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

[Abd ul-Rahman Lomax]

At 12:42 AM 11/26/2008, Kevin Venzke wrote:
>--- En date de : Mar 25.11.08, Abd ul-Rahman 
>Lomax <abd at lomaxdesign.com> a écrit :
> > If we must have a
> > single ballot, and a single winner, period, Range Voting is
> > actually a trick: it is the only relatively objective method
> > of assessing the expected voter satisfaction with an
> > outcome, turned into an election method. It's ideal
> > because it's designed that way. (The only fly in the
> > ointment is the charges about strategic voting, but I've
> > been arguing that this is based on a total misconception of
> > what we are doing when we vote.)
>
>I don't understand how you reconcile the two ideas here. Range is
>"objective" and "ideal because it's designed that way" based on the
>idea that voters have internal utilities and, if they vote them exactly,
>under Range voting, the best candidate according to overall utility
>will be elected every time.

I've responded to this in a prior post, the first 
part of it. I did not make the claim that Range 
Voting was "objective." It is a voting method and 
does not automatically choose the best candidate 
according to overall utility, neither in 
simulated elections with practical methods, not 
even if we assume "fully sincere voting."

It simply gets closer than any other single 
ballot method. Of the methods that have been 
tested through the simulation process, the only 
method that beats Range, if I'm correct, is Range 
with a top two runoff. Not a single ballot 
method, not even considered a voting method by 
many definitions. Arrow, in particular, made 
"deterministic" one of the preconditions for his theorem to apply.

In the simulation process, absolute personal 
utilities must be converted to Range votes, for, 
with practical election methods, it's probably 
impossible to vote absolute utilities, even if 
people wanted to. The conversion process usually 
takes the preference list for candidates 
considered real options and looks only at the 
range of utilities among those candidates. While 
a voter *might* decide to extend the "coverage" 
of the voter's vote, this is not what we normally 
do when we are asked to make a choice. We 
restrict our consideration to the practical 
possibiities. This normalization process, to some 
degree, makes the same "mistake" as preferential 
methods do, it equates what may be a small 
preference with what may be, with another, a 
critical or crucial preference. Hence Range 
Voting which depends on this normalization can 
fail to find the truly optimal winner. It pleases 
some people with little preference at the cost of 
greater absolute preference satisfaction for others.

If readers have been following this, they would 
know the answer to this question: but what if 
voters exaggerate their preferences when they 
vote? That is, of course, a possible objection to 
Range Voting or to the study of real election 
results based on, say, polling data. The 
simulations avoid this entirely, by *assuming* an 
underlying preference profile.

This underlying preference profile could get 
quite sophisticated, but making it more accurate, 
as to how real voters make voting decisions, 
would probably not change the results 
significantly. Good election methods should be 
able to handle the kinds of voter preference 
profiles that are used in the simulations, those 
profiles aren't biased toward Range Voting. (And 
the profiles make sense in restricted 
environments; that real people use more complex 
criteria in determining their preferences doesn't 
change the usefulness of the approach. The goal 
is not to simulate *people* and predict real 
election results from, say, an analysis of 
positions, popularity polls, etc. Rather it is to 
study how election methods perform under reasonably realistic assumptions.

So let me be specific, though we will get back to 
this. Range Voting isn't perfect. It does not 
always choose the best winner. When it does not, 
it is sometimes possible to detect the situation 
and fix it; that is why Range Voting with Top Two 
runoff gets lower regret results than Range 
alone. It detects the relatively rare situations 
that cause Range to fail to find the ideal 
winner. And in my opinion, Runoff Range is not as 
accurate in the simulations as it would be in 
real life; that's because real runoffs test 
*relative absolute preference strength,* free of 
strategic considerations (when write-ins are 
involved, this isn't totally true.) This effect 
is something which has been largely overlooked. 
Or even totally, as far as I know. It's original 
with me, but it's likely someone else has written 
about it somewhere. I don't consider it rocket 
science, just something obvious that's been overlooked.

So TTR Range is better than Range. Range is not 
perfect. Period. It is simply better, as studied 
through this approach, than any deterministic 
single-ballot method that is commonly studied. 
(To get better, one has to find a way to 
facilitate and encourage "fully sincere voting." 
That may be an extraordinarily difficult problem, 
but auctions can do it. Isn't that called a Clarke tax?

