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

Abd ul-Rahman Lomax abd at lomaxdesign.com
Mon Dec 15 20:31:58 PST 2008

At 06:50 PM 12/14/2008, Kristofer Munsterhjelm wrote:
>Plurality voters have to be strategic all of the time because 
>Plurality is a bad voting method.

Well, isn't it totally strange that such a "bad voting method" is so 
widely used? Isn't that just a tad suspicious? Are people really that stupid?

They aren't. Plurality is widely used because it's a fairly decent 
method. It breaks down in some situations, but voters *do* vote 
strategically, which means that they instinctively make certain 
necesssary compromises.

Now, that doesn't mean that we can't improve greatly on Plurality. 
But trying to eliminate all "strategic voting" is trying to eliminate 
much of the *functional* process of Plurality and of elections in 
general. Voting systems are means whereby we simulate a discover of 
consensus. *To a degree.*

We are so focused on how Plurality doesn't work that we don't notice 
how it does. I've seen this blindness before, in many examples, among 
reformers. They see what's wrong, not what's right, so their reforms 
can actually make things worse. They fix one perceived injustice or 
problem but create many....

>  Ideally, there would be a "vote for one" method where people 
> *could* vote their favorites.

There is. I'm tired of naming it. Someone else do it this time.

>  Repeated balloting might come close, but it incorporates feedback 
> to the mechanism and thus isn't a single voting method unless 
> voters mechanically translate ranked votes into plurality-style 
> votes (first vote favorite, then vote next-to-favorite next round, etc).

Repeated balloting is not it, as such. The actual election takes 
place in the final ballot, the one where a majority appears, and 
voters in that election are compromising. Strategy. Necessary. No, I 
have something else in mind.

>Consider Plurality, again. Voting with strategy improves the 
>situation when compared against a situation where everybody else is 
>using strategy and you don't. However, if everybody were sincere 
>(had zero knowledge), the result would be better. By Bayesian regret 
>(which I assume you find valid), this is true for Plurality and for 
>many other methods, perhaps all ( 
>http://rangevoting.org/BayRegsFig.html ), unless Warren's strategy 
>simulations are too simple.

Yes. However, with many candidates, sincere Plurality can become 
totally quirky. Further, IRV can badly break down with sincere votes, 
and to fix it, voters need to realize the danger and vote 
strategically, i.e., not for their favorite. More likely, they don't 
and the method ends up with very poor results. This is with Center Squeeze.

>That voters in Plurality (most likely) can't vote for their favorite 
>is not a property of the ballot input of Plurality. It's a 
>consequence of that no voting method is strategy-proof, and that 
>Plurality is particularly egregious in this respect.

Once again, that assumption that "strategy" is bad. Some strategy can 
harm results, other can improve results.

The problem with Plurality (common inability to vote for the 
favorite, or the vote is wasted) *is* a property of the "ballot 
input" which is "vote for one," *combined* with the aggregation 
method. It's fixed simply by dropping the "vote for one" restriction. 
Count All the Votes. Open Voting (Approval).

>>>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.
>>That's correct, about order reversal. It's a reasonable statement, 
>>because equality is a judgement that does not require any specific 
>>precision. "Equality" means "below some threshold of difference 
>>considered significant." "Sounds like" is a personal statement, a 
>>subjective impression.
>>(We focus on "exaggeration," but it's equally valid to focus on 
>>"minimization," which in Range is rigidly correlated with 
>>exaggeration. In ranked methods which allow or require truncation, 
>>"exaggeration" by ranking in the presence of little or no 
>>preference takes place, and minimization of preference takes place 
>>by truncation, whether voluntary or forced.
>The similarity is that you define a ballot to have some sort of data 
>that's "really important", and leave the rest up to optimization. If 
>you think that ordinal values (preferences) are defined externally 
>with respect to the voter's interaction with the voting method, then 
>yes, preference reversal is insincere. If you think that cardinal 
>values are defined externally with respect to the voter's 
>interaction with the voting method, then exaggeration is insincere 
>too. And if you think one but not the other, why the inconsistency?

I must say that this paragraph appears to be mostly word salad. The 
voter decides what's important, to be on the ballot. The voter 
expresses some preferences and not others. Not expressing a 
preference is not insincere, unless one actually states that there is 
no preference. Equal ranking does not state this; rather, in any sane 
system, it means that the preference is below some level of significance.

