[EM] Approval voting under fire #2 (Mike Ossipoff)

[James Green-Armytage]

> It got me thinking about a whole series of
>> strategy questions,
>> not necessarily ones that Monroe made, but ones that
>> were interesting
>> nonetheless. I am still left with the question as to
>> whether Condorcet or
>> IRV is more strategy-resistant, a question which I
>> explored at length on
>> the EM list last month.
>
Which is more strategy resistant, IRV or Plurality? Is
that really the right question? What is it that we
don't like about Plurality? The fact that it isn't
strategy resistant? What strategy isn't it resistant
to? Well, if Greens know that they need the Democrat
to beat the Republican, and they vote Democrat
therefore, then their strategy succeeds in keeping the
Republian from wining. Therefore Plurality isn't
strategy resistant. But is that really what we don't
like about Plurality, the fact that it _lets_ those
Greens defeat the Republican by burying their
favorite?

Or is it that Plurality _makes_ them do so?

So does IRV. No, IRV doesn't do it every time, as
Plurality does, but how often is acceptable to you?

Approval never does that. No one ever has any
incentive to vote someone over their favorite in
Approval. Condorcet meets some criteria that describe
some plausible conditions under which drastic
defensive strategy shouldn't be needed. IRV fails all
those criteria.

Instead of asking which method is more strategy
resistant, ask which method makes people have to bury
their favorite. Plurality and IRV.

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


Dear James,

You wrote:

But given a choice between moving to IRV and staying
with
plurality, which would you prefer? 

I reply:

Staying with Plurality. I'm not saying that Plurality
is as good as IRV. It's just that adopting IRV will
get us stuck with IRV, and prevent genuine reforms,
such as Approval or Condorcet, from being adopted.
People will say "You want a better voting system?
We've adopted a new one. Do you want us to now drop
that one and go through it all again?" No good.
Anything worth doing is worth doing right. And, as you
said, IRV will discredit itself, its promoters, and
electoral reformers in general. "Yeah right, they said
that IRV was a reform too. We've heard that one
before." 

You continued:

As you know I think that Condorcet 
is
really superior to IRV in a serious way, but I'd
rather have IRV than
plurality. I wrote my thoughts on this question in a
post to the EM 
list
called IRV vs. plurality

I reply:

But it needn't be IRV vs Plurality. Don't let the CVD
"leadership" convince you that IRV is the only thing
that the public will accept as a replacement for
Plurality.

You continued:

I would be much more 
comfortable
using IRV in such a situation than leaving it to
plurality.

I reply:

IRV won't fail as often as Plurality. But we can do
much better than IRV.




	Anyway, IRV at least cannot select a Condorcet loser
while plurality 
can,
plus IRV is much more likely to select a Condorcet
winner when one 
exists.
	Also, I think that IRV is a step in the direction of
Condorcet, 
because
it gets people used to ranked ballots, and the concept
of a single vote
that can nevertheless count for different candidates
in different
situations. 

I reply:

That single vote is the reason why IRV retains
Plurality's worst problems, and the reason why
Approval and Condorcet don't. Plurality's worst
problem is that it makes people bury their favorite to
keep their last choice from winning. IRV sometimes
does that. It won't be rare. It happens in the example
that you gave in the e-mail that I'm replying to now,
and which I'll get to farther along in this reply.

You continued:

	I realize that there are some dangers in going ahead
with IRV 
advocacy,
as it could get locked in place and absorb the energy
needed for deeper
reform, or it could fall on its face and disgrace the
movement. Whether
these dangers outweigh the possible benefits of IRV is
an open 
question,
but at this point, when plurality is still so
ubiquitous, I think that 
the
more productive course of action for election methods
advocates is to 
try
to implement the system they like best, rather than
spending their 
efforts
defending plurality. 

I reply:

IRV opponents aren't defending Plurality. They're
trying to save single-winner reform from CVD.

You continued:

That is, unless they really think that the 
proposed
system is worse then plurality; if this is the case
then I suppose that
cooperation is impossible.

I'm not saying that IRV is worse than Plurality,
though it is certainly worse in some ways. IRV's
failure of the Summability Criterion makes it much
more problematic to implement than Approval,
Condorcet, or Plurality. IRV requires so much more
storage and computation, having to refer to all the
rankings again and again, that it's much more
vulnerable to tampering.