(Consider this proposal: One your ballot, you 
indicate what percentage of your income you will 
pay as tax for the next year. It is not an 
absolute amount, because that leads to 
plutocracy, or at least that is claimed. 
(Libertarians might prefer a dollar amount, but 
it's the idea I'm exploring here, not the 
details, I'm just trying to propose some 
reasonable ones. It's even possible that some 
more complex tax structure would be involved, 
where you would vote a *bracket,* designed to 
make the difficult of "voting" in this way the 
same for all voters.) These would be, we can 
presume, absolute utilities, converted to income 
percentage values. So a voter with little 
preference would not, presumably, be willing to 
pay much, and a voter with a large preference 
would, again, be willing to pay more. It's an 
auction, so the amount actually paid would 
presumably be lower than the votes. The maximum 
vote might be limited. How much would I have been 
willing to pay to avoid the election of Bush? In 
2000, a decent amount. In 2004, probably the 
maximum vote allowed (there might be a limit at 
100% of income, or some lower or higher figure). 
In 2008, to avoid McCain, less, probably. Bush 
was *really* bad, so bad that prominent 
conservatives were complaining, and so concerned 
that McCain would have continued poor Bush 
policies that they recommended Obama. But I don't 
think McCain would have been anywhere near as bad 
as Bush was. In 2008, though, a lower vote was 
probably necessary to elect Obama, because he was 
so popular. I was wondering when he was going to 
bring out the loaves and fishes, with many 
others.... Obama is so popular that he's 
dangerous. Not as a specific criticism of him, 
but generically. It is even more important now 
that we make it possible for the public to get good and trustworthy advice....)

>At the same time you want to defend Range against the charge of
>susceptibility to strategic voting, essentially by denying that the
>Range voter is supposed to be mapping his true, absolute preferences
>onto the ratings.

That's right. Range results shift, and they shift 
to increase regret, when voters vote 
"strategically." This is well know, but it's an 
error to consider this a reason to avoid Range. 
If, with realistic voting profiles, they shifted 
results to make Range worse than other methods, 
it would be one thing. But they do not, if the 
simulations were accurate. Nobody has challenged 
Warren's results. Yee diagrams are a similar 
approach. Nobody has contradicted the basic work, 
even though it is all published and source code 
is available, etc. Instead, we see criticism that 
often misunderstands the basic nature of the study.

The voter *does* map his true, absolute 
preferences onto the ratings. Kevin, you are not 
being careful. There is, in theory, a one to one, 
continuous, monotonic transformation of absolute 
voter utilities (not "preferences") to Range 
votes (neglecting roundoff error, which makes the 
function a step function, still monotonic.) 
That's why we can, with a reasonable definition, 
still call these votes "sincere," since they do 
not violate the derived preference profile of the 
voter. All that they do is to, possibly, equate 
the vote of some candidate pairs when there is a 
non-zero preference strength between them, and 
that is larger than the Range resolution. In 
other words, the voter thinks that, given all the 
conditions, the voter exercises more effective 
voting power elsewhere and -- presumably -- will 
not regret the abstention from voting in that 
candidate pair. This is quite what we routinely 
do with real world choices under analogous 
conditions. We do not bid on things in auctions 
based merely on cost, when we have a limited 
amount to bid. I won't go into describing such an 
auction, but we factor in the probability of 
success, and we put our limited auction dollars 
into the preference pairs that seem more likely 
to be a good investment. But we never try to pay 
*more* for a candidate that we prefer *less.

The transfer function, thus, is monotonic but not 
linear. With "sincere absolute preferences 
normalized to the voting Range," we'd get a 
limited regret-minimized result, and there may be 
some voters who decide to vote this way. I'd not 
advise it, though it's relatively harmless. It 
improves the overall outcome at small cost to the 
voter. (By definition, if the cost is large, the 
sincere preference is large.) In real world 
collective decision making on a small scale, we 
often do exactly this: we reveal our sincere 
preferences in absolutes, where possible, or, at 
least, in terms of preference strength across our personal profile.

So is Range Voting "vulnerable" to strategic 
voting? What does that mean? In practice, it is 
used as a voting system criterion and a black 
mark against Range Voting. But the "harm" done is 
simply institutionalized by other voting systems, 
and the possible improvement through accurate 
expression of absolute preference strengths 
(within the limitations) is made impossible. 
Which, of course, harms the results even more. In 
order to avoid the bete noir, strategic voting, 
which has been redefined to include any failure 
to accurately disclose a sincere preference, 
voting systems students would avoid the only 
method which *minimizes* the effect of such, and 
allows it to operate only where it is relatively harmless.