We don't consider a truncated ballot to be insincere in its bottom 
rankings, at least I've never seen such a charge. Equal ranking means 
"I choose to not express a preference." It is a non-disclosure, and 
non-disclosure is never insincere, sincerity is meaningless with 
regard to nondisclosure, it only applies to expression.

"Prefer" has a meaning. It's like "positive," which refers to no 
particular value, only that a value is greater than zero.

The actions in Range Voting are not preferences, per se. They are 
votes. I have 100 votes in Range 100, or 100 1/100 votes, same thing. 
We place the votes where we think they will do the most good. That 
involves a judgment not only of the preference order of the 
candidates, but also of preference strength *and* relevance of that 
candidate to the election, in comparison to others. Because a 
differential Range vote does not only consider the estimated value of 
the candidate, but also the estimated relevance, "sincerity" becomes complex.

It's been pointed out that apparent preference from Range Votes would 
not always be accurate, that it might indeed show an apparent 
reversed preference. Under very unusual constraints, that placing of 
votes where they count can involve preference reversal. This, as far 
as we can tell, has no effect on practical public elections, but it's 
interesting nevertheless.

Here is one of the situations: There are four candidates, two 
liberal, L1 and L2, two conservative, C1 and C2. Poll data indicates 
that all candidates are equally popular. I'm a liberal, and my 
preferences are L1>L2>C1>C2. Now comes to me information that the 
real contest will be between the two liberals or the two 
conservatives. It's an Approval election. How should I vote?

Voting in preference order, the "sincere votes" are 1000, 1100, 1110. 
However, the strategic vote (twice as likely to improve the outcome 
from my perspective) is 1010. There is an apparent preference reversal.

However, what has happened is that there are only two relevant 
pairwise elections: L1/L2 and C1/C2. the other pairwise elections 
have been suppressed (for unexplained reasons). By voting 1010, I 
place my vote strength where it counts the most.

That example, from the rangevoting.org web site, involves correlated 
candidates. Normally, candidates on a ballot are independent, and on 
an Approval ballot, one would never place a more approved candidate 
in the unapproved category, with a less approved candidate in the 
Approved category. That is, under normal conditions, only the sincere 
voting patterns of 1000, 1100, or 1110, would be the reasonable 
choices. Those are all sincere in the sense of not reversing 
preference, but revealing a sincere preference; it just happens to be 
a setwise preference, and we can derive a whole series of preferences 
from each one of them:

1000: L1>L2, L1>C1, L1>C2
1100: L1>C1, L1>C2, L2>C1 L2>C2
1110: L1>C2, L2>C2, C1>C2

Does this mean that we don't have any other preferences among the 
four candidates? Of course not! We place our vote where it had what 
we considered the most important effect.

This is with two preference slots (0 and 1). Similar arguments can be 
made for three and more. They are votes, not sentiments; normally, we 
can derive sincere preferences from them, because the foundation of 
them is some combination of normalized von Neumann-Morganstern 
utilities and normalized utilities unmodified by probabilities. The 
latter are called "fully sincere," but the former are not insincere; 
indeed, with a nonzero election probability, they preserve preference order.

To use the term "insincere" for VNM utilities, though, runs contrary 
to common speech. "He was insincerely silent" is nonsense.

>Methods that permit truncation accept ranks over subsets of the 
>candidates. Most Condorcet methods handle this by ranking the 
>remainder equal-last, but it's not inconceivable to have a method 
>that simply treats it as if no decision as to whether A's better 
>than B was done if A was ranked and B not - a ranked version of 
>Warren's Range tweak.

Not one of Smith's finer moments. He's got no simulation data, no 
coherent analysis, to show that "average Range" is better than "sum 
of votes" Range, it was simply an idea, and one which flies in the 
face of centuries of political practice. There's precedent for sum of 
votes, not for average vote. And in order to deal with the obvious 
problem, he then needs additional tweaks, an arbitrary "quorum rule." 
On the other hand, if a majority of voters have preferred a 
candidate, and the others did not rank the candidate .... then we 
have some basis. But we don't need average to do it.

>  The point of this is that truncation is the submission of a 
> partial ranking, out of convenience. A strategic use of truncation 
> would have a voter considering, based on LNH* properties, how far 
> to rank to maximize the chance that his vote will lead to his first 
> preference winning (and failing that, maximizing the chance that 
> his vote will lead to his second preference winning, etc).

Sure. Convenience is not the only reason for truncation. It can mean, 
for example, "I utterly reject all these candidates, I do not wish to 
be responsible for electing any of them." Truncation in preferential 
voting systems can cause majority failure, and that is exactly as it 
should work. There are very good reasons for considering it important 
to gain a majority accepting an outcome, it should be the minimum 
normally acceptable in a democracy, or the outcome does not take effect.

