[EM] Approval voting under fire #4 (Mike Ossipoff)

[James Green-Armytage]

Dear James,

>> I could
>> post it to the EM list
>> if you like.
>
Yes, if you would.

>> >So it's a fortuitous situation.
>> 
>> 	I don't think that you have demonstrated this. 
>
All I meant was that our current split-vote problem
appears to not be a mutual majority situation. The
anti-Republican majority, consisting of Nader voters
and Democrats aren't a mutual majority, because the
Republican is much closer to the Democrat than Nader
is, and so the Democrat perferrers will prefer the
Republican to Nader.

IRV's mutual majority criterion compliance won't help
the Democrat+Nader majority.

 The basic
>> point is that the two L candidates have much more in
>> common with each
>> other than they do with the R candidate
>
But if they're so similar, is it really so important
which one wins? And are their voters really going to
be going at eachother with cold, ruthless
Machiavellian strategy?

Suppose we were going to do the 2004 Presidential
election by Approval, with no primary, just one big
general election by Approval. Kucinich and Sharpton
are anti-cruelty progressives. I've recently heard
that Carol Mosely is too. Some say that Dean is also,
but others point out that all Democrats pose that way
in campaigns, and that Dean's history says different.
So, Kucinich, Sharpton & Moseley are the anti-cruelty
progressives.

So it's like your R, L1, L2 example, but with a 3-way
split vote. How would I vote? I'd vote for all 3.
It isn't important to me which one wins. The important
distinction is between them and the others. Will I be
taken advantage of by shrewed Machiavellian behavior
by the Mosely preferrers? Are they really inclined in
that direction. I don't expect that, but in any case,
if she's really a progressive, how important is it
that Kucinich wins instead of Moseley?

Maybe if Moseley's voters did that, I wouldn't vote
for Moseley next time, or for whomever that faction is
supporting.

A few years ago, _Scientific American_ reported the
results of a public-participation experiment that had
been done. People were asked to submit a computer
program that would carry out a strategy for the
prisoners' dilemma. The L1/L2 betrayal/co-operation
dilemma is like the prisoners' dilemma.

People sent in all sorts of strategy programs. All
these programs were run against eachother in pairs, in
the prisoners' dilemma game, which was repeated many
times for each pair of programs. The programs were
scored according to how much they won over all those
games, against all their opponents.

The big winner was a program called "Tit-For-Tat".
Tit-For-Tat was really simple: Start out co-operating,
and then copy what the other player has just done.

Maybe that's what I'd be doing when voting for Mosely
& Sharpton in addition to my favorite, Kucinich.

But in this case there's more information available.
The only poll whose results I know shows Kucinich more
popular than Moseley or Sharpton. So, if it turned out
that progressives were ruthless betrayal strategizers,
against eachother's very similar candidates, I (and
others like me) would publicly point out that Kucinich
is more popular than Moseley or Sharpton, and
therefore Kucinich is the natural
"coming-together-place for progressives.

You mentioned the possibility of negotiations among
the L voters, but then said that would make it a
different voting system. I know what you mean, but
really it's still Approval, helped by pre-election
co-operation.

Of course, since I don't know much about Moseley, it
could turn out that she's really just as good as
Kucinich, in which case why should I care if her
voters cheat me by betrayal stratgegy?

, and
>> together they form a clear
>> majority, but neither one forms a majority on his
>> own. The two candidates
>> are assumed to be not identical.
>
For there to be a problem each L faction would have to
consider the other to be about half as bad as R.
I wouldn't vote for a progressive who is half as bad
as the Republocrats. Problem solved.

>> >Someone could say "But the R voters have no right
>> to
>> >expect to win, since L has a majority". Yes, but
>> the
>> >whole fundamental problem about strategy is that we
>> >don't have perfect information. The R voters could
>> >mistakenly believe that that mutual majority
>> situation
>> >exists, and therefore give the election away to
>> their
>> >more preferred of the L candidates, when actually R
>> >could have won if they'd voted sincerely. Isn't
>> that
>> >the main reason why we don't like voters to be
>> given
>> >incentive to bury their favorite?
>> 
>> 	Yes, this is the reason. But doesn't it apply in a
>> different way in the
>> approval example I gave? 
>
Here's an important way in which it doesn't apply to
Approval: In Approval, no one ever has incentive to
vote someone else over his/her favorite. In IRV, in
every mutual majority situation, there are voters who
have incentive to bury their favorite by voting
someone else over him/her.