The simulations answer the questions of "how 
much" and "how often," which cannot be answered 
through the prior approach, the use of voting 
systems criteria. Approval Voting fails the 
Majority Criterion, according to the usual 
interpretations (which had to be modified to 
apply to Approval Voting, and, clearly, the 
modifications were designed to *cause* Approval 
voting to fail, because the students thought, 
intuitively, that it failed. That's what I mean 
by subjective analysis! See James 
Armytage-Green's study and application of the 
Majority Criterion to Range Voting).

Okay, how often? It would be extraordinarily rare 
in real public elections, because it requires a 
significant number of voters to vote for both 
frontrunners, which is the opposite of standard 
Approval strategy and is, normally, a foolish 
vote if the voter does have a significant 
preference between them. And if the voter doesn't 
have a significant preference, well, there you go. See the second question!)

And how much damage from failure? Little. When 
the Majority Criterion fails, we have multiple 
majorities. The majority has Approved another 
candidate as well as their favorite, and, 
together with other votes, this less-preferred 
candidate has broader support. Is that bad? Many 
would argue it's good, and this again points out 
the subjective nature of the use of voting 
systems criteria to judge election methods.

It's easy to show that there are reasonable 
situations, in real life, where the Majority 
Criterion, if followed by a voting system, would 
prevent the voting system from choosing a winner 
which the vast majority of people -- not voting 
systems experts attached to some other method and 
holding on for dear life to preposterous 
arguments -- would agree is a better outcome than 
the majority first preference.

Quite simply, to make sound decisions from 
preference profiles, we need to know preference 
strength. Preferential ballots can, sometimes, 
approximate this (Borda does that, and works 
better if there is a broad spectrum of candidates 
on the ballot, thus creating, in the real 
preference pairs, an approximation of preference 
strength), and usually the majority preference 
will also be the ratings winner. But a Range ballot directly expresses this.

How about an ideal ballot, no matter what the 
method? Set aside the complexity issue, it would 
obviously be a Range ballot that allows the 
expression of small but significant preferences. 
To be ideal, it must allow the expression of 
equal preference and not force one choice or the 
other. If there were some way to do it, it would 
allow expression of absolute utilities, but I'll 
set that aside and assume that it only allows 
expression of preference on the range of 0-1 
vote. (In fractional increments, of course.)

This ballot contains far more information than a 
pure preferential ballot. *How* the information 
is used is another story. The ballot could be 
used for any preferential voting method, for 
example. The simulations essentially do this. But 
once preference strength information is 
available, and through averaging, even if many or 
most voters vote Approval style, as in some cases 
strategic considerations suggest, we should 
remember that Approval is a Range method and the 
votes in Approval will tend to average out to 
what more "sincere" Range votes would be, as 
voters make different decisions about where to 
put their approval cutoff. Because the voters are 
spread across the spectrum, Approval Voting can 
measure underlying preferences just as an analog 
to digital converter which can only indicate 
whether a signal is higher or lower than a 
reference voltage can measure the signal voltage 
at far, far higher resolution than 0 and 1 would 
imply. An input signal can be compared with many 
random references and the number of *hits* (0 and 
1) results can then estimate the input signal 
value. Here the "input signal" is the average 
approval cutoff position in the candidate spectrum.

In other words, since we are going for 
amalgamation anyway, that individual voters can't 
express fine preferences, but only 0 or 1 for 
each candidate, has less effect on the outcome 
than it does on the individual voter behavior.

If we really wanted to know how election methods 
other than Range were performing, we'd use a 
Range ballot. This may actually be practical in 
small or even large nongovernmental 
organizations. Short of using a Range ballot, 
we'd use a Range poll, as an exit poll (preferably), or as a pre-election poll.

And, of course, we'd compare these results with 
simulation predictions and eventually we might 
build up enough data to confirm or improve the 
models. The problem with this approach for the 
short term is that the simulations can study 
thousands of elections and thus see the behavior 
of a voting system under many different 
conditions, whereas the actual experimental 
approach, with a lot of effort, only shows one 
instance. Useful, still, but probably best used 
to improve the models used in simulations.