Also, Plurality meets Participation, and IRV fails it:

Participation:

Adding to the count one or more ballots that vote
Smith over Jones should never change the winner from
Smith to Jones.

[end of definition]

Admittedly, Condorcet fails too, but probably not as
easily. But Condorcet offers some valuable criterion
coimpliances that outweigh its Participation failure.
IRV offers nothing, compared to what Approval offers.

On balance, I personally feel that IRV isn't quite as
bad as Plurality. But if we let CVD push IRV through,
then we're letting CVD botch single-winner reform.
Better to wait for genuine single-winner reform
proposals. Approval now has a national organization
that is getting involved in public education, and
hopefully public enactment proposals.
 

You continued:

	Myself, while I agree that approval is better than
plurality, and is 
made
very attractive by the fact that new equipment is not
necessary, I am 
not
convinced that it is better than IRV. 

I reply:

Judge them by criteria. Approval meets FBC & WDSC.
IRV meets Mutual Majority (MMC). But, as I discuss
below, every MMC example is an IRV failure example in
wihch IRV fails FBC & WDSC. One must choose which is
more important. More about that in a minute.


You continued:

let's say that these are 
the
sincere preference rankings:

23: right, left#1, left#2
22: right, left#2, left#1
29: left#1, left#2, right
26: left#2, left#1, right

	In this example, left#1 is a clear Condorcet winner.
He also happens 
to
win IRV

I reply:

That example is the fortuitous situation called a
"mutual majority". The L1 & L2 voters are a mutual
majority. Majorities aren't always mutual. In fact
they're probably usually not mutual. For instance, say
a majority prefer Democrat to Republican. That
majority consists of Greens and Democrats. But do the
Democrats prefer the Green to the Republican? The
Democrats & Republicans are so much more like
eachother than the Democrat is like the Green, that
anyone who really considers the Dem his favorite will
like Repub better than Green.

So it's a fortuitous situation.

Also, you're only looking at it from the Left point of
view. How is that example for the Right voters? Say
they believe that the Left has a mutual majority.
That's not so unreasonable, since, it will be common
for no one candidate to have a majority, and so it
isn't so unreasonable to suppose that, since R doesn't
have a majority, then L1 + L2 is a majority. Anyway,
say they know (or believe) only that the Left has a
mutual majority.

Can R win? No. Do they gain anything from sincerely
voting R in 1st place? No. Could they gain by voting
their more preferred of the L candidates in 1st place?
Yes, if it will save him from immediate elimination
and subsequent election of the other L candidate, the
one that the R voters dislike more.

So the R voters have reason to bury their favorite.
That's the case in every mutual majority example. Yes,
a mutual majority is better for one group, while being
bad news for another group.

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?

Another reason is that it conceals R's true support,
even when the R voters are correct in believing that L
has a mutual majority and they need to vote their more
preferred L candidate in 1st place.

You continued:

However, what would happen if these sincere preference
rankings went 
into
an approval election? Would all of the 'left' voters
approve both 
'left'
candidates? In that case, it would be a tie. Would all
of the 'left'
voters bullet vote? In that case, 'right' would win.
	It seems like a pretty severe chicken game between
the left voters who
prefer left#1 and those who prefer left#2. Unlike IRV,
this is a 
chicken
game with no sincere vote to take refuge in, because
it is not clear
whether a sincere vote would be a bullet vote or a
double vote. 

I reply:

Both are sincere. If I'm a L1 voter and I consider L2
a phoney sleaze, then I, and those like me, will
publicly announce that we aren't voting for the sleazy
L2. 

In our elections it seems to me that there are always
completely unacceptable candidates who might win. The
best strategy then, in Approval, is to vote for all
the acceptables and for none of the unacceptables.

If the suporters of one of the other acceptables
strategically withold their vote from your favorite,
at least you don't get an unacceptable winner. But of
course if they do that, you might make it known that
next time that other candidate won't be considered an
acceptable. That's a good reason not to do that kind
of betrayal in Approval. If it's obviously strategic,
not based on sincere dislike of your favorite, then
you might want to retaliate, and they'll know that.
And if it _is_ based on sincere dislike of your
favorite, then I don't consider it a problem.