>> I will elaborate...
>> 
>> >But if there aren't such candidates, then people
>> can
>> >do what they do in Plurality: Vote for their more
>> >preferred of the 2 expected frontrunners...except
>> that
>> >with Approval they can also vote for everyone whom
>> >they like better.
>> 
>> 	Let's say that people follow this strategy in my
>> example, but without
>> perfect information. Let's say that L2 somehow
>> manages to convince people
>> that he is more likely to win, so that the L1 voters
>> double vote and the
>> L2 voters bullet vote. The perception has created
>> the reality. No one will
>> ever know that L1 was the sincere Condorcet winner.
>
I don't know how L2 would convince the L1 voters of
that, unless he could point to credible polls that the
L1 voters trusted. Each L faction could do its own
polling.

If there are polls that are trusted by the L voters,
indicating that one L candidate is more popular than
the other, then that L candidate is the one with
natural claim as the coming-together-point for L
voters.

If one L candidate is more middle-ish than the other
(but not so much as to make him unacceptable to the
preferrers of the other L candidate) then he benefits
from the fact that, in Approval, the preferrers of the
middle candidate in a 3-candidate race have no reason
to vote for anyone else.

No one's saying that Approval is Condorcet. But,
unlike IRV, Approval never gives anyone a reason to
bury his/her favorite by voting someone else over
him/her.

>> 
>> >Another way to put it: Vote for the candidates who
>> are better
>> >than your expectation for the election.
>> >That's called the better-than-expectation strategy.
>>  
>> >I'd often use it when there are no completely
>> >unacceptable candidates who might win.
>>  
>> 
>> 	It is not clear to me how this strategy would be of
>> help in my example.
>
I'm not saying it would help the betrayal strategy,
but it would typically be a way of maximizing
expectation.

Depending on one's utilities and win-probability
estimates, One L-preferrer might place the expectation
for the election below or above the rival L faction.
That would determine whether or not to vote for him,
when using better-than-expectation strategy.

When choosing to use better-than-expectation, one is
choosing to ignore betrayal strategy, and to just try
to judge the expectation for the election.

How barbarous will the Kucinich, Sharpton & Moseley
voters be against eachother?

>> 
>> >	The more you find out about Approval, the better
>> it
>> >turns out to be. It's deceptively, elegantly
>> simple,
>> >but it has a lot of unexpected desirable
>> properties.
>> 
>> 	I wish I could believe this, but I don't think that
>> approval can
>> successfully navigate this sort of mutual majority
>> situation.
>
It doesn't automatically avoid it like IRV or
Condorcet. That's why it's Approval and not Condorcet.
Simple methods require more strategy than the best
rank methods. But remember that every mutual majority
situation is an IRV failure in which someone is given
incentive to bury their favorite--something they'd
never have reason to do in Approval.

If the R voters expect that L has a mutual majority,
but they don't have other details, then they have
incentive to rank in 1st place whichever L candidate
they prefer to the other, burying their favorite.

Mutual majority = favorite burial incentive in IRV

>> >
>> 
>> 23: right > left#1 > left#2
>> 22: right > left#2 > left#1
>> 29: left#1 > left#2 > right
>> 26: left#2 > left#1 > right
>> 
>> 	Basically, I just don't see how approval voting
>> offers any way for voters
>> to effectively choose between these three
>> candidates. 
>
No problem. As I said, I'd vote for Kucinich, Moseley,
and Sharpton, because they're all much better than the
alternatives. If the voters of Moseley or Sharpton
cheated me by bullet voting, how much would that
matter, if they're all 3 progressives that I'd like to
have win? 

But how dastardly can we really expect progressives to
be against eachother's candidates, candidates whom
allk progressives greatly prefer to the Republocrats?

Of course if one of those other 2 got lots more votes
than Kucinich, then I'd know that bullet voting was
widespread, and I'd have the opportunity to retaliate
next time, a la Tit-For-Tat. Or maybe, if Kucinich
appears more popular, then I'd, in that eventualilty,
start voting only for him for that reason, publicly
stating that intention, along with other Kucinich
preferrers. So, if I wanted to act on the betrayal in
the next election, there would be 2 justifications
that I could give for bullet voting. The difference is
that if it's because Kucinich is more popular, and he
remains so, then I keep on bullet voting, having found
out that progressives are cold, calculating
rivalry-oriented betrayers. But if it's Tit-For-Tat
strategy, then I bullet vote once, and then resume
co-operation.