>>>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.
>>Okay. However, the definition by criteria was never widely 
>>accepted, beyond certain simple ones, such as the Majority 
>>Criterion, and Arrow blew the whole thing out of the water. 
>>Paradoxically, Arrow rejected ordering by utility, based on alleged 
>>indeterminacy or other incomplete consideration; but it turns out 
>>that it's possible to satisfy the Arrovian criteria, that are 
>>allegedly incompatible, with a minor tweak to IIA, which has often 
>>been considered the weakest link in Arrow's chain. The substance of 
>>IIA is preserved. See Dhillon and Mertens, Relative Utilitarianism, 
>>Econometrica, May 1999, pp 471-498. See http://rangevoting.org/DhillonM.html
>Okay, but I can't make use of that. I don't know what CONT is (or 
>their weaker version of monotonicity, for that matter), and the 
>notation from hell deters me.

Indeed. However, read it again, maybe later. It kinda grows on you. 
Smith has an explanation of these terms. Note that the paper itself 
is linked at the bottom of the page, as part of the citation.

>Also, I'll note that the page mentions a version of Range where the 
>favorite gets score 1 and the most-hated gets score 0. If this input 
>is used for Range, and voters would try to optimize their votes and 
>vote Approval-style, would that constitute insincerity in your view?

Of course not. (It is incomplete disclosure.) Dhillon and Mertens 
actually propose Approval Voting as an implementation of Relative 
Utilitarianism, they wrote:

>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 possibly with very small sets of 
>voters, voters will clearly find that, for their vote to have 
>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)).

Back to quoting Kristofer:

>Is there such a thing as a preference strength information in a vacuum?

Vacuums suck.

>  If there is, then altering that information (beyond rounding 
> errors) misrepresents the input.

It does not represent the input. It does not misrepresent it, because 
the correlation between Range Votes and  preference strength is not a 
linear one, it was never claimed to be that. *If* voters transform 
their absolute utilities into Range votes in certain ways, it's 
possible to maximize overall voter satisfaction, but voters are not 
required to enable this; nevertheless, if they maintain preference 
order, the results tend to average to the maximization of overall 
satisfaction. Essentially, this is how Borda works. Fix Borda by 
allowing equal ranking and empty ranks, much better.

Yes, that can damage overall satisfaction *because the exaggerating 
voters pretend to be more satisfied than they are!* That is, if we 
take approval style voting in Range as "pretending" to be histrionic. 
It isn't. The Bayesian Regret figures are based on underlying 
satisfaction, not on the votes.

We lost the basic concept here, in our enthusiasm for the concept of 
maximizing overall satisfaction. Voters are not voting, per se, to 
tell us how satisfied they will be. Rather, we've handed them some 
power, and we see how they use it. Range Voting is just voting, just 
like Approval, but with fractional votes allowed. We may *assume* 
that those votes represent preference strength, but we can't nail it 
down. If I rate three candidates at 10, 20, and 40, it cannot be 
presumed that I prefer the third over the second with twice the 
strength as I prefer the second over the first.

Rather, the information flows in the other direction. I start out 
with utilities that might indicate that and I *might* have used that 
alone to determine my vote. But I may equally well have started with 
different utilities that were transformed into those by my 
consideration of relevance. A Range vote is a combination of relative 
preference strength and estimated relevance.

>  If there isn't, then the voting method is resistant to strategy 
> simply because strategy is no longer strategy, it's just part of 
> finding which of the set of "potentially correctly represented 
> inputs" that maximizes the chance that you get what you want.

A practical voting system will use the input of voters, seeking to 
improve their own expected satisfaction, to find an optimal outcome. 
If we could extract from them absolute utilities, we could maximize 
social utility, but we can only request votes. It turns out that if 
"votes" are VNM utilities, the sum of votes is a voting system that 
satisfies Arrovian conditions. I think this holds true for Approval. 
But I could be wrong.

We badly need a better exposition of the Dhillon/Mertens paper.

>>A strategic Range vote does not "misrepresent the input," because 
>>the input to the system is a product, in the voter's estimation, of 
>>the relative utility of the outcome and the probability that the 
>>outcome is relevant.
>That means that there'll be a feedback loop in the system; the 
>voters vote in mock elections (that is, polls), then take the output 
>of those to further refine their next input. Now, in the ideal 
>situation for ranked vote methods, there is no feedback loop, and 
>what loop exists in practical situations exists because no method 
>can be strategyproof.

