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

[Abd ul-Rahman Lomax]

At 01:38 PM 12/5/2008, Kristofer Munsterhjelm wrote:
>Abd ul-Rahman Lomax wrote:
>>
>>Ballots do not ask for the voter's sincere opinion. They ask voters 
>>to make a choice or choices.
>
>I think that is incorrect. Ranked methods ask for the sincere opinion of
>the voter, and that opinion can be well defined.

Hmmm.... A ballot is a piece of paper with words on it. It can "ask 
for" a "sincere opinion," using words that express such a request. 
Turns out that the RCV ballots I looked at don't do that. They 
instruct the voters to mark choices, which is totally free on any 
request that these marks be "sincere." Some ballot designs may indeed 
request a preference order. Now, what if the voter equally prefers 
two candidates? If the voter is not allowed to so indicate, is the 
ballot asking the voter to lie? Or what?

Basically, what Kristofer is doing is confusing the thinking of a 
voting system designer for what the voter is requested to do on the 
ballot. The designer may have in mind that voters will mark in order 
of preference. It's absolutely true that it's generally easier to 
determine preference than to determine preference strength, but if 
equal ranking isn't allowed, then a sincere vote may be impossible, 
i.e., the ranked method forces the voter to show a preference that 
does not exist. Preference order was an obvious and simple way of 
voting, and it's got a long and venerable history, but it was by no 
means a logically rigorous procedure. A great deal of work was done 
studying how preference order would translate to social order, but it 
was, unfortunately, mostly isolated from a real-world understanding 
of normal human decision-making. We don't use preference order in 
isolation from preference strength; a small or infinitesimal 
preference is not the same as a strong one, and has very different 
implications.

>  The first preference is
>the opinion of "who would you pick, were you the dictator".

Hmmm.... if I were the dictator, and I wanted the world to be safe 
for my children, I'd want to know what everyone else wanted, in as 
much detail as possible. Dictators who only follow their own whims 
sometimes live out their lives, but after them, chaos. Their families 
tend not to survive.

So ... this dictator would vote strategically, as many have defined 
it. That's an oxymoron, isn't it? The reductio ad absurdem of 
"sincere voting?"?

I'd put it differently: which candidate would you pick, if you knew 
that it was a total tie as far as everyone else thought, or, 
alternatively, you don't know and can't know what their preferences 
are, to any degree of confidence except none, in advance of the canvass.

>  The second is "who would you pick if the first choice was not 
> available", and so on down.

How many write-in votes do I get?

>  Because of Arrow, we know that ranked methods are going to be 
> vulnerable to strategy (optimization). However, that's a flaw with 
> ranked voting methods. Knowing that they are vulnerable to 
> optimization does not make an optimized vote sincere.

Nobody has claimed that they are, in the ordinary sense, but neither 
are they necessarily insincere, because they are not sentiments, they 
are, generally, *votes*. As actions intended to cause an effect that 
is desired, they can be seen as sincere in a way.

Optimized votes in ranked methods necessarily reverse preference, 
which, if we do expect preference order expression, we can term 
"insincere," but it is a term of art and should be separated from the 
moral implications of "sincerity."

For example, there is an election in which IRV is being used. There 
are three candidates, and you expect that your favorite will, if you 
and your friends vote for A, your favorite, because your first 
preference vote for A will edge B out to elimination, leaving A and C 
to face each other, and you fear, and reasonably, that C will win in 
this case. B is the compromise candidate, the Condorcet winner, and 
the preferences are significant; but is also the sincere Range 
winner, by a good measure. This is absolutely not a rare scenario, 
except in two-party partisan elections which, conveniently, are most 
IRV elections outside the U.S.

Since B is a much better winner to you than C, you and your friends 
decide to vote for B. Is that a sincere vote? In IRV, it involves 
voting B>A>C. On the face, it's insincere, but the motivation is to 
improve the election outcome, not only for yourself and your party, 
*but for most voters.*

Under some circumstances, this could be considered a moral necessity!

