[EM] Why the concept of "sincere" votes in Range is flawed.

[Abd ul-Rahman Lomax]

At 02:58 PM 11/25/2008, Michael Poole wrote:
>Your definition is wrong.  A strategic vote is one that is not
>representative of the voter's honest views or ideal outcome.  When
>using strictly ranked systems (where no ties are allowed), the only
>possible form of insincerity is order reversal.  When using approval
>and range voting, preferences may be insincerely magnified or diluted,
>in addition to being reversed.

Mr. Poole, I think you should look at the old definitions. Take a 
look, also, at James Arymtage-Green's efforts to consider whether or 
not Approval Voting satisfies the Majority Criterion. He has to stand 
on his head to come up with a definition of "sincere" that makes Approval fail.

"Insincerely magnified or diluted" implies that there is a "sincere 
expression," which is then not expressed. Preference reversal is 
certainly possible in Approval and Range, but provides no advantage 
to the voter.

How did it come to be that a political scientist like Brams would 
claim, in his early publications, that Approval was strategy free? He 
claimed that within the context of the time, simply. It was free of 
what was called strategic voting at the time. But what I'm pointing 
out here is that it is *still* free, if we are careful about what we 
mean by "strategic voting," which, it turns out, must mean preference 
reversal. Otherwise what the voter has done is to consider a 
preference of no importance, either because it is small in absolute 
terms, or because one of the options is unlikely and the voter does 
not want to waste voting power expressing a moot difference.

(Note that it is possible to design a ballot and method where full 
and accurate preferences are expressed without loss of voting power; 
I've suggested how to do this many times; it's pretty simple. One 
method would be a preferential ballot where one ranks the candidates, 
equal ranking allowed (that means no preference, true indifference), 
*and* rates them. It would probably be sufficient if there were a 
"plus" indicator, as in the voting method A+ that I proposed years 
ago. I.e., you mark a candidate Plus if you have rated another 
candidate the same, to express that you prefer this candidate over 
the other. Yes. That would only allow two ranks at any rating, but 
that is quite likely to be adequate for public elections. Plus could 
be a necessity in some places where laws allocate ballot position 
with an assumption that voters have voted only for their favorite. 
Bucklin, with equal ranking allowed, would be similar to Plus, for 
most practical purposes. (Bucklin won't find a supermajority winner 
if there is a majority one, unless equal ranking is allowed; it could 
still fail.)

What Approval sincerely represents from a voter is a *decision* as to 
where to place an Approval cutoff. Once the Approval cutoff is 
determined, the vote then follows from preferences in comparison to 
the Approval cutoff. It is easiest to understand this with Approval, 
without the complications of Range. What I've seen from those who've 
written on this, as Mr. Poole wrote above, is that they do not define 
"magnified or diluted." How do we determine if a vote has been 
"magnified or diluted?" Is there any absolute Approval cutoff, so 
that we could know if a voter has either voted for a candidate that 
the voter really does not approve of (diluted) or has not voted for a 
candidate who the voter actually approves (magnified)?

>As a thought experiment, consider the case where I would score three
>candidates as 100, 50 and 0 on a uniform scale.

Would under what conditions? That's the whole point I made! Did you 
read the quoted material? Those are, perhaps, absolute utilities? 
Which aren't commensurable, by the way. Okay, I'll assume that they 
are absolute utilities normalized to the same scale, perhaps a scale 
of 0 to 100. But what about probability assessment? Voting is a 
real-world collective decision-making method, and to expect it to 
ignore expected probabilities is to ignore how intelligent creatures 
operate. We pay no attention, for the most part, to irrelevant 
alternatives, we don't invest in them, would be a more accurate way 
of saying it.

I'm not convinced that it is useful to discuss this until the 
underlying problem is recognized. Where did these 0, 50, 100 scores 
come from? What is that scoring sincere and 0, 1, 100, or 1, 99, 100 
is not? The latter might be von Neuman-Morganstern utilities. They've 
been adjusted according to outcome probabilities. von 
Neuman-Morganstern utilities, if I'm correct, preserve full 
preference order unless a probability goes to zero. I still prefer 
the million dollar tax credit over the $100 one, but I'm only going 
to put miniscule voting power into it, and my assessment of the 
likelihood that the option is a meaningful one is so low that it 
probably would not be expressed in any practical voting system. I'd 
vote 100% for $100 and also for $1,000,000. But if I can vote the 
accurate utilities, it might be $100, 99.999% and $1,000,000, 100%.

>   If I know that the
>first two candidates are close in the polls, I may vote for them as
>100, 10 and 0 so that my preferred candidate's chance of winning is
>increased.  This is a strategic vote in the usual sense.  You attempt
>to redefine "strategy" so that it is not called one.