Strategy is not based only on polls. It is first of all based on the 
voter's knowledge of self. It is based on the voter's understanding 
of other people in general, not just in this election. The Saari 
misexample was based on voters not understanding that they are people 
and that others think like them; instead, they simply follow some 
mechanistic zero-knowledge strategy when, in fact, if they assumed 
that they were *reasonably* typical, they would get much better results.

That is, the optimal strategy for Approval, zero-knowledge, may be to 
bullet vote for the favorite, unless the favorite is reasonably 
cloned. Exclude the clones, and this is Plurality. That's been 
claimed to be a defect of Approval! It isn't. People don't have zero 
knowledge, so votes will be shifted away from this pure bullet voting strategy.

(And this brings up, again, that voting for your favorite is a 
*strategy.* Quite a reasonable one! Just not always! In Approval, 
though, *always vote for your favorite.* The question is whether or 
not you should vote for someone else in addition.)

>>I.e., the full preference profile consists of a rank order, with a 
>>preference strength in each adjacent pair in the order. The 
>>preference strength is then adjusted according to the probability 
>>that this pair is a relevant one, that there is some finite 
>>probability that the vote in that pair will improve the outcome. 
>>Further, there is a constraint: the sum of all the adjacent 
>>pairwise preferences must equal one full vote.
>>In this social welfare function, preference order is preserved with 
>>two exceptions: where the probability of relevance is zero, the 
>>preference strength in the pair goes to zero, thus equating the two 
>>outcomes; as long as there is nonzero probability, no matter how 
>>small, the preference order is maintained. It will be noticed, I'm 
>>sure, that this sets up independence from irrelevant alternatives, 
>>IIA, because if an irrelevant alternative appears in the full 
>>candidate set (which Dhillon/Mertens also define), it does not have 
>>any effect on the other preference strengths. Only relevant 
>>alternatives can do that.
>Again, is Approval-style insincere under this welfare function?

No? The word "insincere" doesn't appear in the paper, I think. Above, 
I quote them on Approval Voting. It's simply a maximized vote. One 
way to look at it is picking the relevant contests to vote in. All 
the votes are sincere. But some contests, one is not voting in. Is 
the not-voting insincere? Is silence insincere? Are we communicating 
in English?

>>Further, if the preference strength is below the resolution of the 
>>voting system, the preference may be lost. In pure RU, there is no 
>>resolution limit. I don't know of any significant opinion that a 
>>resolution beyond 1/100 of a vote is needed in practical systems.
>Granted. That's kind of like truncation in a system that has 
>infinite write-ins; the latter's a quantization of a set with 
>regards to another set, and the former's an uniform (but not total) 
>quantization of the data of all candidates.
>>The problem here is that estimating probabilities is "strategy." 
>>Thus what we may call "strategy" is part of the system.
>And since strategy involves adjusting opinions based on others, this 
>implies the need for external feedback systems.

Not necessarily. There can be simple anticipation. But, remember 
this: voting systems are a shortcut, a device for accomplishing 
quickly and efficiently what would be too difficult to deliberate on 
the large scale involved in elections. Deliberative process is 
iterative, it involves "feedback systems." Polling data is a kind of 
feedback system, used to drive strategic voting decisions.

This is essential in the process of negotiation and compromise that 
is how democracy works. Parties negotiating a contract may start out 
by stating what they want. Plurality. If those statements overlap, 
i.e., they are both acceptable to each other, they will quickly 
settle, probably in the middle if one doesn't simply say Yes 
immediately. But when they diverge, then new possibilities are 
proposed, shifting toward compromise. The equivalent in Approval is 
shifting an approval cutoff down to include less preferred options. 
Trying to do it all in one ballot is quite difficult, hence Range 
which can ease it, and hence my proposed use of runoff elections when 
the best choice from Range votes is ambiguous.

>>The large majority of people with Open Voting will, under anything 
>>resembling current conditions, Bullet Vote. *That is a strategic vote*.
>Yes, it is. My simple example here is the Nader-Gore-Bush case. If 
>this was Approval, most Nader voters would vote Nader only in the 
>first "round" (poll round).

Yes. That's normal as a first negotiating position. But it depends on 
the individual voter. Some might not have a strong preference, so 
they would indeed add approvals immediately.

>  Then they'd see that they're splitting the liberal vote, and would 
> vote Nader-Gore afterwards.

