[EM] Why I think IRV isn't a serious alternative 1

[Abd ul-Rahman Lomax]

At 03:08 PM 12/6/2008, Kevin Venzke wrote:
> > > In your previous message you seemed content to say
> > that voters can't
> > > vote "accurately" under Range because they
> > don't know how and because
> > > the ratings have no inherent meaning.
> >
> > The two considerations should be kept rigorously separate.
>
>I don't see how they can be kept separate if you want the one to
>say something about the other.

Use of utility analysis to simulate election methods and therefore 
their performance is entirely separate from the use of Range Voting 
as a method. It's conceivable that Range Voting turns out to be 
impossible to actually use, for whatever reason -- I can't imagine 
one, other than pure political opposition -- and the method of 
studying voting system performance through utility simulations and 
Bayseian regreat would still stand as a way of comparing practical systems.

Range Voting happens to be a method that allows voters to cast 
approximations of utilities. While it's theoretically possible to 
allow voters to cast absolute utilities as votes, and probably only 
practical -- if practical at all -- to do so where a vote represents 
some cost to the voter, either absolute or relative, that's not 
generally at issue in these discussion. There *is* a cost to voting, 
and that *does* affect outcomes, but that is another story, I've told 
it elsewhere.

It is not true to say that the ratings have no inherent meaning. From 
them, one may infer sets of preferences, which are, we can presume, 
sincere (sincere with a preference is not "accurate," because it does 
not express preference strength. We may be able to place, should we 
desire to do so, constraints on the underlying relative preference strengths.

That there is more than one sincere vote in Approval does not prevent 
extracting valuable preference information from the expressed vote, 
and the same is true with Range, which is as expressive as an 
Approval Vote, as a minimum, and possibly much more expressive of 
true preferences.

Entirely neglected in Kevins consideration here is the possibility 
I've mentioned: that the very fact that voters can express 
intermediate ratings, and the near certainty that some do so, 
improves the method performance. I've shown how the presence of 
fractional votes in a zero-knowledge Range 2 voting scenario raises 
the expected utility for *every* voter, i.e., the voter who votes the 
intermediate vote *and* the voter who votes the approval-style vote. 
That seemed paradoxical at first. It no longer seems so to me. It 
increases the chance that the vote is an effective one, flipping a 
result fully, whereas the most that a single voter can do without 
that is shift a loss to a tie or a tie to win; generally, this is 
half the utility increase resulting from a vote which can actually 
change the result from loss to win. Ties are less likely in Range 
(half as likely in Range 2 compared to Approval).

(Adding what amounts to a random offset to what might be generally 
Approval style votes results dithers the output, which can be 
expected to improve results. I don't know about how much this would 
improve absolute utility, though, if it would be significant or not.)

> > That's an objective method of studying voting system
> > performance. Strategy comes in when translating voter
> > absolute utilities into votes.
> >
> > From the absolute utilities, we can generate preference
> > lists, even more accurately than a voter could.
>
>That is the *problem*.
>
>It's useful in that it helps you measure performance, but with Range it
>is a hindrance, because you don't know how accurately voters will
>actually be able to vote.

No, it's purely that it is useful in measuring performance in 
simulations. It does not "hinder" Range, unless you insist on being 
able to predict how voters will vote from their utility profiles. 
There *is* a model for predicting the voter's votes, but it takes as 
input not only their absolute utilities, but also their assessment of 
election probabilities, and this model is far more complex than just 
determining a preference order.

So it's far more difficult to predict the votes, though with good 
models of voter behavior in general, which would be much more than 
anyone has done so far, we could certainly get better at it. However, 
we can still do something, which is explore the *limits* of voter 
behavior. It's a practical certainty that voters will not all vote 
approval style, and they will not all use intermediate votes, and 
they may use various strategies, and have varying assessments of the 
election probabilities, relatively accurate or quite rough. They 
might even use some internal sense to judge which candidates are 
likely to not be moot, and, essentially, exclude them from their 
rating strategy, except perhaps to add them in after the backbone is 
built. I.e., if you decide that the only two likely winners are the 
Republican and the Democrat (in U.S. partisan elections, lucky guess, 
eh?) and you want to maximize your participation in that race, you 
know exactly how to vote for them, for any candidate you prefer to 
both of them, and for any candidate you prefer both of them to, and 
you still have a reasonable option only for candidates in the middle. 
You may certainly vote outside these restrictions, *but it conveys no 
advantage to you in terms of election result.*