>If the idea of a sincere set of ratings irrespective of context is "a
>total misconception of what we are doing when we vote," then what useful
>theory is Range based on? What makes it "objective" and "ideal" if not
>what I stated above?

It does not depend on relatively subjective 
considerations like which voting systems criteria 
are more important than the others. It defines an 
optimal winner in a manner that, once understood, 
most people would agree is reasonable, and that 
matches how we make decisions, when we are sane 
and collectively functional, in real life. The 
approach defines the "ideal winner" in a way that 
works when we know absolute utilities, and there 
is no reason to expect that it would stop working 
simply because the utility profile can't be 
directly determined. (It works when we can see it 
and test it, why would it stop working when we can't?)

There is no usable definition of "a sincere set 
of ratings irrespective of context," because 
there is no way for voters to even determine such 
in a manner that they could vote them. The 
ratings that we can determine, in practice, are 
not absolute, independent ratings. Now, as I've 
noted, it's not totally possible, but we have to 
go far beyond an ordinary voting system to do it, 
we probably need an auction of some kind, or 
perhaps voting on lotteries, and I'm not going there now.

We can approach, this, though, in certain 
respects, through runoff elections, and we can 
approach it through binary choices in sequence. 
In a binary choice, we can assume sincere 
preferences are expressed, there is little reason 
to do otherwise (I'm not ruling this out, there 
might be under some usages, a turkey-raising 
motive, but that's in a fixed and predictable 
series of votes. Highly dangerous in standard 
majority required process, particularly where no 
candidates are eliminated -- i.e., with standard 
Robert's Rules of Order decision process. I keep 
mentioning this because, without it, I know that 
many critics will think I'm describing some 
bizarre creature, never used. Wrong. Actually, in 
very common use, just not in public political 
elections except certain ones which take place, 
for example, at Town Meeting. Majority of a 
quorum required to make any decision.)

>I also wonder, what, theoretically, does it look like when Range fails
>and gives a poor result. Is such a thing allowed?

Well, what's a "poor result"? My claim is that 
the only way to objectively study this is to see 
how the method performs when absolute utilities 
are known. That's what the simulations do, the 
"know" the absolute utilities by assuming them, 
in some hopefully reasonable way. (Don't think 
it's reasonable? The simulators are configurable. 
Use a better simulation of underlying utilities! 
Until then, Warren's work is the best we've got!)

Now, following Warren's work, Range would very 
rarely give a truly "poor result." It would take 
some very bizarre preference profiles. You can 
construct them .... but for them to occur in real 
life would be practically impossible. What it can 
do, and the simulations show it, is to miss the 
true ideal winner according to the normalization 
of absolute utilities, and, as well, due to the 
non-linear expression of utilities (but still 
monotonic) by voters seeking to maximize the 
effect of their vote. However, when it does this, 
it would not then flip to a much worse candidate, 
unless, again, the conditions were truly bizarre. 
It would simply choose, in almost every 
simulation (quite likely all or nearly all), the 
next best winner, and the best would be in second place.

That's why top-two runoff Range is better at 
picking the ideal candidate than Range alone. 
When Range fails, it picks a candidate who is 
second best, almost always, with any kind of 
reasonable preference profile. And then sincere 
preference in a runoff *may* pick the better 
candidate. Not always. What's the better 
candidate? Is it the majority preference or is it 
the absolute utility maximizer, or the relative 
utility maximizer? Or what. Until you can answer 
this question, how we decide what is a poor or 
suboptimal result, whatever claims you might make 
about poor results are *purely subjective.* These 
standards are different. Probably the "best" is 
the absolute utility maximizer, because what goes 
around comes around -- on average -- but the 
runoff procedure tests for the majority 
preference. Usually the same, but not always.

In real life, though, the majority will surprise 
us. The runoff will have different turnout than 
the original election, and some voters will 
change their votes, and both of these effects 
will favor the *fully sincere, absolute* Range 
winner over the majority preference, because, in 
this situation the majority preference must be 
weak. So only if the normalization or strategic 
voting have sufficiently distorted the Range 
results, I'd predict, would the apparent Range 
winner fail to win the runoff. You hold the 
runoff, indeed, because of this possibility, the possibility of distortion.

Are you starting to see this, Kevin? I'm not 
writing just for you, as I assume you know, and 
much of this, I'd think, you already understand. Or did you? Or do you?