>Now, you may say that only order reversal is insincere. This sounds 
>a bit like a ranked vote advocate saying that only altering your 
>first preference is insincere, and therefore, ranked methods that 
>pass FBC are strategyproof because altering your subsequent 
>preferences is mere optimization.

Huh? *This* sounds a tad like a ... non sequitur?

Only order reversal is clearly insincere, because it clearly 
expresses the opposite of the true preference. Voting equally does 
not state a preference, it's actually a kind of abstention, "I'd 
rather not say which of these I prefer." Is that statement insincere? 
It indicates, in any voting system I'm aware of, that the suppressed 
preference is not maximal, it makes no sense if such a preference is 
not disclosed. I'd only conceal a maximal preference if I preferred 
one of the other candidates over another of them, and that 
contradicts the assumption that the preference concealed is maximal.

(Ranked voting theorists are accustomed to thinking of preferences as 
absolute things, with no concept of preference strengths being 
additive with a limit to the sum. But if A is the absolute best, and 
C is the absolute worst, B is in the middle, and something increases 
our preference for A over C, it must decrease our preference for A 
over B. In voting terms, we only have one vote, and if we pretend 
that A over B is all or nothing, we might be called on it, we are 
claiming that we are indifferent to B over C. Nader re Gore and Bush. 
Tweedledum and Tweedledee. If anyone believed him. I'm not sure he 
believed himself, but maybe ....)

Kristofer, are you aware that what I'm claiming here was published 
with a straight face in peer-reviewed journals, years ago, that 
Approval was "strategy-free" and that one of the complaints of 
critics of Approval was that there was more than one possible sincere vote?

Some seem to think that I'm trying reduce the whole concept of 
"sincere vote" to nothing. But of all possible sincere votes in 
Approval, most of them are not sincere, that is, they reverse 
preference. Only certain votes that do not violate preference order 
can be considered sincere.

This is an entirely different issue from whether or not the votes are 
"strategic." But with Approval, all votes could be considered 
"strategic," depending on how the voter arrived at the vote! If the 
voter considered who might win the election, and not simply absolute 
utilities, we might consider it strategy free. Except we still have 
the problem of how the voter sets the approval cutoff. There isn't 
any absolute! The voter would still need to use some strategy, I'd 
think. If the method requires a majority, in fact, the voter, zero 
knowledge, can simply vote for the favorite. That's a "strategic 
vote." But with other methods, *the same vote*, with similar effect, 
would clearly be considered sincere.

(Seriously, we see critics of Approval claiming that a vote is 
insincere where the voter bullet votes, because, allegedly, the voter 
"also approves" of another. A voter supposedly, "also approves of B," 
but votes only for A, and this causes A to win, whereas the other 
voters "sincerely approved both A and B," even though they actually 
preferred B to A. Thus the selfish "insincere" voter gets his 
preference, whereas the "honest" other voters lose out. Look, it's a 
total mess, replete with contrary assumptions. The voter voted for A 
because the voter preferred A, with enough preference strength that 
it mattered. The other voters decided that it didn't matter enough to 
them to not vote for B also. What's the problem? All the voters we've 
mentioned accepted A, A has to be, from the votes, a reasonable 
winner. But, wait! The B voters voted for A also because they feared 
that C would win. Aha! They voted *strategically*, whereas A was the 
sincere one. Oops! Which is it? It's neither, these are votes, not 
sentiments, and all the voters presumably voting to maximize the 
outcome as they saw it. They all voted strategically, except perhaps 
with differing degrees of correct knowledge.)

Approval, like other Range methods, simulates to a degree 
deliberative process, where we reveal what we would "also accept." 
Range does it most accurately. In all deliberative process, in normal 
society, people vary in how much they will disclose of what they will 
"also accept." Some people are very stubborn, others are more willing 
to compromise. It takes all kinds. Range allows accuracy of 
disclosure, that is the difference between Range and Approval.

>Election methods in general are thus algorithms that take individual
>opinions as input and returns a good common choice, or a social
>ordering. What is a good common choice may be defined by criteria (e.g
>Condorcet) or by utility.