This means that it is very easy to vote maximal strategy in Range, 
for the large majority of voters in the large majority of elections. 
A minority of voters will want to back off on the votes for the 
frontrunners, knowing that this has a cost. But with higher 
resolution Range, the cost is negligible, and there are variations on 
Range which make it cost-free to express a "distinction without a 
difference," which really means a preference expressed without 
expressing a magnitude other than zero. There are arguments to not 
allow this.... Borda *completely* disallows it, making all 
preferences equal in value, which is taking the matter to the other extreme.

> > But if I want to increase the accuracy of the vote, which
> > may not maximize my personal utility (it's not likely to
> > harm it much, if at all)
>
>Well, to say it again, one's entire vote is usually completely impotent.
>In general how much will it hurt you to vote for 3rd place under FPP?

We are voting on lotteries, not actual outcomes. Yes, there is quite 
a risk that the vote is moot; it is by far the most common situation. 
However, there are many of us, and we are much more alike each other 
than we are different. However we approach the problem of voting, and 
resolve it with an attempted solution, nearly always, there will be 
many others who do so in the same manner. Hence, collectively, our 
votes are, in fact, powerful. It's not the individual vote, per se, 
but the *approach*. What we do, others will do.

There is an absolute value to election outcome. One of us may be 
paying $10,000 per year in income taxes, for example. How is the tax 
level determined? How is that spent? What value does the voter 
receive for it? Is it a total loss, confiscatory, or is there value 
returned, as with free health care? Improving the personal value of 
the way that government operates -- or reducing the cost in taxes, 
say -- has an individual utility. And there is much more. What is the 
value of freedom? Sure, the probability of the individual's action 
affecting the vote is small. But the cost of voting is not large, and 
the return can be a cumulative one. I don't know that a good utility 
analysis has been done, I do know that many common statements about 
the value of a vote are often based on incomplete understanding.

It's obvious, really. Many people vote, in some places turnout is 
very high, and it's pretty arrogant to assume that they are stupid sheep.

Many people rationally don't vote because they don't see realistic 
utility in it, the options available are too restricted, their 
absolute preference strength between the options is too weak. In 
runoff elections, that can come in two basic ways: weak preference 
indicates nothing about whether or not the voters approve of the 
expected result (generally one of two candidates on the ballot). They 
may approve of both, or neither, they may be pleased (i.e., pleased 
*already*) or not pleased (likewise.) There are two kinds of voters 
who vote in a real runoff: those who have a stronger preference, and 
those who simply vote because they like it or consider it a duty. I'd 
actually advise the latter to skip it: results are improved by not 
voting if you have a significant preference. Voting on elections when 
you don't have any clarity on preference is not likely to improve the 
outcome. But a clear "hunch" or "feeling" may be quite enough. Those, 
amalgamated, can be quite intelligent! Or deceived, to be sure, when 
the election environment has been manipulated by those skilled at it. 
That's another reason why I prefer Asset: far less likely to be 
manipulable through transient spin, sound bites, etc.

>The problem is that an objective comparison (especially one that is
>suitable for all methods) is going to be extremely difficult and will
>always be open to attack when people don't agree with the assumptions.

That's true, but there are objections and there are objections. So 
far, most objections to the approach don't offer any reasonable 
alternative. The models used in Smith's simulations are configurable. 
Don't think the models are good ones? Design better ones.

Note that as long as the models produce reasonable distributions of 
utilities and preferences, they work for the purpose. It's highly 
unlikely that these models will somehow select for a particular rare 
election pathology.

Now, it's true, it would be possible to try or come up with lots of 
different models and try to pick one which makes some method look bad 
and another look good. An obvious example is to use a voter model 
where the voter simply expresses their absolute utility, 
non-normalized to the candidate set on the ballot. This will make 
Range look very good, and most will agree -- who understand the 
approach. Range, voted sincerely, under various definitions of 
sincerity, is a very, very good method. But, of course, real voters 
won't vote these utilities, they will vote differently. Still, it's 
useful to compare methods, because I, for one, and I think others, 
would like to know how voting systems perform where voters are 
motivated to be as sincere as possible, which can be the case in 
highly cooperative environments.