Mike

#################

Dear James,

You wrote:

	To eliminate the possibility of a solution based on
anything but voter
strategy, imagine that the sincere cardinal ratings
(from 1 to 100) 
look
something like this:

23: right 80 > left#1 40 > left#2 30
22: right 80 > left#2 40 > left#1 30
29: left#1 90 > left#2 80 > right 30
26: left#2 90 > left #1 80 > right 30


I reply:

But probability estimates, along with the utilities,
are needed in order to have information about
strategy.

Of course it could be a "zero-info" election, in which
no one knows the win probabilities or pair-tie
probabilities.

Pulbic political elections are rarely  0-info, though.

But, assuming that the above example is 0-info, then
0-info Approval strategy says to vote only for 
above-mean candidates. Both L factions should double
vote, in a true 0-info election. 

If the L2 voters bullet votes and won, then, if the L1
voters care anywhere near as much as they do about
winning, then the L2 voters' candidate won't be
getting votes from the L1 voters next time.

By the way, under 0-info conditions, the above-mean
strategy is the same as the better-than-expectation
strategy.

In general, by a few plausible approximations, one
maximizes one's expectation by voting for the
candidates who are better than one's expectation for
the election.

You wrote:



	I would say that the outcome of this election under
approval is 
anybody's
guess

My best guess is a tie between L1 & L2, if their
voters use Approval's expectation-maximizing strategy,
and aren't risking R victory in order to cheat
eachother out of winning. Say you're an L2 voter: If
you're considering bullet voting, how do you know that
the L1 voters aren't considering the same thing. What
will happen if both factions bullet vote. Would bullet
voting by wise?

Sure, a few bullet voters will typically cause either
L1 or L2 to win. But they're very similar, so does it
really matter much which one wins?

You wrote:

, which is I think a fatal problem.
	What is it that will induce L2 voters to capitulate
and double vote 
for
L1? What will induce L1 voters to double vote for L2? 

I reply:

1. The fact that expectation-maximizing strategy says
to vote for both.

2. The fact that Tit-For-Tat strategy says to vote for
both.


3. The fact that if you, as an L2 voter are
considering bullet voting, then surely L1 voters must
be considering it also. Shall we all bullet vote and
elect R? What makes the most sense? That we all double
vote. If later it turns out that you've been betrayed
by defection strategy, then _that's_ the time to deal
with it if you want to, according to Tit-For-Tat.

You continued:

It can't possibly
have anything to do with the relative margins of
preference for those
candidates, because they are approximately equal.
	
I reply:

Then why would L voters want to risk R victory by
bullet voting? If I were the 2nd L candidate to file,
I'd make it very clear to my constituents that they
must vote for both L1 & L2.

...unless the other L candidate was really corrupt or
phoney, in which case I'd say so, and would urge
people to not vote for him. Not out of Machiavellian
stratgegy, but merely out of disgust.

You wrote:

It is of course not necessary for the rankings to be
this similar for
this situation to be an approval voting nightmare. I
am just pointing 
out
that there is no reason to assume that one of the two
L candidates is
preferred by a substantially greater margin than the
other one.

I reply:

Usually it will be known from polling, and from
conversations, which L candidate is more popular. He's
the obvious one on whom the L voters should come
together. If anyone is even thinking about betrayal
strategy, turning the election into a betrayal
strategy election, then the bigger L candidate's
voters should announce that they're bullet voting
because their candidate is the rightful winner.

You continued:

	Even if so, it will not necessarily be possible to
get accurate
information on the margin of preference amongst the L
voters. If they 
get
a chance, the L2 voters will have an interest in
telling the L1 voters
that they only barely prefer L1 over R, and that they
plan to single 
vote,
thus trying to scare the L1 voters into double voting.


I reply:

I can't speak for others, but if I were an L1 voter,
and the L2 voters announced that they would bullet
vote, and they didn't  have a credible claim that L1
is sleazy, dishonest, corrupt, phoney, etc., then do 
you think I'd say "Gee, we'd better vote for L2, and
let them have the election."

If things had degenerated to that level, and it had
become a betrayal strategy election, then I'd suggest
a meeting and a vote among L voters, or at least a
coin-flip, to decide which L candidate should get our
support. It would be understood that the faction that
wins that vote or coin-flip will single-vote. That way
no one has to trust anyone, because we're assuming
that the L voters are thoroughly untrustworthy
characters.

