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

[Abd ul-Rahman Lomax]

At 08:03 AM 11/26/2008, Michael Poole wrote:
(I may not have separated this out correctly, attribution may be 
incorrect. Paragraphing and quotations were largely lost, somewhere 
in email formatting.)

>Jonathan Lundell writes:

>"Sincere" is a term of art in this context, not a
> > value judgement. An insincere vote is simply one that does not
> > represent the preference of the voter if the voter were a dictator.
> > There's nothing *wrong* with voting insincerely (or, equivalently,
> > strategically), in this sense; a voter has a right to do their best to
> > achieve an optimum result in a particular context.

>---- "Sincere" is fine as a term of art.  The limitation with 
>"sincerity" under that definition is that it only applies to the top 
>N choices in an N-winner election.  Most strategies involve 
>manipulation of lower rankings. Abd's post made the error of 
>conflating insincere voting with strategic voting, and the further 
>error of claiming that neither approval nor range systems are ever 
>vulnerable to strategic voting -- rather than restricting the 
>hypothesis to sincere votes.

Actually, I didn't conflate them, I found them conflated. Notice the 
subject header: "Why the concept of "sincere" votes in Range is flawed."

I did not claim that Range or Approval were never "susceptible to 
strategic voting." In fact, I noted many times that strategic voting 
-- which must be properly defined, something that Mr Lundell has not 
contributed to, at least not here -- negatively impacts Range results.

"Strategic voting" has a different meaning with Range Voting than 
with all other methods (for the moment, consider Approval as a 
special case of Range).

With ranked methods, strategic voting always refers to preference 
reversal. (Strategic, in the ordinary sense, would include voting 
"sincerely," i.e., straight preference, when this is advantageous, 
but the word is used to mean preference reversal, which is clearly 
what is described as an insincere vote.)

Thus "insincere voting" and "strategic voting", with ranked methods, 
were synonymous.

But Approval was designed to be strategy-free, and was asserted as 
such by some very smart people. If it was vulnerable to "strategic 
voting," what happened? Well, the definitions shifted. From 
insincere, preference reversal, strategic voting, the word 
"strategic," in its ordinary meaning, was expanded to mean a planned 
vote, one which is altered from some presumably *more sincere* vote, 
we might consider this "more sincere vote" a zero-information vote, 
because of assumptions or knowledge about how other voters are 
expected to vote. I.e., no longer zero-information. In Approval, not 
insincere, still can be reasonably called "sincere," but not "fully 
sincere" in the sense of disclosing some information. Which, in 
Approval, may be impossible to disclose anyway.

In Range we confront the problem more directly, because the method 
may allow the expression of accurate relative utilities. If the voter 
does not accurately express those utilities, is it an "insincere vote."

Many of the writers on Approval used the term "sincere vote." But 
other writers pointed out that in Approval, there was not just one 
"sincere vote," there was a whole family of them. But they all do not 
reverse preference, they merely fail to disclose some preferences, 
perhaps. So this isn't insincerity, these "strategic votes," it is 
merely not full disclosure. With Approval, the voter is forced, by 
the severe restriction on allowed ratings, to conceal some 
preferences. Which ones does the voter conceal? Naturally, the voter 
conceals preferences considered moot! Or the voter can vote 
zero-information, which means that the voter is essentially unlikely 
to exert full voting power. The vote will be sincere, but which 
sincere vote? It's better to have the information and use it! It 
provides guidance as to how to vote.

I call Range votes that aren't merely mistakes, intrinsically 
sincere. That does not contradict their being stratgic. They are 
intrinsically sincere in the same sense that reasonable Approval 
votes are, they disclose basically the same information. That is, we 
can determine from the votes, preference order, with possibly some 
missing (conflated) ranks.

 From an Approval ballot, I can see that candidates are divided into 
two groups: and all the candidates in one group are preferred to 
candidates in the second. That's a sincere expression, and there is 
no preference reversal that can confer an advantage. This is what the 
original claim that Approval was strategy-free was based on. It did 
not mean that there was no strategy involved in voting. It meant that 
preference reversal based on election expectations never rewarded the voter.

 From a Range ballot, I can again determine preference order. In some 
cases, candidates are lumped into groups with the same rating, and 
thus I cannot tell if the voter has a preference between them. But 
every expressed preference is sincere (or a mistake not conferring an 
advantage). So, again, in this sense, Range is strategy-free.

