At 12:56 PM 4/11/2010, Kevin Venzke wrote:
--- En date de : Dim 11.4.10, Abd ul-Rahman Lomax
<a...@lomaxdesign.com> a écrit :
In a given election yes, it is easy to miss the mark. But in
general,
aiming for the median voter is the most reliable. (That is
assuming you don't know utilities, which I'm really not sure you
showed how to find.) To see this, you assume utility is based on
issue space distance, and that the voters aren't distributed
unevenly.
I didn't show how to find utilities, I only showed various
possibilities consistent with the votes.
Actually, I did follow an algorithm. I'd say it's reasonable. No claim
that it is definitive. Obviously, how people will vote may depend on
how the votes will be counted. But less than we might think
Yes, and my response is what can I possibly do with that? You used one
method that was rather Borda-like in character. One can't evaluate
methods
using a Borda-like criterion or you'll end up advocating something
Borda-like.
The algorithm was not "Borda-like" because it did not prohibit equal
ranking bottom. It's true that I did not use equal utility top,
because there was no information to justify it.
To study voting system performance, I'm saying, one must
*start* from utilities, not from preference order without
preference strength information. Voter behavior is not
predictable without preference strength information.
Strategy, in general, doesn't make sense without an
understanding of preference strength.
We sort of have been doing this when Juho questions the story behind
my
scenarios.
Yes. But the long-time use of voting systems criteria that depend
solely on preference order is a hard habit to break. And the whole
discussion of "strategy" has been often off the point. The use of
"strategy" (as being about the idea that people will bullet vote to gain some
advantage, which is assumed to be improper) neglects that a bullet
vote reflects a strong preference. The voter wants their favorite to
win, strongly enough that the voter suppresses
the expression of remaining preferences.
IRV encourages this lower expression, because it
doesn't require a true majority, but it
"eliminates" candidates, hence lower preference
votes will only be counted if your more preferred candidate is eliminated.
In other words, in a non-LNH method like Bucklin,
A>B means that you actually are willing to elect
B, enough to risk the possibility that B beats
your favorite, A. With higher preference
strength, you will vote only for A. Whereas with
IRV, A>B (>C) tells us nothing about the
preference strength of A>B, nor, in fact, about
the strength of B>C. It only tells us that some preference exists.
Thus when you have a situation where every voter
chimed in on some question, and they didn't do that for any other
question, you shouldexpect (on average) a utility problem when the
outcome goes against the majority opinion.
I'll agree that this is the "norm." However, it can go
drastically wrong.
How can we detect the exceptions?
Right, that's the question.
In order to detect the exceptions, and use that
information, we must risk some level of error in
that. Let's be clear about something.
Suppose a set of voters has, for a complete
candidate set, internal absolute utilities. We
can imagine a set of voters all with the same
resources financially. They have, however,
various degrees of interest in politics and who
wins elections. The utility is the "value" of the
election of a candidate to the voter, and may be
negative. Assuming that all voters have equal
resources, the positive value is what the voter
would pay to be assured that the candidate would
win, and a negative value is what the voter would
find adequate as compensation if a disapproved candidate wins.
Can we agree that the ideal winner of an election
is the one which would maximize the sum of
utilities of the voters? Note that these are
*not* normalized utilities, and that if there
were a Clarke tax or the like, collecting from
those who assigned positive values and paying
this to those with negative values, such that the
benefit of the election is equalized across all
voters, the best candidate would represent
maximized value for *all* voters, not just those
whose preferred candidates won.
These utilities, except in certain narrow
situations, cannot be directly determined. We can
only infer them, to some degree, by voter
behavior in elections and, as well, with respect
to campaign donations and responses to polls. But
it is not necessary to know them in order to use,
in simulations, such a social preference profile
to predict voter behavior under various voting
systems, and to compare performance.
Okay?
This is roughly Warren Smith's approach, of
course, though details may certainly differ.
The Majority Criterion require majority
preferences to prevail, at a point where the
majority may not have sufficient information to
choose the social utility winner, assuming that
the majority would want to do so. In fully
discussed deliberative election, a serious
"utility error" may be detected and avoided
through two means: abstention by voters with low
preference strength, and, as well, a posible
deliberate choice by voters to please those with
stronger preferences, i.e., socially cooperative
behavior. In top-two runoff, if the primary fails
to forward the social utility winner to the
runoff, and if the error is large, and if
write-ins are allowed in the runoff (which makes
it closer to deliberative process), a write-in
might well win. If the runoff voting method is
such that a write-in candidacy doesn't need to
create a spoiler effect, this can be facilitated.
