrong about it.

No, don't quote Woodall's monotonicity requirements. I'm
asking what's wrong with MMT's rules, themselves.

Ok, now that we agree that MMT's rules aren't, of
themselves, wrong:

MMT's rules were chosen to achieve FBC compliance, avoid the
co-operation/defection problem, and enforce majority rule in some way.
Different methods do that in different ways. MMT's mutuality requirement 
is a
precaution that makes it possible to entirely eliminate the
co-operation/defection dilemma.

As I said, MMT is a new kind of method, with a new kind of
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.

Generalities can be useful, but we must remember that they are 
generalities. There can be instances where they aren't useful ormeaningful.

Yes, MMT's strategy will be unfamiliar to you, Chris.

I'll just say a few brief things about that strategy. Unless
you're sure that your candidate has a top-ratings majority, you should
coalition-accept other candidates. You could do so sincerely, accepting
candidates who are the best ones with whom you could put together a 
majority.
Your candidate will be accepted by their voters if they regard your 
candidate
similiarly.

If you're only interested in electing your favorite, then you
should accept a set of less popular candidates (so that your favorite 
will be
the winner within that coalition), and, of course, the set's support 
should add
up to at least a majority of the voters.

Those candidates' supporters will coalition-accept your
favorite if they want to elect hir as a more popular compromise. Note that,
because the coalition-acceptance must be mutual, the coalition is in the 
best interest of
all concerned. You don't coalition-accept a more popular candidate 
unless you
really want to elect hir as a compromise.

Looking at your example, then, what should the A voters do?

I'll copy your example here:

Sincere preferences:

49: C

27: A>B

24: B>A

20: A

The A>B and B>A voters should  obviously coalition-accept eachother's
candidates. What should the 20 A voters do, who are indifferent between 
B  and C?

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. They need a
coalition. They probably know that A has roughly the same popularity as B.

But even if they didn't know those things, there are still
things that could be said: If  A is
strong in top ratings, enough to win without a coalition, then A must 
have more
top ratings than B. If so, then A would be the winning candidate in an 
{A. B}
coalition. If A doesn't have as many top-ratings as B, and would 
therefore not
be the winning candidate in that coalition, then obviously A couldn't be a
winner without the coalition either. So, at least A has a chance in the
coalition, since A might have more top-ratings than B.

So, obviously, the 20 voters should should
coalition-accept  B. Should they
coalition-accept C, whom they like as much as B? The only difference is 
that,
if they know anything about the numbers, they know that C is much more 
likely
to dominate a coalition than B is. Maybe they have a 50:50 chance of
top-ratings-beating B. They probably don't know for sure if A and B 
voters add
up to a majority, but it's a hope.

But it doesn't matter whether they
include C, because of course it turns out that C voters don't accept anyone
else, and none of the A>B and B>A voters accept C. So C  won't be in the 
coalition anyway.

Are the A-plumpers wronged? Yes. They're wronged by Chris, when
he makes them vote as foolishly as they did.

Are the A>B voters wronged? Yes. They're wronged by the
stupid voting of the A-plumpers.

Now, what about Chris's claim about how the A-plumpers were
wronged?

He says that their ballots were given negative weight. That
statement is incorrect. The A-plumpers were positively counted toward A's
top-ratings total.  The only kind of mark
that the A-plumpers made was fully and positively counted. Chris, read that
sentence again.

Though we looked closely at each part of MMT's rule, and I'm
guessing that Chris isn't going to be able to find anything wrong with MMT's
rules, themselves, Chris is still objecting because, by refusing to accept a
mutual-support coalition, the A-plumpers made there not be one. Well, 
where I
come from, a majority coalition doesn't exist if it isn't accepted by a
majority.

You don't accept a majority coalition. Therefore there isn't
a majority coalition. Therefore your candidate doesn't benefit from one,
because there isn't one.

 We can make A win if we pick and choose among the voters,
removing some, to reduce the total number of voters, to manufacture a 
majority
coalition via that tinkering.

Chris's objection isn't justified  by, and shouldn't be based on, a 
claim that
MMT's rules, of themselves, are wrong. He's unlikely to find anything wrong
with them. It's the _result_ that Chris doesn't like. He's saying that the
result had a kind of nonmonotonicity: Selective removal of some  voters 
who top-rated A could make A win.

It's that the rule did something that Chris doesn't like. It
isn't that he finds something wrong with the rule itself, or any particular
part of it. 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. Excuse me, 
Chris, but
where does it say that?

In Woodall?  :-)

"The Truth according to Woodall"?

Note that, though Chris doesn't like that result, he can't
say that it is wrong, other than according to his own taste. Or only 
according
to Woodall. So let's distinguish between "That's wrong" versus "I personally
don't like that, and Woodall says it's bad."

Aside from that, is such nonmonotonicity impossible or never
found in everyday life?  No. It isn't
even anything new to our everyday experience:

Dennis's mother says to Dennis:

Dennis, Mr. Wilson here says that he isn't going to make us
pay for his living room picture window through which you hit a baseball. 
That's
because I told him that you're sorry, and you promise not to play 
baseball in
the street anymore.

Dennis  says:

Mr. Wilson,  kiss my
a**.  I'll play baseball in the street
anytime I want to. It wasn't my fault that your picture window was in 
the way
of my baseball, and so go ahead and try to sue us.

[end of Dennis story]

Dennis and his mother both vote to not pay for the window.
But even though Dennis arrives, and registers his wish to not pay for the
window, his arrival has made it so that his family will have to pay for the
window. Nonmonotonicity,  just as in
Chris's example.

It happens in everyday life.

You can cry about it if you want to, Chris, but it's a fact
of life.

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?

Could there be a method that would protect the A-plumpers
from their own stupidity? Sure.

Is the voting system obligated to do that? No. The voters
are adults, responsible for their own actions.

But don't get me wrong. It would be nice to afford that
deluxe, extra, foolproofness protection, for such as the A-plumpers.

There are some FBC/ABE methods that do that:

GMAT, MTAOC, and MMPO.

But I've been told that GMAT and MTAOC don't have the
simplicity and brevity of definition needed for a successful public 
proposal.

And an MMPO public proposal could be vulnerable to the
distraction that could be achieved by a criticism based on Kevin's MMPO
bad-example. I've told why that criticism isn't valid, because no one is
significantly wronged by the election of someone to whom no one prefers
anyone  other than their favorite.
Nevertheless, the opposition using that criticism could make a 
distraction from
the more relevant issues of the proposal. As I said, the opposition will 
have
more media money to broadcast the criticism than the proponents will have to
answer it.

So that leaves MMT as the feasible FBC/ABE proposal.

Mike Ossipoff

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