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

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> 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.
> 
> Understand that before writing this, I actually looked at some real 
> ballots. Quite possible, some real ballots ask for ranking in order of 
> preference. But the RCV ballots in the U.S., just like the name implies 
> (Ranged Choice Voting) asked for "First Choice," "Second Choice," etc. 
> Which leaves it up to the voter how to vote.
> 
> In my view, to ask for "First Preference" on a ranked ballot would be 
> just as offensive as asking voters on a Plurality ballot to vote for 
> "their favorite." It would generate a political bias, making "Core 
> Support" the standard in elections. Plurality tends to choose a 
> Condorcet winner because voters strategize and make their compromises 
> based on information about each other. "Strategic voting" is how voters 
> can improve the performance of a voting system. The problem, of course, 
> is that when the voting system gets very good, strategic voting can 
> sometimes reduce the overall voter satisfaction. However, my contention 
> is that when it does this, it does not do it to any great extent, and I 
> have yet to see an example, of any reasonableness, that contradicts this.

Plurality voters have to be strategic all of the time because Plurality 
is a bad voting method. Ideally, there would be a "vote for one" method 
where people *could* vote their favorites. 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).

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.

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.

>> 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?

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. 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).

>> 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.

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?

>> As for Range, either Range, the method, has a well defined input or it 
>> has not. 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)?
> 
> The input is well-defined, it's provided by the voters. What cannot be 
> done is to define the input exclusively by a preference profile, 
> additional information my be incorporated. "Preference profile" is 
> clearly inadequate information to allow utility optimization; preference 
> strength information is also necessary, and, for practical decision 
> making (even by individuals, and voting systems involve individual 
> decision-making), lottery probabilities are also necessary. The voter is 
> making choices in a lottery, and to do this intelligently requires 
> estimating the lottery probabilities for each option.

Is there such a thing as a preference strength information in a vacuum? 
If there is, then altering that information (beyond rounding errors) 
misrepresents the input. 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 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.

When I say this, I'm excluding external feedback loops, like ranking a 
candidate for re-election lower because he didn't fulfill your 
expectations the last time around. Those are parts of democracy. But 
let's say you froze time just before the election. The voters shouldn't 
need to use mechanisms external to the voting method to get a good 
result, or run feedback loops within that frozen world. If they're 
absolutely necessary, have a computer do it as part of the method itself 
and let voters vote.

> 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?

> 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.

[snip]

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

> 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.)

> 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?