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

[Abd ul-Rahman Lomax]

At 09:51 AM 1/23/2009, Jobst Heitzig wrote:
>I did not mean to say the voter has no opinion. He may well hold the 
>opinion that, say, A is much better than B in some respect, and B is 
>much better than A in another respect, so that neither is A 
>preferable to B nor B to A nor are they equivalent (equally 
>preferable). This is just an ordinary case of what some people 
>pejoratively call "incomplete" preferences. Or the voter may hold 
>the opinion that A is better than B in two of three respects, B is 
>better than C in two of three respects, and C is better than A in 
>two of three respects, so that A is strictly preferable to B, B to 
>C, and C to A. This would be a case of "complete" but cyclic 
>preferences. Or, even more simple, A and B may just be completely 
>equivalent, so that neither is preferable to the other. In all these 
>cases, a "favourite" is inexistent, not just unknown.

Yes. However, this problem actually doesn't afflict Range Voting, it 
is a *voter* problem. In the end, the voter risks his or her vote, 
spends it. How much of the voter's vote will the voter risk?

Put it another way. Suppose the voter can decide the outcome of the 
election by bidding. The voter still has the problem of choosing 
between A, B, and C, but the choice *between* them isn't forced. 
I.e., the voter can bid equally for them. Now, in real elections, the 
voter has something that the voter can "spend" as a bid. It's a vote, 
one single vote. How the voter will spend this depends not only on 
the voter's preferences and preference strengths, but also on 
probabilities of success. That's what VNM utilities are: bids in 
lotteries, determined not only by absolute utilities, but also by 
estimated relevance. The voter doesn't normally want to spend the 
vote discriminating between moot candidates. But if the voter doesn't 
care that much about which of the frontrunners is elected (perhaps 
they are all equally bad, or equally good, in the voter's eyes), then 
the voter may indeed invest the vote in moot pairwise races.

To understand what I mean by investing the vote, imagine a Range 
election with three candidates, A, B, and C. The voter has one full 
vote to invest in influencing the outcome. How does the voter vote? 
It's a fairly straightforward problem in game theory. Let R(A) be the 
range rating of A, similarly with B and C. Arrange the candidates in 
preference order, and we'll assume that they've been named in that 
order, i.e., A>B>C. A "strategic" vote is, first of all, a normalized 
one, so R(A) equals 100% and R(C) equals 0%. Actual votes are V(A), 
V(B), V(C). The vote is distributed as follows: V(A:B) = R(A) - R(B), 
V(B:C) = R(B) - R(C). The Range constraint is that the votes are all 
in the range of 0 - 100%, and V(A:B) + V(B:C) is not greater than 1 
full vote, i.e., 100%. If the vote is normalized, the sum of 
preference strengths is 100%. V represents preference strengths 
between adjacent candidates in the Range spectrum.

If there is a cycle as described by Jobst, how does the voter express 
the votes? We face this problem all the time with choices; in the 
end, a particular choice is worth something to us; the worth is not 
cyclic; we do not, in fact, do Condorcet analysis, we do Range 
analysis. With VNM utilities; we don't invest our resources in moot 
choices. We might not even consider them, but if we do, we don't 
shift our non-moot votes, or if we shift them, we shift them only a little.

The voter determines the vote to invest by effectively multiplying 
the value of a pairwise election, then multiplying it by the 
probability that the vote is effective. (It's a relative probability, 
the actual probability is very low in public elections unless there 
are very few voters.) Voters already do all this; voters don't 
actually do the math, or at least such voters would be rare.

We vote this way in plurality; complicating it is that we have other 
values to satisfy besides election results. However, that's covered 
in the "calculations," if they are complete. It's all about how much 
the voter cares about an election result. If the voter is indifferent 
between A and B, but strongly prefers C to either of them, and A and 
B are frontrunners, that a vote in the A/B pair is the only 
"effective vote," as we would normally look at it, i.e., only A or B 
can realistically win, that the probability of an A result is close 
to one can't overcome the value of the election pair, which I just 
expressed as zero.