But if L2 is more popular, then I'd double-vote, 
because L2 is more the rightful wininer. Likewise if
L2 appears to be CW, without being centerward enough
to be unacceptable to me.

But no, a mere threat of single-voting by the L2
voters isn't going to make the L1 voters double-vote.
Not unless the L2 voters give a good justification for
their single-voting, a reason that the L1 voters agree
with.

You continued:

	Also, I should note that voters don't have to be
especially devious
strategy wizards to realize to hesitate in double
voting in hopes that
adherents of the other candidate will help vote in
your favorite. 

I reply:

It won't work. If L2 voters want to threaten to
single-vote, to make L1 voters double vote, they need
to convince the L1 voters that L2 is CW, is more
popular than L1, or that L1 is corrupt, sleazy,
phoney, dishonest, etc.

You continued:

For
example, an L2 voter doesn't have to be a genius to
realize that L1 is 
one
of L2's main competitors, and if it comes down to L1
versus L2 then 
they
will have screwed up by double voting.

I reply:

They know that if they're thinking that, then the L1
voters are too (unless it's well-understood that the
L2 voters are much more dishonest than the L1 voters.
But if that's so, then it's a sure thing that the L1
voters will single-vote, for a justifiable reason).

So what should the L voters do? Double vote. 
Betrayal, if it happens, must be dealt with afterward,
not pre-emptively, with 2 paranoid factions giving
away the election to R because they don't trust
eachother.



	The only way I can think of to avoid this sort of
thing is to have
primaries. That might help to prevent this particular
example from
happening, but there are not always situations where
primaries are
appropriate, where they will be consented to by all
the candidates, or
where the candidates who form the mutual majority will
have enough in
common to consider a primary. Also, if you have more
than two 
candidates
in the primary and you use approval for that, than you
might run into
exactly the same problem again. If you use a method
other than approval
then this is a cop-out as far as saying that approval
works.

You continued:

	In the absence of a primary or negotiated agreement
(which effectively
makes a different election method), there is no
civilized way for 
voters
to effectively choose between L1 and L2. 

I reply:

Tit-For-Tat strategy says to double vote. In your
example, utility-expectation-maximization strategy
says to double vote.

You continued:

That is, a reasonable 
mechanism
for such a choice simply isn't built into approval
voting, because 
voters
cannot express such a preference while still noting
that they would 
prefer
either candidate to R.

I reply:

Simple methods require more strategy than the best
rank methods.

But it will be rare for neither L candidate to appear
bigger than the better, or to appear to be the CW. And
I'd double-vote. You probably would too. I don't think
progressives are as dastardly as you suggest. And if a
faction were that low, then it's good that they defeat
themselves by splitting their vote.

Mike

###############

Dear James,

It could be said that it isn't a disadvantage that
Approval rewards factions that co-operate and
penalizes factions whose members are devious and
inclined to cheat eachother.  Let's hope the
Republocrats do that to themselves/eachother every
time.

By the way, some time ago I suggested, on EM, some
simple remedies for that Approval split-vote:

If X gets more votes than Y, that's because more
people have voted for X and not Y than have voted for
Y and not X.

Give voters the option of indicating that a vote for
someone is a "mutual vote", which could also be called
an "equalling vote". If N equalling votes are received
by X, from people who also voted non-equallying votes
for Y, and if X beats Y by less than N votes, then
it's declared a tie between X & Y. When you cast an
equallying (or mutual) vote, it's understood that you
don't want that vote counted for anyone to whom you've
given it if they have more votes than anyone for whom
you've given a non-equalling vote.

Or maybe the voter could have the option to indicate
that an equalling vote shouldn't be counted if it's
for someone who has more votes than _anyone_ that
voter has voted for. In that way the voter could
protect a number of candidates against eachother's
voters' betrayal strategy.

Of course your vote for your favorite won't be an
equalling vote.

Some have suggested Majority Approval, in which the
ballot gives you a space to indicate your favorite, in
addition to the ones that you want to give an Approval
vote to. If one or more candidates are indicated
favorite by a majority, then the winner is whichever
of those has the most votes. Otherwise the Approval
winner wins.

Those are 2 improvements in Approval that complicate
the ballot a little. I like Approval's completely
simple ballot, nothing other than a Plurality ballot
that says "Vote for 1 or more" instead of "Vote for
1".

But if people were expressing concern about betrayal
strategy or majority, then I'd suggest one or both of
those modifications.

Of course I'd prefer Condorcet.

Mike