[EM] Generalizing "manipulability"

[Abd ul-Rahman Lomax]

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.

>  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.

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.

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?

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,