[EM] Generalizing "manipulability"

[Kristofer Munsterhjelm]

Abd ul-Rahman Lomax wrote:
> At 03:57 PM 1/18/2009, Kristofer Munsterhjelm wrote:
> 
>> Wouldn't it be stricter than this? Consider Range, for instance. One 
>> would guess that the best zero info strategy is to vote Approval style 
>> with the cutoff at some point (mean? not sure).
> 
> Actually, that's a lousy strategy. The reason it's lousy is that the 
> voter is a sample of the electorate. Depending on the voter's own 
> understanding of the electorate, and the voter's own relationship with 
> the electorate, the best strategy might be a bullet vote. Saari showed 
> why "mean cutoff" is terrible Approval strategy. What if every voter 
> agrees with you but one? The one good thing Saari shows is that this 
> yields a mediocre outcome when 9999/10000 voters prefer a candidate, but 
> also approve another "above the mean."
> 
> Essentially, the voter doesn't need to know anything specific about the 
> electorate in a particular election, but only about how isolated the 
> voter's position *generally* is.
> 
> For most voters, zero-knowledge indicates a bullet vote unless there are 
> additional candidates with only weak preference under the most-preferred 
> one, such that the voter truly doesn't mind voting for one or more of 
> them in addition.

Perhaps. My point is not this. I explicitly said that I didn't know the 
zero info strategy ("not sure"). But also note that what I'm talking 
about is /zero info strategy/, i.e. how you'd vote if you were stuck on 
Mars with the candidates (who had broadcast systems with which to run 
their campaigns), and then you all traveled back to Earth just before 
the vote. The zero-info strategy may be something else than mean cutoff 
(again, *I don't know!*), but it may also just be lousy because the 
method has a bad zero-info strategy and voters have to know how others 
are likely to vote.

>>  However, it would also be reasonable that a sincere ratings ballot 
>> would have the property that if the sincere ranked ballot of the 
>> person in question is A > B, then the score of B is lower than that of 
>> A; that is, unless the rounding effect makes it impossible to give B a 
>> lower score than A, or makes it impossible to give B a sufficiently 
>> slightly lower score than A as the voter considers sincere (by 
>> whatever metric).
> 
> Yes. Indeed, I've suggested that doing pairwise analysis on Range 
> ballots, with a runoff when the Range winner is beaten by a candidate 
> pairwise, would encourage maintenance of this preference order.
> 
> Think of Range as a Borda ballot with equal ranking allowed and 
> therefore with empty ranks. (Not the ridiculous suggestions that 
> truncated ballots should be given less weight). If a voter really has 
> weak preference between two candidates, the obvious and simple vote is 
> to equal rank them. But then where does one put the empty rank?
> 
> There are two approaches, and both of them are "sincere," though one 
> approach more accurately reflects relative preference strength. There 
> are ways to encourage that expression.
> 
> But here is the real problem: trying to think that a zero-knowledge 
> ballot is somehow ideal is discounting the function of compromise in 
> elections. That is, what we do in elections is *not only* to find some 
> sort of supposed "best" candidate, but also to find compromises. That's 
> what we do in deliberative process where repeated Yes/No voting is used 
> to identify compromises, until a quorum is reached (usually a majority, 
> but it can be supermajority). Deliberative process incorporates 
> increasing knowledge by the electorate of itself. It extracts this with 
> a series of elections in which sincerity is not only expected, it's 
> generally good strategy. In that context, "approval" really is approval! 
> If a majority agrees with your approval, the process is over.

A few nits: first, equal preference allowed doesn't imply empty rank, 
though I see that Borda would have to in order to be equivalent to 
Range. For that matter, any weighted positional system where you can 
give fractional votes and all positions have a nonzero weight can be 
reduced to Range in that way.
Second, zero-information strategy may still be strategy, and this 
possible presence of strategy would show that voters could expect a 
personally better result from altering their ballots. For instance, if 
Range has a zero-info strategy that lies in voting Approval style 
according to some cutoff, and if all voters were limited to zero 
knowledge and voted one way, yet this person voted according to zero 
info strategy, and the latter voter got greater power because of this, 
then strategy exists. This strategy presents as noise whenever the 
zero-info strategy results in a different ballot than a sincere ballot does.