Approval doesn't let us rank the candidates, but
Approval reliably counts every pairwise preference
that we _do_ vote. That can't be said for IRV.

In my 5-candidate example, Approval only looked at a
fraction of the voted preferences, and that's why it
messed up so badly.

At least in Approval _I'm_ the one who decides which
of my preferences will be counted.

Another thing: Though Approval doesn't let us indicate
all our pairwise preferences, Approval gives us an
expression of how much we like or dislike candidates,
in a way that rank balloting doesn't give us:

For the very reason that we don't rank candidates,
which ones we vote for or don't vote for measures
degree of like or dislike, something that rankings
don't tell. That's one reason why Approval does so
much better than IRV on social utility.

There are various good Approval strategies. I mean it
when I say that with Approval I wouldn't really miss
voting all my preferences, because of the preference
degree information that Approval lets me give. Whom
you vote for or don't vote for in Approval is a
statement.

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

Dear James,

You wrote:

It 
looks
like the winner will either be the right candidate, or
the left 
candidate
who has more bullet-voting supporters. I'm really not
comfortable with
this; it seems like the outcome is being decidedly
entirely by voter
strategy, while the actual preferences for the
candidates takes a
secondary role. 

I reply:

Yes, strategy is definitely part of Approval voting.
But that doesn't have to be a bad thing. After all,
strategy is needed often in IRV too, and that IRV
strategy will often be favorite-burial, something that
Approval will never give incentive for.

So sure, people will use strategy in Approval. But
there's one strategy that I can assure you that
they'll never use: Favorite burial.

When you're used to rankings, and the expression of
all our pairwise preferences thereby, you feel cheated
by Approval. But as I said, Approval at least counts
all the pairwise preferences that we choose to vote.
And in Approval, people will typically vote about half
of their preferences. So we aren't as 
preference-cheated as you might expect. 

Which is better?: Twice as many preferences voted,
which may or may not be counted; or half as many
preferences voted, which are all reliably counted?

In Approval, when there are no compltely unacceptable 
candidates who could win, he strategy isn't as simple.
But I feel that there are such candidates in our
political elections. Look at the Repubs & Dems and
tell me if I'm mistaken :-)

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.

That's for if there are 2 clear frontrunners.

Say there aren't. Another good strategy is to vote for
each of the candidates whom one would rather have in
office than hold the election. Vote for each candidate
who is better than the value of the election. 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. Sometimes I'd
use best-frontrunner, the strategy that I described
earlier, in which we vote for whom we would in
Plurality, and for everyone whom we like better.
Best Frontrunner has elaborations that I describe at
our website:

http://www.electionmethods.org

At that website there are 3 Approval Strategy
articles.

So there are good strategies for Approval, and you can
be sure that no one will bury their favorite. For me
that's the important thing. When voters bury their
favorite, we don't find out what people want. The
voting system can't act on what it isn't told, and the
public never gets that information either. How good is
democracy when voters find it necessary to buty their
favorite?

I feel that Approval gives us degree of dislike
expressing power that makes up for only letting us
typically express about half of our pairwise
preferences. 

When you entirely deny a vote to a candidate, you're
saying something strong, something that he & his
supporters can't ignore. I feel that Approval is very
expressive. As I said, because preference degree is so
much a part of Approval strategy, Approval does
excellently at social utilitly, significantly better
than IRV.

You continued:

What worries me isn't just that the method doesn't
guarantee that the Condorcet winner is chosen 

I reply:

Approval did better than IRV in Samuel Merrill's
computer simulations. He did spatial simulation
studies in which he randomly placed candidates &
voters in N-dimensional issue-space, with rankings &
ratings based on distances in that space. He assumed
that it's a zero-information election, for which the
Approval strategy is to vote for all the above-mean
candidates.

You can see the social utility benefit of everyone
voting for all the above-mean candidates, as they
judge them.

And it's been shown that any strategy that maximizes a
voter's utiility expectation in Approval is, by
reasonable approximations, the same as voting for all
the candidates whom that voter would rather have in
office than hold the election. And that gives us
another social optimization: The winner is the
candidate whom the most people would rather have in
office than hold the election.