That is not a strategic vote in the original sense. Please translate 
this into Approval and look at it. And lets make the supposed sincere 
utilities be 100, 90, 0. Note, as well, that these utilities are 
truncated and normalized, almost certainly. Are there other possible 
candidates with utilities outside that range? With VNM utilities, it 
doesn't matter. A zero probability of election, and infinite 
resolution on the utilities, means that a new candidate with very 
small probability can be inserted without significant shift to the others.

Now, how would an Approval voter vote? Where do we put the Approval 
cutoff? There is no absolute reason to set it at 50%. Nor is 
"sincerity" any guidance. What if the voter was a strong supporter of 
someone who didn't make it through the primaries, so the utilities of 
the candidates in the election, on the ballot, are really 50, 45, 0.

How do we decide to "accept" an offer, or to "approve" an outcome? We 
compare the offer with what we think we can get! I.e., we consider 
probabilities. In Approval Voting, we are casting a vote accepting 
the outcome of an election of any one of a set of voters. How do we 
choose which candidates to include in this set?

Surely it depends on who is running, and our perception of what the 
electorate may realistically approve. If I have a choice between the 
absolute best candidate in the world, in terms of my personal 
expectation, and someone who is merely good, better than average, 
etc., or maybe even better than anyone who has ever been elected to 
the office, and I think that if I can get the best, I'll vote for the 
best. If I might get something worse than the good candidate, if I 
don't approve of him or her, then I'll vote for both the best and the 
good. And in a good method, I can say that I prefer the best and, at 
the same time, not risk failing to elect the good by giving the good 
insufficient votes. (Pure Range, quite simply, doesn't do this, nor 
does pure Approval, but it's easy to add: the question is whether or 
not that additional preference information is sufficiently valuable 
to be worth the trouble. I think it is, actually, though with 
high-resolution Range, it's probably moot. (I consider 0-100 to be 
high-res.) I'd sacrifice 1/100 of a vote in order to express a 
significant preference, and the probability of this causing a poor 
outcome is truly minute,  not worth worrying about.

>Rambling about ideal abstractions,

Moi? Ramble? I'm looking for constructive criticism, not personal insult. Ahem.

(Comment added later: I dish some back.)

>  inevitable voter knowledge, and so
>forth does not change that it is a distortion of my honest ratings
>based on desired outcome and beliefs about other ballots.  Strategic
>voting works *only* in the case of (believed) knowledge about how a
>significant number of other voters vote.

Consider a vote as if it were a bid. You have so much to spend. You 
can split your money between campaigns. The campaign that collects 
the most money wins. Now, who in the world is going to say that your 
"vote" is insincere?

You've posited sincere utilities that can be simply translated into 
votes. That's a myth. Smith uses, in his simulations, utilities that 
are generated according to models; these, then, can be used to 
predict voter behavior. In some models, voters know who the 
frontrunners are and they vote depending on this information. Such 
models are far more realistic than models which assume fixed 
utilities, unmodified by probability information.

Yes. "Strategy" is required, i.e., smart voting. A voter who isn't 
smart may waste his or her vote. That, actually, might be a good 
thing, it may improve overall outcomes. Remember, we are talking 
about voter expectations, but some voters know more about what 
candidate will be good, overall, and some don't. Many vote contrary 
to their own real interests, being deceived by propaganda, or are 
simply ignorant. In no way would I suggest that such voters should be 
deprived of power. But neither should I take it as tragic that such a 
voter, with plurality, votes for a candidate with no chance of winning!

But "strategy" is not the same thing as strategic voting as was used 
in the study of voting systems. The concept of "exaggeration" of 
preference strengths didn't exist, and that's what Mr. Poole has 
presented as an example. His example did not distort preferences, but 
Range allowed the voter to decide what choices, what pairwise 
elections within the voters' preference list, were more important than others.

>If you delude yourself into thinking otherwise, and on that basis
>convince yourself that range voting does not suffer from -- or even
>permit -- strategic voting, you will only undermine your own
>credibility.

Horseshit.

Does this writer from Trollus.org imagine that I'm going to conceal 
what I think and know because he imagines I'm deluded and threatens 
me with loss of credibility? Who, indeed, is deluded?

Here is what I'd suggest to him. He should read what I wrote, read 
about von-Neumann Morganstern utilities and the work of the authors I 
cited, and also do a little research into the history of Approval 
Voting and strategic voting. And try to understand these before 
imagining that he can truly criticize them. Dhillon is going to be 
tough, Smith wrote that the paper used "notation from hell." I don't 
expect readers to understand the details of Dhillon, and Dhillon's 
claim that Relative Utilitarianism (which we might as well call Range 
Voting) is a unique solution to a modified set of Arrovian conditions 
has not necessarily been verified, and I certainly can't follow their 
proof. But what von-Neumann Morganstern utilities are is not so 
difficult, and the claim is, and it seems to be widely accepted, is 
that summing these is a mathematical simulation of how we (and 
presumably other intelligent creatures) make decisions, individually. 
We do not use pure preference lists; rather we use, as Smith has 
claimed many times, something like Range Voting, and the "votes" are 
modified by probabilities, we do not invest our resources in 
preferable outcomes that are improbable, even if we maintain an 
awareness that they are preferable. Pure VNM utilities do maintain 
preference distinctions.