> I consider election methods as shortcuts, attempts to discover quickly 
> what the electorate would likely settle on in a deliberative 
> environment. As such, it is actually essential that whatever knowledge 
> the electorate has of itself be incorporated into how the voters vote.
> 
> And that's what happens if, in a Range election, voters vote von 
> Nuemann-Morganstern utilities. They have one full vote to "bet." They 
> put their vote where they think it will do the most good. They can put 
> it all on one candidate, i.e., bullet vote. They can put it on a 
> candidate set, thus voting a full vote for every member of the set over 
> every nonmembe, i.e., they vote Approval style. They can split up their 
> vote in more complex ways. What they can't do in this setup is to bet 
> more than one vote. I.e., for example, one full vote for A over B, and 
> one full vote for B over C. If we arrange their votes in sequence, from 
> least preferred to most, the sum of votes in each sequential pairwise 
> election must total to no more than one vote.

My opinion is that this places a burden on the voters because now they 
don't just have to model themselves, but they have to model the other 
voters (and the other voters' models of themselves) in order to devise 
the "correct" way of voting.

It's not so hard to see that this could lead to a true compromise if the 
iteration happens for long enough - say that the communication is 
sufficiently advanced that one can run a deliberative assembly on top. 
Then everybody votes [whatever was agreed upon] > [everything else] 
afterwards. For some, that's not a sincere vote (it's even an order 
reversal), but it would "work".

You say that VNM utilities are instinctive. To me it seems they make 
things more complex. They introduce feedback, and through it, possible 
cycling. If there's a Condorcet situation and there are poll iterations, 
the poll winner could change from A to B to C then to A again.. whereas 
Condorcet methods handle this implicitly if they deal with sincere votes.

Beyond simple VNM utilities, there's also Range zero-info strategy (vote 
Approval style - again I don't know where the cutoff is, but it doesn't 
matter in this respect). However you may present it, I think that voters 
will say that that looks like Plurality strategy - "so I have to vote 
Approval style in order to maximize the punch of my vote, but then I 
have to vote for the frontrunner unless he's not a frontrunner - do I 
have to vote for the lesser evil?". In Condorcet (or Bucklin or 
whatnot), you simply vote minor > lesser > greater and that's it.

> Calling them VNM utilities sounds complex, but it's actually 
> instinctive. If we understand Range, we aren't going to waste 
> significant voting power expressing moot preferences. Suppose someone 
> asks you what you want. But you understand that you might not get what 
> you want. You prefer A>B>C>D, lets say with equal preference steps. You 
> think it likely that A or B might be acceptable to your questioner, but 
> not C or D. You have so much time to convince your questioner to give 
> you what you argue for. How much time are you going to spend trying to 
> convince the person to give you C instead of D?

When you vote, it's not against the clock. To some extent, ranked 
ballots are contingent ones. If you vote A > B > C and A wins, that you 
voted > B > C doesn't really matter (unless B was a compromise, in which 
case A wouldn't have won). IRV takes this to an extreme - too far, 
probably - but the point is that votes don't have to be "out of a fixed 
pool". In a method that satisfies local independence of irrelevant 
alternatives, if you vote A > B > C > D or A > B > E > D, which you vote 
has the same effect if C and E were not in the Smith set, so you can add 
as many write-ins as you desire.

> You might mention it, but you wouldn't put the weight there unless you 
> thought that the real possibilities were C or D.
> 
> Voter knowledge of the electorate is how elections reach compromise, and 
> it's very important. Of course, there is also the process for getting on 
> the ballot, in some places, but where ballot access is easy, it's about 
> the only way we have in single-winner elections of finding an acceptable 
> compromise.
> 
> That's not to deny the value of voting systems which can extract a 
> probably reasonable compromise from expressed preferences, but one of my 
> points has been that unless preference strength *can* be expressed, we 
> are presenting distorted information to the voting system.
> 
> At least the voters should be able to "distort" as they choose, seeking 
> compromise, instead of the system inherently distorting.... we know that 
> some voters will simply vote as accurately as they can and, it turns 
> out, from at least one study (mine) this tends to improve expected 
> results for all the voters,

You provide the method with the option to accept more information, 
though exactly what that information is is not very well defined (at 
least not in the sense of the voter's own preferences). The question is 
whether the push towards a more accurate result will be stronger than 
the push away due to distortion (both unintentionally, e.g from having 
to vote Approval style or from cycling, and intentionally, as with 
parties using central resources to calculate the optimal vote).