This opposes criteria and utility, implying that utility isn't a 
criterion. It is. It was an error to not use utility in the first 
place, an oversight. I've seen a little of the rationale, because it 
wasn't like the idea didn't occur. Utility was not used because there 
was no way, it was thought, to objectively judge utilities or 
preference strengths.

This was confused, in fact. There can be ways, and, further, we can 
posit utilities and see how voting systems perform under varying 
assumptions and mixes of how voters will translate their underlying 
utilities to votes. We know the utilities by *assuming them*. And, in 
fact, in some situations utilities can be directly predicted; 
financial choices, for example. But what is needed isn't just raw 
utilities for the choices, it is also probabilities, and that is 
where game theory and economic choice theory went, and the political 
scientists, largely, got caught in a rabbit-hole of studying 
preference alone. Even though preference, in fact, is almost as 
difficult to determine. It's a pretty bad assumption to assume that a 
trivial, even random preference, the whim of the moment, is the same 
as a preference that people would literally die for. Yet that is what 
the Condorcet criterion assumes. Preference strength does not matter. 
It's preposterous!

Sometimes I feel like the little boy crying out that the emperor has 
no clothes! Except that I'm not the first to notice this stuff. I'm 
just re-emphasizing it, bringing it up when the old preference myths 
come up. It can take a long time for new ways of thinking to 
penetrate the common psyche.

(Want to see some fireworks? State what is common knowledge among 
most academics: race does not exist except as a social construct, a 
myth that only affects people because some believe in it. Watch 
people sputter, "But it's obvious! Are you blind?" Gradually, people 
are getting it. It's not what some imagine, about being "politically 
correct." Just correct.)

>As for Range, either Range, the method, has a well defined input or 
>it has not.

It doesn't, as a voting method. The sum of utilities approach, 
however, as a way of studying voting methods, which is distinct from 
the Range methods, has three prominent inputs:

(1) Absolute utilities.
(2) Normalized absolute utilities.
(3) Normalized absolute utilities modified by probabilities.

Remember that Arrow's theorem is not about voting methods? I wish 
political activists would stop claiming it was! It was about a method 
of determining a social preference order from a collection of 
individual preference orders, and Arrow, of course, showed that 
certain commonly assumed desirable traits of amalgamating the 
preferences were incompatible, that no amalgamation could satisfy all of them.

But Arrow's theorem was missing something: cardinal ratings as input, 
or utilities. He simply did not allow it. The input to the black box 
Arrow was studying was preference order, period. Equal rankings not allowed.

I'm recommending that anyone following this discussion who wants to 
see some depth read Dillon and Mertens. There may still be a copy of 
their paper on rangevoting.org. Otherwise get thee to a library which 
keeps Econometrics, Vol. 67, No. 3, (May, 1999), pp. 471-498. Warren 
calls their notation, "notation from hell." However, the text is 
fairly readable, and here is some of it:

>A Social Welfare Function (SWF) maps profiles of individual 
>preferences to a social preference. For preferences over lotteries, 
>we axiomatize such a map, "relative utilitarianism" (RU), consisting 
>of normalizing the nonconstant individual von Neumann-Morganstern 
>(VNM) utility functions to have infimum zero and supremum one, and, 
>taking the sum as social utility (Arrow (1963, Ch. III, para 6, p. 32))
>
>Our approach, in the sense of an axiomatic SWF, is very close to 
>Arrow's tradition. The main difference seems to be the motivation. 
>Given his insistence on the full strength of Independence of 
>Irrelevant Alternatives (IIA), his approach seems more oriented 
>towards understanding the voting paradox, and getting a general 
>social choice paradox. Because voting situations are indeed 
>characterized by successive votes between pairs, or at least small 
>subsets of alternatives, imposing full strength IIA is almost 
>necessary for analysing the consistency between successive votes. 
>Our concern is more the normative question of finding a "good" SWF, 
>effectively and justifiably useful for public policy 
>recommendations. This is the original question of social choice 
>theory, as well as the fundamental question of normative economics, 
>and goes back implicitly at least two centuries ago, to the early 
>utilitarians, and explictly more than a half century ago, to the 
>work of Bergaon and Samuelson (Arrow (1963)). The full force of IIA 
>is then no longer compelling [as discussed later in the paper] ... 
>some aspects of it are suspect, and contradict the most obvious 
>intuition of what a good SWF should do. It is precisely those that we avoid.
>
>While his axioms were inconsistent, ours yield a unique solution. 
>IIA is substantially weakened, indeed almost dropped, its only 
>remnants being the IRA axiom [Independence of Redundant 
>Alternatives], the monotonicity axiom (MON), and a continuity axiom. 
>The other axioms are trivial cases of his Pareto axiom (or 
>nontrivial cases of "Citizens' Sovereignty"), except for the 
>classical anonymity axiom (ANON) strengthening his nondictatorship.
>
>This paper clearly relies strongly on the additional mileage, in the 
>form of more restricted preferences, obtained in decision theory by 
>going to lotteries....
>
>Why not take interpersonally comparable utility functions as 
>primitives? The basic argument is Arrow's (1963), that primitives 
>should be empirically meaningful ... lest the axioms themselves 
>become meaningless, and so the whole theory. See also Rawls (1971, 
>e.g., p. 322) for a more recent expression of the mythical character 
>of the numbers behind preferences: they are just a construct in the 
>"observing mathematician"'s mind, and without any uniqueness 
>property in addition. But if until Arrow this ordinalist position 
>was almost the consensus, apparently his theorem itself, together 
>with the very influential work of Hirsanyi, turned the tide 
>partially, and led to the conclusion that interpersonal 
>comparability was a must to obtain SWFs. The present theorem proves 
>this conclusion false....
>
>... to apply RU meaningfully, one has to, and it suffices to, 
>consider a set of alternatives sufficiently encompassing as to 
>include, besides the actual alternatives of interest, each person's 
>best and worst alternative within the "universal" set A, limited 
>only by feasibility and justice. This leads in turn to a concept of 
>"absolute utility:" the "correct" scaling of an individual's utility 
>is determined solely by his own preferences and by the philosophy of 
>the state adopted. This brings us almost back to classical 
>utilitarianism, but this time, without any "moral judgement" as 
>primitive, and with a complete axiomatization.
>
>For two alternatives, RU amounts to majority rule, so our result can 
>be viewed as a generalization of May (1952) that, for this case, 
>majority rule is the only "reasonable" solution. And, when viewed as 
>a mechanism, RU suggests letting each voter assign to every 
>alternative some utility in [0,1], and to choose the alternative 
>with the highest sum. Except possiblty with very small sets of 
>voters, voters will clearly find that, for their vote to have a 
>maximal effect, they should assign either 0 or 1 to every 
>alternative. Hence the corresponding direct mechanism seems to be 
>"approval voting" (Brams and Fishburn (1978)).

Range Voting was not on the table at the time. All that Range Voting 
does is to allow the direct expression of the assigned utilities, 
within the limit of [0,1]; Dhillon and Mertens seem to assume that 
voters will maximize their vote, if they could express it more 
accurately. Our understanding is different: some will maximize, some 
will not, the result will be intermediate between full expression and 
approval-style voting. The paper deals with the full version, showing 
that it is a unique solution to the Arrovian conditions, with the 
modification they note. This, quite reasonably, meets a reasonable 
definition of "ideal voting system," contradicting the common claim 
that there is no such thing.