There is no law that says that political elections can't be highly 
cooperative, but if we don't use voting systems that work well in 
such an environment, we may be acting to prevent such an environment 
from arising!

Hence I consider it important to know that Range, with minor problems 
due to normalization, is just about ideal as an election method with 
fully sincere voters, and that many other methods break down with 
sincere voting, under many conditions. Plurality, for example, works 
best in the real situation that many voters don't vote sincerely, 
unless you assume that this is a modified vote with a reduced 
realistic candidate set -- which we have been calling "strategic." 
People vote sincerely in Plurality, especially when write-ins are 
allowed, chaos! But people don't vote that way, for the most part, 
and we only see the chaos of Plurality under special conditions.

>Warren's approach could be useful when:
>1. they simulate realistic voter profiles (and some of them apparently do,
>but again, anyone can argue about whether they really are realistic)

I've pointed out that they don't have to be realistic, only unbiased, 
not warped against one method and for another. So, if someone thinks 
that a simulation is distorting the real behavior of a method, simply 
find an alternate model. If you want to contribute to the field, 
focus only on making the model more realistic. If you want to deceive 
people, possibly even including yourself, try a lot of models and 
pick the one that makes your favorite method look best.

Warren, I'm pretty sure, did not do that at all. If I'm correct, he 
got excited about Range as a result of the simulations, he did not 
pick the models to make Range look good, though it's pretty easy to 
predict that sincere Range will look quite good in utility 
simulations. What wasn't so easy to predict was the effect of 
strategic voting behavior.

People are people, they will argue long past the point of 
rationality, sometimes. But it can get pretty obvious if this is long 
continued.

>2. they simulate nomination strategy that is customized to the method

This, of course, would be more useful. It's *very* tricky. Obviously, 
with the right nomination strategy, Plurality works just fine! So 
what's the ideal nomination strategy? Kevin, it probably uses Range 
polling data. But it would be much more sophsticated than that. And 
what's the goal? Overall SU maximization, or SU maximization for the 
members of the party? And it all depends on the voting strength of 
the party, the loyalty of party members, this is not an easy task.

>3. they simulate voter strategy that is customized to the method

That is relatively easy, and has been done.

>4. they simulate pre-election information

This is necessary for Approval and Range strategy, for sure, so I 
believe this has been done. It can actually be done, in the 
simulations, with perfect strategy, though, obviously, if you take 
this too far, you could run into loops, so I'd guess that the best 
strategy used would assume some uncertainty and would only iterate so 
many times, simulating polls and then shifts in votes as a result, 
then another poll, etc. The "polls" would solicit how the voter 
intends to vote, and the model can assume that the voter can't hide 
the information. After all, just how complicated do we want to make the model?

Heavy use of serious strategization is pretty unlikely with ranked 
methods, in my opinion, most voters will simply do as the method 
implies, rank in preference order, and they can do this a bit more 
easily if equal ranking is allowed. Note that if we have a Range 
method with N equal to the number of candidates minus 1 (Range 1 is 
Approval), this is equivalent to Borda count with equal ranking 
allowed (and a fixed number of ranks instead of Saari's insane 
proposal that incompletely ranked votes be devalued; this, in fact, 
reveals his elitist approach; he wants to force voters to do what he 
thinks best for society; but I'll grant that this is less harmful 
than the mandatory ranking in Australia. At least it more closely 
approximates sincere relative utilities.)

>5. they can simulate other rank ballot formats that allow equal ranking
>and truncation.

They should. Truncation should represent "insufficient preference 
strength," i.e., preference strength below some level that makes it 
difficult to discern. That's with sincere voting. With strategic 
voting, it is determined by effect, and truncation only becomes 
relevant when there is a majority requirement.

To my knowledge, majority requirement hasn't been simulated with 
other than top two runoff, which is a shame, I hope that is correctted.

>In their current state I don't think the numbers can be used except for
>the "sincere" methods and potentially for strategic Approval.

No, there is some data on Range that can be used. However, it will be 
important that more work be done, and independently. Warren should 
publish, not merely self-publish. He may need help, he may need a 
co-author. Or someone else should do it. The Election Methods 
Interest Group could potentially facilitate it, or, more accurately, 
members of EMIG who want to support that would could use EMIG as a 
peer-review device. And then publish based on that, whatever survived 
the process with general support.