Unless they aren't looking at it that way. Surely some would vote 
that way. But Nader's claim was that Bush v. Gore was irrelevant, not 
a difference, not worth putting votes into. Do we think he'd have 
argued differently had it been Open Voting? (I don't.)

>  In my opinion, a voting system should permit the Nader voters to 
> say Nader > Gore > Bush and not have to deal with the iteration. 
> Range can do this, sort of; if you're a Nader voter and vote Gore 
> higher than (Bush margin over Gore)/(number of Nader voters), and 
> all Nader voters do this, Gore wins. But if the voters are adamant 
> about optimizing their votes, they're going to vote Approval-style.

Sure. But we might use Bucklin. Bucklin could, in fact, use a Range 
ballot. You cascade down the Range values, adding in votes, until a 
majority is found or they all have been counted.

Bingo! Just realized something. That scheme, if counted as Range was 
found unconstitutional. Those lower preference votes are fractional 
votes, and Bucklin, with fractional lower preferences, was ruled 
unconstitutional in Oklahoma. So some caution would need to be 
required. The counting of lower preference votes as fractional votes, 
though, may have been quite a good idea, semi-Borda.

I don't think that anyone before has mentioned that Oklahoma ruling 
in connection with Range Voting or Borda Count. Bucklin with 
fractional lower votes is a kind of Borda.

>>Strategic voting generally *improves* outcomes, in real voting 
>>situations. When the voting system gets very good, such that "fully 
>>sincere and accurate" voting will choose the optimal winner, this 
>>becomes untrue, but it never goes to the point of serious damage.
>Then why is the Bayesian regret of strategic Plurality greater 
>(worse) than that of honest Plurality? Plurality is by no means a 
>"very good" method. (Of course, BR could be wrong - a bad metric.)

No, the metric is good. Strategic voting in Plurality fixes some very 
obvious problems. That would represent some kinds of strategy in some 
kinds of situations. Other kinds of strategy, other situations, not 
good. The simulations weren't necessarily sophisticated in strategy used.

>>And we have to remember that "fully sincere and accurate" voting 
>>with a Condorcet method can sometimes choose a very poor winner, 
>>*in realistic social choice situations.* It's not common, but it happens.
>I'm not familiar with that. Which situations were you thinking of?

Pizza election. Three people must, for some reason, choose a single 
variety of Pizza to share. Two prefer Pepperoni. The third is Muslim, 
pork is haram, forbidden. However, everyone's second choice is 
Mushroom. There is another possibility, plain Cheese.

Let's assign normalized utilities of

2: Pepperoni, 10, Mushroom, 9, Cheese 0.

(This doesn't mean that Cheese is hated, but these are normalized to 
the available candidate set.)

1: Pepperoni, 0, Mushroom 10, Cheese, 8.

What's the best choice? Two thirds prefer Pepperoni. Majority choice. 
Condorcet winner. But not the SU maximizer. If Mushroom is chosen, 
everyone is happy. If Pepperoni is chosen, two are slightly happier, 
one is unable to eat. Note that the normalized utilities conceal the 
true preference strengths. Absolute utilities might be more like (on 
a scale of foods, best food possible is 100, worthless foods are 0):

2: P 50, M 49, 40
1: P 0,  M 49, 40

Two people give up a tiny preference to enable the third person to 
enjoy the meal equally with them. The overall satisfaction with 
Pepperoni is 100. With Mushroom, 147. It's not even close.

Would they use Range Voting? Of course not. They would talk about it. 
Each might state their favorite first (Plurality), but they'd also 
say why. And why not Pepperoni, in the case of the Muslim voter. 
Deliberative process. I've seen Approval polls work very well in a 
deliberative environment, they can easily be done very informally. 
Approval would have immediately settled on Mushroom.

FairVote gives the example of 99 voters voting A 100, B 99. And one 
voter votes A 0, B 100, and prevails. FairVote seems to think that we 
will be outraged by the violation of the Majority Criterion. Of 
course, we aren't. Clearly the one voter had a strong preference 
against A, we don't know why. Since the A voters really had an almost 
indistiguishable preference for A over B, it's reasonable for them to 
give up the tiny increment of preference so that everyone can be pleased.

I that election, though, I'd want to see a confirmation with a 
runoff. Do the A voters consent to this loss of their favorite? We 
have far short of a majority preferring B, the Range winner. We 
*could* take their votes as consent, though, and thus not need a 
runoff.... I'm coming to think that we should set >50% range as an 
approval cutoff, with majority approval required to complete.

More information about the Election-Methods mailing list