And if one's expectation for the election is about as
good as the status quo, as it often will be, then that
means that Approval elects the candidate whom the most
people consider better than the status quo.

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.

You continued:

-- the problem is that I
don't see any particular reason why the Condorcet
winner would be 
chosen
rather than one of the other candidates. 

I reply:

True, Approval isn't a pairwise-count method, and so,
like IRV, it doesn't look for the CW. But Approval has
the social optimizations that I described. Some people
say they'd rather elect the Approval winner than the
CW.

In Merrill's simulation study, Approval did better
than IRV at electing CWs.

That's because of IRV's "squeeze effect":

75: ABCDE
84: BACDE
100: CDBEA
78: DECBA
67: EDCBA

Let me simplify this by only listing the preferences
that IRV ever looks at and counts:

75: AB
84: B
100: C
78: D
67: ED

A bit sparse, isn't it? That's because it only shows
the preferences tht IRV looks at.

Not only is C the CW, but C is the favorite of more
people than any other candidate is. But IRV fails to
elect C.

That's the squeeze effect that caused IRV to do so
much worse than Approval in Merrill's simulations.

The simulations are described in:

_Making Multicandidate Elections More Democratic_, by
Samuel Merrill. Probably out of print, but available
in many or most university libraries.

You continued:

Does the amount of candidates 
who
bullet vote rather than double vote reflect the
relative strength of
preference for the candidate? I don't think that this
is necessarily 
so.

I reply:

Approval strategy is fundamentally based on preference
intensity. Sure, bullet voters can take advantage of
sincere double-voters. But those examples suppose that
there's no way to choose between the 2 L candidates.
Usually one will be more winnable-looking than the
other, or more positioned as a CW compromise, etc.

That candidate's voters are in a better position to
expect shared votes from the other L candidate, and it
could be understood that therefore they'd bullet vote,
if that kind of strategy were on people's minds at
all.

And remember that what people are going to do will be
talked about. And actually organizing a strategy is
impossible to do in secret. When you tell all the L1
voters do bullet vote, the L2 voters will hear about
it.

Then, as I said, the consequences of that betrayal,
for future trust and support, also discourages the
betrayal.

So then, for all those reasons, I don't consider that
betrayal/co-operation dilemma to be the problem that
it might at first sound like.

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

Approval's social optimization can be worded in
another way:

Approval maximizes the number of people who are
pleasantly surprised by the result.

That's because saying "Vote for the candidates who are
better than what you expect from the election" is the
same as saying "Vote for each candidate whom you'd
rather have in office than hold the election."

You wrote:

Anyway, approval has its good points, and IRV has its
nightmares, but 
are
things clear-cut enough to say that approval is
definitely better?

I reply:

Yes, if we go by criteria. Criteria are precise yes/no
tests for voting systems.

Approval passes FBC & WDSC (defined at our website).

http://www.electionmethods.org

IRV passes the Mutual Majority Criterion, but, as I
said, every mutual majority situation is an IRV
failure in which people are given reason to bury their
favorite.

My concern about IRV enactment is that it will prevent
genuine reform.

Mike

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


Dear James,

Suppose, in Approval, a candidate was considering
running, but noticed that a candidate nearly identical
to him was already in the race.

For one thing, if they're really that identical, then
why would he feel any need to run. And if they're
significantly different, then the problem's
assumptions, that they're both equally winnable and
neither is more CW-like than the other are unlikely to
hold.

But say they're really extremely similar and he wants
to un anyway, though there's no need for an additional
identical candidate:

That new candidate might decide not to run, to avoid
the split-vote problem that you described. But does he
have to? Why not just run and tell people, 

"I don't want to make our policies lose due to
split-vote, and so it's important that if you vote for
me, you vote for ______, whose policies are very
similar to mine."

In fact, that solution could become customary, or
understood, so that, when there are 2 identical
candidates, equally winnable, equally CW-like, the one
who filed first is understood to be the one who more
deserves to win. It would be understood that, if
voters were inclined to have the split-vote
betrayal/co-operation dilemma, his voters would only
vote for him. The new identical candidate's voters
therefore would know that they need to vote for both.

So, in this message and in a previous one, I've told a
number of reasons why Approval's split-vote
betrayal/co-operation dilemma isn't the problem that
it might at first seem to be.

Mike