> > The comparisons have been done, by Warren. His work is
> > published and should be verifiable. If not, I'm sure
> > that reasonable questions unanswered by his publications
> > could be addressed here or on the Range Voting list. If they
> > couldn't be answered, that would radically impeach his
> > work, wouldn't it?
>
>I've listed deficiencies here and probably there. There are no questions
>that need to be answered. The simulations just need to be improved.
>They need a lot of improvement and I doubt it's worth it to him.

He tends to move on, as do I. We can, collectively, use his work or 
ignore it. Lewis Carroll published what may be the best voting system 
invented, in about 1883. Ignored. What was the cost of this 
ignorance? How different the world would be! Asset is more than a 
voting system reform, it is practically a revolution, though I don't 
know, at all, that Carroll realized it. He was just looking at STV-PR 
and how to fix the exhausted ballot problem, and the related problem 
that STV seeks and needs more information than most voters could 
reasonably be expected to supply. I don't think he went far into what 
would occur to the whole election process as a result, once *fully 
sincere, unconstrained voting* was possible. It becomes 
representation by proxy rather than representation by contested 
election, or at least it approaches that. (The representation could 
be made, in effect, complete, in some Asset systems. And that is, in 
fact, what I'd propose, being quite happy with lesser implementations 
to start.)

>Some of this isn't difficult, it's just again a question of how far you
>take it. Strategic voter behavior needs to be made less ridiculous.
>But what kind of strategy should be allowed, for (let's say) Condorcet
>methods? If everyone votes sincerely, then Range will look bad. So
>clearly the line has to be drawn somewhere else.

No, you'd have to compare sincere Condorcet with some kind of sincere 
Range. The biggest problem with Condorcet is that voters may be asked 
to express preferences they don't have. You'd need to simulate 
truncation, it is very, very real. The Condorcet simulations that 
made sincere Condorcet look good probably did not do this, thus 
squeezing some very marginal information from the Condorcet ballots.

In any case, strategic voter behavior in Approval and Range is not 
only not ridiculous, it's realistic and corresponds to what is needed 
for Rational Utilitarianism, which is probably fairly realistic as an 
intelligent social welfare function utilizing voter knowledge in more 
than one way (preferences, preference strengths, and probabilities).

> > Essentially, poor simulation -- if it is poor -- is better
> > than none.
>
>I'm not sure why you say that.

Because people object to the simulations but have nothing better -- 
and something worse -- to offer. The simulation approach addresses 
performance and frequency of failure and magnitude of failure. There 
is only one other approach that I know of: the use of voting systems 
criteria, and, until Arrow, the holy grail was trying to find a 
voting system that satisfied them all, or at least all "reasonable" 
ones. Later No Harm wasn't among these!

> > If the simulation were designed to make Range
> > look good, that would be one thing. But it appears that the
> > reverse is true: Warren went for Range Voting because
> > simulation work -- as well as theoretical work -- showed it
> > to be ideal, with sincere votes (it must be! -- with the
> > right definitions of sincere). He didn't set out to
> > prove Range was best, he wanted to know.
> > And he wanted to answer the question of "how
> > much." How much is, say, IRV better than Plurality? Or
> > Approval than IRV or Bucklin? Voting systems criteria
> > don't even begin to approach this.
>
>But if we can only accurately measure methods in the case that voters
>are sincere, I'm not sure it's very useful.

I think it is quite useful. Other things being equal, a method that 
works with sincere votes is better than a method which requires some 
kind of strategic voting, but, of course, we need to define sincere 
here. I think it is ridiculous to expect voters to not use 
information they have about election probabilities, and I think it 
makes the job of the voter much more difficult, on average, to make 
this information moot. Avoiding all "strategic voting" is guaranteed 
to make it more difficult to vote, i.e., to make it more complex. 
Election probabilities simplify the voting decisions.


> > It's too much work, and get it wrong, you can seriously
> > regret your insincere votes!
>
>But if you're doing it correctly, you've decided that your expectation
>is better by voting insincerely. You can regret a vote no matter what
>it is.