Then, if we normalize these utilities, following the democratic 
principle of one person, one vote, we can make collective decisions 
in the same way. Not perfect, because of that normalization, 
actually, and also because of defects in how we estimate 
probabilities. But probably as good as we can get.

Look, suppose a society says to a person, it's up to you, which do 
you prefer, A or B? This is the situation in every election where 
your vote will turn the election. (In a Range election, one vote can 
actually turn the election, whereas in most whole-vote methods 
(including Approval), one person can't change a winner from one to 
the other, but only from one to a tie, or a tie to the other.) In a 
close Range election -- the only one where your vote counts, 
actually! -- society is essentially saying, "We are, overall, 
indifferent between A and B. So you choose." Now, what is a "sincere 
vote" under those conditions? Because the issue of probabilities is 
removed, we get pure choice. Which is *not* pure utilities. The voter 
will vote to produce the outcome that the voter desires.

Our voting systems work because every voter may be in that situation, 
which is most likely if they are voting in a certain way. And 
standard Range and Approval strategy encourage them to do exactly 
this: assume that your vote counts, and vote that way. This means, 
quite simply, voting 100% for one frontrunner and 0% for the other, 
almost no matter what your supposed "sincere utilities" were for 
them. Unless they truly are equal, and both acceptable, in which case 
you can thank your lucky stars that you were facing such an election, 
I've never seen one in my life.

So some voter who votes, for two frontrunners, 100% and 99% -- 
FairVote posits a whole electorate of 99 voters who vote like that, 
except for one, who votes that nasty strategic vote of 0% and 100% -- 
is saying, well, we have a "slight" preference for one. But, really, 
we don't care enough to make a strong vote for that. The "strategic 
voter" is faced with a choice, and makes it. And thus, supposedly, 
the decision is made by that last voter who, the critics posit, was 
really the same as the others, having a very slight difference in 
preference, only reversed. The whole thing is preposterous. If those 
are really some kind of sincere, absolute utilities, *it does not 
matter which candidate wins,* it is almost the same. If you care, 
vote strongly. If you don't care, you can vote however you like! 
Also, if a candidate has little or no chance of winning, and this 
candidate is neither the best nor the worst, you can vote however you 
like. But -- don't vote so that if you were wrong, and the candidate 
wins, you will regret it, and try not to vote so that if someone 
worse than that candidate wins, and this candidate would have won if 
you voted more strongly, you will regret it.

(If an election has two candidates, and Range Voting is allowed, 
which means fractional votes are allowed, and voters decide to vote 
fractional votes in the election, they are making partial 
abstentions, they are saying, to some degree or other, "We don't 
care." So if they say that, presumably, they will not complain if 
someone who *does* care makes the decision.)

I'm approaching this from a theoretical standpoint, on the one hand, 
and from a practical point of view, with respect to how people make 
decisions, on the other. Smith has approached the study of voting 
systems from another, using simulations. Generally, the results 
agree. The work of Dhillon and Martens is known, and has seen some 
quotation in the literature, almost entirely in the field of 
economics, as far as I know.

It's true that if voters could vote what Smith has called "fully 
sincere" utilities, that this would maximize overall "sincere 
utility." Voting "strategically," where every voter shifts the 
utilities to maximize their personal expectation, must, therefore, 
lower overall satisfaction with the result.

Note that for this to be fully true, the utilities must be 
commensurable and absolute (or all modified by the same factor from 
absolute). This would be utterly insane and probably impossible in 
real elections. The assumption is made, instead, that the possible 
range of satisfaction of every voter is the same as for every other 
voter, the utilities are normalized to fit into one full vote and, 
usually, they are also truncated to the election set before being normalized.

By the kind of arguments Poole has presented -- and he's certainly 
not alone -- I would be required, if I added the name of an obscure 
candidate whom I personally consider to be the absolute best by far, 
to lower the utilities of all the other candidates (except for the 
worst, of course). And then, at the other end, I could dredge up a 
truly bad, awful, horrible candidate, and thus would be forced, to 
maintain my vote as sincere, to raise the votes of all the others. 
Since these candidates aren't realistic possibilities, what I've done 
is to, for no good reason except making a statement irrelevant to the 
outcome of the election, weaken my vote.

As I've said, perhaps people who weaken their votes in that way 
should be allowed to do just that, society can benefit from this. But 
the ballot instructions will not say, "Vote sincerely." They will say, "Vote."

(It's simple with Approval, "Vote for any candidate you choose to 
support for election. The candidate with the most votes will win." 
But for various reasons, we may need more than pure Approval; people 
want to express first preference, for example. Hence Bucklin may, 
indeed be a way to go, or some other hybrid.)

Approval probably will function in public elections well enough that 
the difference with higher resolution Range is academic.