I consider it an unresolved question, how common
it would be in real elections that picking a
majority preference will cause utility error.
(Bayesian regret in Warren's work.) But I'm sure
it happens. How much damage is done, I don't
know. But it could be significant. And the
scenario we have been working on does show this.
Sure, the majority criterion and the condorcet criterion
are usually a sign of good performance, but it is obvious
that exceptions exist, and we should not denigrate a voting
system if it, under an exception condition, it violates the
criteria!
I wouldn't, no. But I would presumably have some model that explains
why violation of the criterion worked.
Sure. Now, let's assume that the votes given as
the election scenario were sincere, and reflected
sincere preferences. Shouldn't we start there?
From the classic study of preference, it has
been assumed that a bullet vote is strategic, not
sincere. It is assumed that if the voter votes
just for A, instead of, say, A>B, the voter does
have a preference between B and C, and is
suppressing that to gain advantage. However, that
is not a realistic assumption.
Suppose a voter is only familiar with A and
"approves" of A, will be pleased to see A
election, and has no opinion about either B or C.
The voter, then, assigns no value to the election
of B or C, but does assign value to the election
of A. The bullet vote for A is a perfect
expression of the voter's preferences. Suppose we
shift this to a situation where the voter does
have some preference between B and C, but it is
small. If C is elected the voter will emigrate,
if B is elected, the voter will merely make sure
that there is enough money to buy a ticket, and
that the voter can emigrate quickly! In IRV,
rationally, the voter should rank B. But in
systems that are collecting utility information,
the utility of B is small and speculative. (It's
negative in the system I proposed).
In a full-on Range voting system, with high
resolution, the voter would indeed show a
preference for B. But only in the second
scenario. In the first the value for B is zero.
The voter, by bullet voting, is totally
abstaining from all other pairwise elections.
(I'll neglect average range, which I consider
politically foolish as a proposal, requiring
judgement about something where we have only air to build on.)
I took the proposed votes, and inferred from them
what votes would be equivalent expressions of
preference in, not Borda, but Bucklin,
specifically 3-rank Bucklin-ER, and I've come to
the (tentative) conclusion that rational votes in
Bucklin-ER are actually sincere range votes,
particularly if a majority is required or there
is further process. For 3-rank Bucklin ER, the
votes would be Range 4, with possible ratings of
0, 2, 3, 4, and midrange represents approval
cutoff. That's why rating 1 is missing, it is a disapproved rating.
(In a more sophisticated Bucklin system, rating 1
would be allowed, and could be used to determine
ballot configuration in a runoff. This would
encourage, a little, bumping up, to a rating of
1, an only-disapproved-a-little candidate.)
I was just pointing out that the outcome you claimed was
obviously bad wasn't. It might be that, on average, this
outcome would be poorer than the other,
Yes, I'm afraid that's what I call "bad." If I didn't call this
"bad" I would also have to be pretty undecided about the resolution of most
two-candidate FPP elections.
Actually, if the Bayesian regret was low, using
"bad" would be hyperbole. Two-candidate elections
are not the kind of scenario considered here. I
do not believe that choosing the majority
preference is an error in two-candidate
elections, on average, and the incidence may be
rare. We don't have a two-candidate election, the
campaign was not over two candidates, it was over
three, and it was very close. These are
conditions where, in fact, utility error may be
much more common, if we require the Condorcet
criterion. The election does not fail the
majority criterion. If we require a majority, the
election simply fails. Now, take results like
that and require a runoff between A and B. Who
will win? Most voting systems students will
assume that B will win, based on the votes in the
first election. However, we know that in
one-third of runoff elections, and these were not
as close as this election, there is a "comeback."
That means that in two-thirds there is not.
Usually, the plurality winner goes on to win the
election. Note that it only takes a very small
amount of shift among the B and C voters to allow
A to win, perhaps some lower turnout (which tests
preference strength). In a real runoff with
initial votes as described, A will almost certainly win.
We know, from the bullet voting, that the
preference of the A voters is strong, it is less
likely to shift in a direct campaign between A and B.
And, as I hope I show, the simplest analysis of
likely normalized utility profiles shows that A
is, indeed, the range winner (Range 4). That is the center, not the extremes.
This kind of thinking leads me to conclude that
plurality is a better voting system than we often
think. We dislike plurality because of the
breakdowns, not because of the normal function!
but it was not a truly bad outcome,
under reasonable assumptions of likely
utility, the first utility scenario I gave, which used Range
2 utilities, i.e., normalized and rounded off so as to make
all the votes sincere and sensible. The bullet voters then
had equal bottom utilities for the other candidates, and
those who ranked had stepped utilities. Simple. And showing
that A was, indeed (with these assumptions, which seem
middle-of-the-road to me), the utility maximizer, by a
fairly good margin!