But wouldn't this work on the other pair, but in reverse, the value 
is 100% for C, but the probability of "success" is zero?

Sure it would, if the voter doesn't have a value for simply having 
contributed to the vote count for C. Voters who don't have a high 
value for that *don't vote.* However, voters *do* value voting for 
candidates who can't win, we know that. So insignificant value 
between A and B, and high value in voting for C, leads to a vote of 0, 0, 100.

And the vote is sincere. Further, most voters will probably vote 
similarly for frontrunners. They may bullet vote, or, alternatively, 
if they value minor candidates, they, again, may consider the vote 
itself to have value, and in this case, they are likely to vote more 
or less accurately, or even approval style, i.e., we will see some 
voters who prefer Gore, say, voting 100% also for Nader. In doing 
this, they risk electing Nader; but if they'd be adequately pleased 
by that result, even though Nader isn't their favorite, they might 
take that risk. Small risk, I must assume, plus the loss is 
relatively small. They have cast a full vote in the critical frontrunner pair.

Basically, excluding consideration of election probabilities makes 
voting into an exercise in pure abstraction, rather than an efficient 
substitute for full deliberative process with many rounds of voting 
being possible. Attempting to abstract from voters sincere absolute 
utilities may not be desirable at all, besides the detail of it being 
extraordinarily difficult and not even clearly defined and not 
necessarily commensurable unless we make some simplifying (and 
inaccurate) assumptions. Systems where voters are actually bidding 
something of real value, something that costs voters something of 
significant value to them, will encourage more sophisticated VNM 
utility voting, perhaps, but doesn't change the need for strategic 
consideration, a consideration which is part of ordinary, everyday 
decision-making.



> > For a voter that doesn't have a sincere
> > opinion it is also difficult to vote in any
> > way (not just sincerely).
>
>Again, I talk about voters who *do* have sincere opinions which 
>however happen do not fall into the narrow set of possible opinions 
>the voting method's designer cared to take serious. The problem is 
>on the designer's side, not on the voter's. One must not assume that 
>such thiings as "favourites" always exist or that preferences are 
>complete or transitive as long as one cannot prove that this is 
>indeed the case for all voters. And by "prove" I don't mean "show 
>its validity in some arbitrary narrow-minded economic model of utility".
>
>One does not have all these problems when one avoids to speak of 
>"sincere" votes!
>
>Yours, Jobst
>
> > --- On Wed, 21/1/09, Jobst Heitzig <heitzig-j at web.de> wrote:
> >
> > > From: Jobst Heitzig <heitzig-j at web.de>
> > > Hi Juho!
> > >
> > > > What is the problem with
> > > > sincerity in Plurality?
> > >
> > > Well, that's simple: Any voter who does not have a
> > > unique favourite option (whether that is because of
> > > indifference or uncertainty or because of cyclic
> > > preferences) cannot vote "sincerely" in Plurality!
> > >
> > > Yours, Jobst
> >
> >
> >
> > .... and the older mail ...
> >
> >
> > --- On Fri, 16/1/09, Jobst Heitzig <heitzig-j at web.de> wrote:
> >
> > > To determine how I should vote, is that quite complicated
> > > or does it depend on what I think how others will vote?
> > >
> > > Or is my optimal way of voting both sufficiently easy to
> > > determine from my preferences and independent of the other
> > > voters?
> > >
> > > If the latter is the case, the method deserves to be called
> > > "strategy-free". The whole thing has nothing to do
> > > with "sincerity". Refering to
> > > "sincerity", that concept in itself being
> > > difficult to define even for methods as simple as Plurality,
> > > complicates the strategy discussion unnecessarily.
> >
> > Are you looking for the English language
> > meaning of sincerity or some technical
> > definition of it (e.g. some voting related
> > criterion)? What is the problem with
> > sincerity in Plurality?
> >
> > Juho
> >
> >
> >
> >
> >
> >
> >
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