But that, again, certainly does not mean that it is not affected by 
"strategic voting," which now has shifted in meaning. It means not 
representing true preference strengths. I cannot, from a Range vote, 
derive true preference strengths, but only preference order. I may be 
able to place some constraints on the true preference strengths, 
especially if I know something about the environment the voter faced. 
If a voter, for example, equal rates two frontrunners, I could assume 
that the voter has no strong preference between them. If a voter 
expresses strong preference between two candidates, I can assume that 
the preference strength is not weak. But I can't necessarily compare 
that preference strength with those between other candiate pairs, 
except I can make some educated guesses about non-adjacent pairs. 
Every expressed preference can be assumed to represent a finite 
sincere preference (or an error). A series of these in sequence will 
represent a greater preference.

It is correct that Range Voting is affected by strategic voting, now 
defined as any modification of some supposed "sincere vote" due to 
expected votes by other voters, in order to maximize the voter's 
personal expectation. For our purposes, a "sincere vote" would mean a 
vote which accurately represents the voters true preferences, within 
the resolution of the method, and their preference strengths. This is 
equivalent to saying it is a linear mapping of the voters true 
absolute utilities for the candidate set to the range of one vote. Or 
is it absolute utilities? It's undefined! By normalizing the vote, 
the voter has already modified the utilities to make them strategic. 
Voting max for at least one and min for another is a *strategy*, and 
it maximizes the voter's personal voting power, a voter who does not 
do it is partially abstaining from the election entirely independent 
from judging how other voters will vote.

And, in fact, this "strategic vote" which is simply normalized, 
damages the outcome to a degree. It tends to average out, but one of 
the reasons why Range isn't perfect is normalization. Normalized 
votes don't sum to an average utility such that if we maximize it, it 
maximizes overall absolute utility.

If there were a way of doing it, we'd want every voter to vote 
absolute utilities so that the method could optimize overall 
satisfaction. However, by equating the range of utilities for all 
voters, we do something different: we equalize the power of all 
voters, tolerating the possible loss of overall utility do to this distortion.

If you review what authors have written about Range here, it's been 
common for a writer to say, "I can't support Range because it is 
vulnerable to strategic voting." But what's missing from the analysis 
of these voters -- if they have actually done any -- is a 
consideration of *how vulnerable* Range is. *How much* do voters who 
act to maximize the impact of their votes affect the quality of the 
outcome. Not much, apparently. Strategic voting in Range causes the 
result to shift toward an Approval result. Almost always the same! 
And when the result shifts, it isn't a drastic shift. And, through it 
all, Range maintains better election performance, shown in the 
simulations, than ranked methods.

This is the bottom line: Range allows the expression of critical 
preference information, necessary to determine what candidate will, 
overall, most satisfy the voters. If every voter were to accurately 
express this, it could accurately determine the best winner. 
Strategic voting represents a loss of accuracy; as a voter shifts the 
result toward their personal preference, which they can only 
effectively do if they have information about the other voters, they 
may occasionally succeed. But this is highly unlikely to be a major 
shift in overall satisfaction. If it were, it would not work.

By not allowing this information to be expressed, ranked methods 
can't select that optimal winner, sometimes, and thus cannot be 
diverted away from that winner by strategic voting. So the supposed 
freedom from strategy of some kinds for some ranked methods is 
purchased at the cost of being unable to even find the optimal winner 
except by accident, even with fully sincere ranked votes.

If we cut off your arm, it will not be vulnerable to being broken. 
This is not an improvement, it's a loss.

With Range voting it is *possible* to improve results over Approval. 
Not guaranteed, because an unknown number of voters will vote 
Approval style. That these voters, then, cause the improvement not to 
happen is not an argument against Range Voting.

The arguments I've seen simply assume that "strategic voting" is a 
Bad Thing, and having a method which can be affected by it is 
Encouraging a Bad Thing, which is, of course, a Bad Thing. Yet *this 
kind of strategic voting*, which is shifting expressed utilities, one 
way to put it, according to expected probabilities that the votes 
will improve an outcome, is what is *normal* human decision-making.

It's been shown by Dhillon and Mertens that a method of amalgamation 
where von Neumann-Morganstern utilities are normalized and summed, 
they call it relative utilitarianism, satisfies the conditions of 
Arrow's theorem, though IIA must be defined a little differently, and 
it is a unique solution. Ahem. Range Voting is a unique solution to 
the conditions of Arrow's theorem.... But I'm not convinced I 
understand the paper. Smith says it uses "notation from hell." 
(Others do refer to this paper with apparent understanding, and have 
built on the result, if I'm corrrect.)

This much I do understand. VNM utilities are absolute utilities 
modified by probabilities and normalized to he range of 0-1. This is 
Range Voting, voted "strategically." The result is that if there is a 
non-zero probability that a vote will change a result, the preference 
strength actually expressed in the vote will be non-zero, but will 
approach zero as the probability approaches zero. What is "voted" is 
not the absolute utilities, nor normalized absolute utilities, but a 
non-linear transfer function is used that places voting power where 
both utility differential and probability indicate it will maximize 
expected return.