This was the Borda-like thing I mentioned above.
Borda is Range with what is, in the end, a
bizarre assumption. Use a Borda ballot and stop
discarding "illegal votes," but count them
rationally, i.e., allow equal ranking and
therefore empty ranks, and keep the rank values
the same, and it is a Range ballot. Since the
only difference between Borda and Range is this,
the system I used was Range, not Borda.
You can make a contrary assumption, that the A voters were
"strategic." That they "really" would be happy with B. I'm
assuming, instead, that their votes would be sincere. And
likewise the votes of the other voters.
Look, A *almost* has a majority in first preference. I'm
very suspicious of claims that an election outcome is
"terrible" if it depends on some close-shave majority that
failed.
You are really missing my complaint then. According to your stepped
utility analysis C voters don't like B that much at all. If they know
that the method interprets such votes that way, then it is really bad
to vote sincerely for C.
We don't know how much they like B. We know that
they like B more than A, that's all. So I
inferred the middle assumption, that their
utility for B was midway between that for A and
C. That gives equal wiggle room in both directions.
What you are doing now, Kevin, is criticizing the
original votes, which were the assumption. And,
it seems, you are criticizing as well, possible
(unstated) ballot limitations. Clearly, the
ballot allows equal ranking bottom, but it seems
you assume it does not allow equal ranking top. I
assumed, instead, that an expressed preference
had real value, was not merely forced by the
ballot. I gave it a middle value, neither
extreme. Could you suggest an analysis more likely to be accurate?
I initially read your last paragraph with disbelief. In my
interpretation,
C and his votes are just noise. The task of the election method is
to pick
the right candidate between A and B, just as it would be in FPP
(where C
would probably have died off pre-election). To be unable to do this is
quite useless in my view.
If that is the task of the election method, why
is C on the ballot? Suppose that C is *not* on
the ballot, suppose that C was a write-in. If
that's true, then C would very likely be the utility winner. Not A or B.
What is the "right candidate" between A and B and
why are we limited to that? I agree, it is likely
that the right candidate is either A or B, but it
is not at all impossible that it is C. With my
middle-of-the road assumptions, I came up with A
as the utility maximizer, and B and C not that
far apart from each other. From pure preference,
sure, it looks like C is noise. If, in fact, to
the C voters, B and C are almost equally
prefered, C is indeed noise, and the "sincere
vote" for C is indeed strategically foolish.
Indeed, if B and C were to agree on who runs, and
it would probably be B, then all the campaigning
would be dedicated to B instead of split, and the
likely result would be an increase in B support, and it's already close.
But from the voting preferences given and
reasonable assumptions about the normalized
utility profiles behind them, A is the best
winner! So criticizing a voting system because it
gives A the victory with those votes is
backwards. I would claim that, ideally, no
election would ever terminate the process with
other than a manifest condorcet winner, this
would always go back to the voters, as is normal
with deliberative election process, which never
elects without a majority of the votes supporting
the winner. But there is no condorcet winner in
the election being studied, because, while B
beats A 51:49, C beats B 27:24, and A beats C 49:46.
So, since there was no majority for A, this
election, ideally, would go back. For practical reasons, it might not.
--- En date de : Dim 11.4.10, Abd ul-Rahman Lomax
<a...@lomaxdesign.com> a écrit :
This should rather say, if I proposed utilities behind
the scenario, I
could make those utilities say anything I wanted.
I pointed out some extremes, which reveal as the ideal
winner A, B, or C. In other words, you are apparently
agreeing with me.
Yes.
However, I believe that I showed that a
middle-of-the road assumption about underlying utilities,
with stated assumptions that were not designed to make it
turn out some particular way, A could indeed be the best
winner.
Yes you did.
Here, you accept it, but I want to make sure that
was not accidental. I wrote "could be." I'll make that stronger. "Likely is."
(I did not set out to "prove" that A was the best winner,
but rather just to attempt to infer utilities from the
voting patterns, which didn't allow me to assume equal
ranking except at the bottom).
The matter hinges on the A voters, who are, after all,
almost a majority. Why did none of them rank B or C? The
only reasonable assumption is that they have strong
preference, and that's what ices it.
I'm happy to say that A voters have a strong preference, but why
should only the A voters get to benefit from this? Are you saying the other
voters don't have a strong preference against A?
No, they do, and they are given full credit
("benefit") for it. The problem is that they
don't explicitly agree on strong preference *for* B or C.