It depends. In Range, the "regret" is modified by sincerity. Serious 
regret for a sincere vote in Range is unlikely to be deep. You've 
already voted min for a candidate you rmost don't want elected, and 
you've already voted max for your favorite. If you vote approval 
style, your opportunities for deeper regret can be greater, just as 
your opportunity for improving the result can be greater. The sincere 
vote has less variation, that's what I found with an absolute utility 
of voting study. In that study, where it was possible to vote an 
exact intermediate utility, the average relative expected utility was 
the same for the approval style vote (both of them) and for the 
sincere (accurate) vote. But the variation was larger for the 
approval style vote. Choose the wrong direction (i.e., the vote of 
110 or 100 that turns out to waste the vote when it could have 
counted), the outcome could be the worst; get it right, it was the 
best. With the sincere vote, the result lowered the expectation of 
"best," but also lowered the expectation of "worst."


> > I don't think that
> > Warren's work covered this difference: voters who vote
> > strategically are likely to be those who have stronger
> > preferences.
>
>Well, if you vote strategically, you are not "playing nice" for whatever
>reason.

I don't agree. You may be attempting to improve overall results, not 
just your own. And this is a voting system, not a social interaction. 
Yes, being fully sincere -- which can take work -- improves overall 
performance in Range. But it could be more work than it is reasonable 
to expect of the voter, and potential damage from the failure might 
be easy to avert. The damage in Range isn't large. It can flip a 
"best" result to an "almost best" result, not a "best" result to 
worst. (The converse is true: voting sincerely in Range doesn't make 
a large difference in outcome, overall satisfaction, compared to 
voting strategically.)

In some ranked methods, voting with reversed preference can be the 
only hope of a set of informed voters to avoid a disaster, the 
election of the worst candidate, and, if it's a pure ranked method, 
that can represent very strong preference. (I.e, by voting 
insincerely, they secure the election of the compromise. In Range, 
they could do similarly by moving to or toward an approval style vote 
including the compromise. That doesn't involve preference reversal, 
only, potentially, minimization of preference in order to overcome, 
possibly, expected extreme votes from the supporters of the worst 
candidate (from their perspective).

>  (Either you don't want to, or you haven't read the Range Yahoo
>forum and didn't realize you were hoped to.) So it need not be that
>you have stronger preferences, it's just that you don't care about the
>other voters' input.

That can be the case, but it's actually unlikely for most people. I'd 
say that if you have a strong enough preference to express a full 
preference vote in Range, you have a strong enough preference to 
express one. yes. tautology.

It is up to the voter to decide how strong their preferences are, and 
to decide where to express them and not to express them.


>I am not sure if Warren ever argued that strategic voters are more likely
>to be sociopathic (etc).

Not sure what this means. He does use language like that sometimes.


> > > > Now, to prevent the advantage that knowledgeable
> > voters
> > > > would have from being able to vote accurately,
> > should we
> > > > damage the outcome averaged over all voters?
> > >
> > > How is it even clear that it would be damaged?
> >
> > That's what the simulations show, and nobody has
> > controverted that result. It's quite reasonable, by the
> > way, it's not likely to be generally wrong. How
> > carefully have you looked at this work, Kevin?
>
>What I was getting at was again the lack of basis for trying to vote
>accurately. Plus the inability of the voter to accurately determine
>all his ratings. When people use the intermediate ratings, the data
>could be garbage, and we would never know. This isn't a question that
>simulations can answer decisively.

There are strategies for voting accurately, i.e, in a manner such 
that if everyone votes this way, the overall result is maximized. 
*Not* voting this way may improve the voter's individual expectation, 
or, if the voter gets it wrong, can reduces them. I don't think that 
people will use the intermediate recommendations randomly. The will 
have meaning. But it's not truly predictable.

Sure, there are questions that the simulations can't answer. But I 
don't see any big surprises lurking there. We don't know *how many* 
voters in real elections will vote approval style. From polls we know 
that, when strategic considerations are absent, they use them. My 
sense is that *many* voters would vote the same way in a real 
election using Range as in a poll. It's simpler and easier. That it's 
not specifically determinate doesn't change its usefulness. That some 
voters won't express the intermediate ratings does not remove their 
value, generated by those who do. Set 50% or 50%+ as an approval 
cutoff, requiring a majority, and sincere voting will improve, at 
least a little, and majority failure can be detected -- otherwise 
Range has no indicator for it. (Approval does, of course.)