But what about "sincere votes"? The utilities expressed in the full 
version, VNM utilities, preserve preference order entirely. Every 
voter preference can be found there, if we assume a nonzero 
preference strength and nonzero probability. In common language, an 
outcome with zero probability is, indeed, irrelevant! It should not 
affect the "votes." Then, these VNM values can be expressed with any 
accuracy, and, it happens, the voter gains the maximum personal 
utility voting them in binary fashion. More accurately, the extreme 
votes in some situations have the same expected utility as the 
accurate ones without resolution limit, and in others they have more; 
however, that assumes that the voter has chosen accurate 
probabilities in deciding where to vote 0 and where to vote 1. It 
may, in fact, be safer to estimate an intermediate value, that 
conclusion is based on my own relatively primitive work with absolute 
expected utilities. My own sense is that voters should vote whatever 
they prefer to vote, they should understand the basic principles of 
"strategic Range voting." Don't reverse preference is one basic rule, 
it never helps you, and it can hurt you, in terms of expected 
outcome. And cast a full vote within the reasonable election outcome, 
i.e., vote at full or close to full vote for a preferred 
"frontrunner," and a minimal or close to minimal vote for the worst 
of the frontrunners. "Frontrunner" here includes any candidate the 
voter considers a real possibility for winner, or, in a system using 
a runoff, for making it into the runoff. Beyond that, the voter is 
relatively safe just using common sense. And can decide to violate 
the "rules" I just gave, and there can be situations where that 
would, indeed, be a better strategy.

And all that "strategy" slightly harms overall results over voting 
non-probability adjusted utilities, as long as these votes are 
confined to a reasonable election set. If the voter cares about that, 
trying to accurately represent preference strengths is, possibly, a 
morally superior position, but the difference between that and 
strategically optimized votes is small. I suggest voting which ever 
way is easier! One should not have to rack one's brain for days to 
figure out exactly how to vote! Quite simply, the difference it will 
make isn't worth that. What's much more important is to understand 
the political situation and the candidates. I.e., what we normally 
think of as important: which candidate is best? which is worst? Which 
ones have a chance, which ones don't. We are totally accustomed to this!

To continue with Kristofer's response, repeating a little:

>Election methods in general are thus algorithms that take individual
>opinions as input and returns a good common choice, or a social
>ordering. What is a good common choice may be defined by criteria (e.g
>Condorcet) or by utility. If it has, then incentives to misrepresent 
>the input is bad, and would count as strategy. If it has not, then 
>how can it make sense of the input to find a good output (choice or 
>social ordering)?

Ah! I thought so! "Strategy" is "bad."

What's missing from Kristofer's comment is an understanding that 
full-on "strategic" voting in Range does not "misrepresent the 
input." Yes, full optimization of result needs accurate utilities, 
but it still takes place with less information, and yields a result 
which cannot deviate far from what would have been found if the voter 
had voted with full disclosure. If a voter votes approval style and 
so conceals a large preference, i.e., the voter, simply rounding off 
the utilities, would have voted differently, the voter is abstaining 
from an election seriously important to the voter, the voter may 
regret the vote. The one most likely to suffer from an "exaggerated" 
vote is the voter, which seems eminently fair to me.

Example: the voter has non-strategic votes (probabilities not 
considered) of 1, 0.9, 0, for the set of frontrunners. The voter 
wants the favorite to win, of course, who doesn't? So the voter 
bullet votes. If the 0 were not a frontrunner, that would be a very 
reasonable vote. But if, say, the probability of election of the 
worst candidate is 0.5, there is a very good chance that the voter 
will regret not adding a vote for the middle candidate in that set. 
But it's up to the voter, both votes (1, 0, 0) and (1, 1, 0) are 
sincere. The first expresses A>B and A>C, the second expresses A>C 
and B>C. All these are true. The second is a bit more expressive of 
the underlying utilities.

Game theory would suggest that we vote for each alternative that 
exceeds, in utility, our expectation for the election outcome. If we 
assume zero knowledge, we could assume that the probability is 1/3 
for each candidate. So the expected election outcome is 1/3 plus 
0.9/3 plus 0 equals .633. Voting for B would not be a "strategic 
vote," but neither is bullet voting. (The most reasonable definition 
of "strategic vote" that has been used in our discussion here is a 
vote modified by understanding which candidates are reasonably likely 
as winners. A zero knowledge vote is not strategic. So there is more 
than one non-strategic vote!