I was not analyzing the votes from the point of
view of strategy in the voting system used, and I
don't really know what that system is. I was
assuming, in fact, sincere votes, votes that
express preferences accurately. If the 51% did,
in fact, have strong preference for both B and C
over A, they therefore had weak preference
between B and C. (That is the restriction that
comes from normalization, the assumption that all
voters have the same range of preferences. One person, one vote.)
If they have weak preference between B and C, in
Range 4, they would rationally vote max rating
for both. But you have 5% of voters who vote
contrary to that, because they bullet vote for B.
The linchpin voters are the C voters. If the
method is plurality, their strategy is obvious,
if they want to improve the outcome. But what if
some of them, say, anything over 1% of total
voters, have weak preference for B over A? They
will prefer to express their clear preference for
C to betraying their favorite, and that is real
voter behavior. It was Nader's message in 2000,
and, obviously, many voters bought it.
In IRV, their strategy is also obvious. IRV works
with an election like this, unless. Unless enough
C voters abstain from ranking B. Some will. And
there you go, IRV is likely, still, to give this
to A! Only a Condorcet method will give it to B, narrowly.
This is the classic
reason to violate the Condorcet or Majority criteria: a
strong preference of a minority, particularly when the
margin is thin.
If, in fact, B and C were true clones, with only minor
preference between them, the assumption of a significant
reduction of utility between them (which is the other factor
that lowers the rating for B and C) would fail.
If the method allowed equal ranking, we'd see that in the
votes, and B might win. The A votes would be the same, the B
bullet voters would be the same, but the other B and C
voters would equal rank B and C. Because of the B bullet
voters, B would win by a small majority.
So my result for A could be an artifact of the voting
system not allowing equal ranking. I used Range 2, which
doesn't give a lot of room for "creative interpretation."
That was much easier with Range 10, as I showed. With Range
2, there wasn't any other reasonable way to interpret the
votes.
It's possible that with equal ranking it would be different, but if we
are not going to ask a method to behave unless voters use equal
ranking, I guess we could just use Approval.
Approval is Not Bad, but this would be the
problem: what about the C voters? Approval would
not allow them to express their preference for C,
and if it is strong, some of them will not express it, and A will win.
So, in fact, Bucklin.
49 A
5 B
19 B>C
27 C>B
B wins, assuming these are the votes. Bucklin is an approval method.
However, the election scenario is unrealistic,
because we have almost half of the voters voting
monolithically, and then the other half does so
as well. For these voting patterns to arise, the
election must be highly partisan. Non-partisan
voters do not vote like this. In a real election,
some of the non-partisan voters who prefer A
would also approve, at lower rank, of B or C. And vice-versa.
For the rest of this post, I will repeat the
utility analysis, which is Range 4, with the
approval cutoff being 2. A rating of 2 represents
indifference between the election of the candidate and the expected outcome.
49 A was analyzed as A=4, B and C are 0. This was
overly pessimistic. If I'm going to be "central,"
I should rate them as 1, i.e., the middle
disapproval rating. This is an average, some
voters might rate B or C as zero, some as "almost 2".
5 B likewise.
19 B>C This is analyzed as B= 4, C = 3. This is
accurate, because the actual voter rating would
be in the range of 2 to 4, so I'll assume that
the mean is 3. A, however, should be considered
to be 1, for the same reason as with the A voters with regard to B and C.
27 C>B likewise.
So, the new analysis:
A B C
49 A 4 1 1
5 B 1 4 1
19 B>C 1 4 3
27 C>B 1 3 4
totals 247 157 170
Notice this phenomenon: the social preference
order matches the first preference order. This, I
suspect, is very common. This is why plurality voting is a decent method!
What would happen if a majority were required?
Suppose that the runoff is between the top two
candidates, using an analysis like what I just
did, which assumes that preferences are spread
such that they average as I indicated. The runoff
would be between A and C, not A and B, and that
is probably the best. After all, C beats B pairwise.
Dhillon and Mertens showed that Rational
Utilitarianism, which is tantamount to Range
Voting with von Neumann-Morganstern utilities, is
the unique system that satisfies all of a set of
Arrovian criteria modified to allow consideration
of equal ranking and preference strength
expression, and, here, the assumption is that
normalized utilities are not modified by
probabilities, i.e., they are zero-knowledge.
They are raw utilities, then, normalized to the
range of 0-4, and averaged across the factions.
The average votes end up (average out) as if each
faction voted in a Range 3 election, and it is
possible that I could or should redo the analysis
stated that way. In this re-analysis, a bullet
vote is equivalent to ratings of 3, 0, 0, and a
ranking of two candidates is equivalent to 3, 2, 0.
----
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