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

[Abd ul-Rahman Lomax]

At 12:35 AM 12/3/2008, Juho Laatu wrote:
>Approval is a special case since the votes are so
>simple that it is hard to tell when one votes in
>line with one's sincere opinion and when not.

Rational Approval votes are never "out of line" with one's sincere 
opinion." In Approval, equal ranking, when there are more than three 
candidates is *required.* There is no way to not vote equal rank for 
at least one pair; we often overlook bottom ranking, which is also 
important. But Juho does make a suggestion, albeit a defective one.

>  One
>could say that any placement of the approval
>cutoff is sincere as long as it respects the
>sincere preference order of the voter. But one
>could also require that the approval cutoff should
>be placed on some "main gap".

Why? I don't see any reason why that particular position is better 
than any other. It is simply *easier*.

>  I mean that if the
>sincere ratings are A=93, B=31, C=30, D=4, and B
>and C are the front runners, then Approval vote
>{A, B} is probably a strategic/optimized vote.

Really? Suppose A is a write-in, Jesus Christ by name. He didn't 
register as a candidate, but I really do want to always think about 
him. (I'm a Muslim, but that doesn't contradict that.) And B is a 
total loser, nobody likes him, he's irrelevant. B and C are ordinary 
candidates, a Democrat and Republican, with the usual relatively 
minor difference between them. Neither one is going to save the 
world, A would do that. And neither one is going to wreck it, D would 
do that. There is enough gap between B and C that I will bother 
voting! So I vote. Technically, this is optimized, but anyone that 
doesn't optimize with the situation being as I described it is not a 
serious voter, trying to deal with the real world and make it better 
instead of imagining that voting is an exercise in pure, absolute 
opinion and sincerity. It's an exercise of *power*. We each have one 
vote's worth of power. We should use it wisely, and using it wisely 
implies not wasting it on empty and useless expression of opinion. If 
it's more important to me to say that I support Nader, with my vote, 
than to actually affect the result, that's my decision. I must think 
that political speech is more important than effective action. If 
progressives think this way, no wonder they are so often out of power.

For me to vote A only is to abstain from the election, and I know it. 
For me to vote A, B, C is likewise to abstain. That's fine if I don't 
care about the result. Do I care about the result between B and C? 
The ratings imply not, generally. Suppose this was 2000 and A was 
Nader, B was Gore, C was Bush, and D was Badnarik.

A Nader voter might well have utilities like this. This voter, 
however, would be likely, even with Approval, to vote A only. Unless 
the voter truly thinks Nader is the Messiah, hence B and C have been 
shoved together, the preference strength between them paling in significance.

Not normalizing to the *relevant* candidate set, the set of 
candidates who could win, leads to all kinds of preposterous 
conclusions as to what a sincere vote would have to be. Bottom line, 
this was ApprovaL?

Did the thought of C winning make you feel ill? And the thought of 
Gore winning seemed like, well, okay, not terrible, it's actually 
better than I was worried would happen. If so, hang the numbers, it's 
quite reasonable and sincere to vote for Gore and not for Bush. And 
we could call those votes, quite reasonably, sincere. The voter votes 
A, B. But if the 31 vs 30 does represent very weak preference, as it 
seems it was intended to represent, I might easily not vote for B. 
Sure, that's the only vote that would count, if these were 
frontrunners, but there are other considerations, as we know: a fair 
number of people voted for Nader. If it's more important to show 
exclusive support for your favorite, and many would think so (and I 
agree that there is an importance to it, this is not valueless, it's 
just that we need to be careful about other considerations as well), 
then I'd think it quite "strategic" to not vote for B.

>  It
>doesn't strictly violate the sincere preference
>order but probably the voter would have voted in
>some other way if he had not had some strategic
>considerations.

You just can't tell. Is the preference discernable to the voter? (I 
have trouble, I think, directly discerning a preference distinction 
of 10%, within normal choice ranges, much more so 1%.) If the 
preference is discernable, the ratings have been compressed by the 
presence of A, the Messiah. Ask him to hide until the election is 
over, he's messing it up, and he's not a citizen, ineligible for the 
office. Really want to do some good, ask him how to vote, don't hand 
him an empty and useless endorsement on a ballot!

If the preference is discernable, then it's reasonable and not 
insincere to set the approval cutoff there.

There is no absolute approval cutoff, and the attempt to define one 
using the idea that a small preference step, relative to overall 
preference, is only likely to be expressed if strategically affected, 
may be true in terms of probabilities, if the candidates are all 
reasonable possibilities. But when one is obviously outside reality, 
voters are simply going to neglect that and re-examine utilities. We 
simply don't know what 31:30 means. That might be a *huge* 
preference, as elections go.

>In Range this is clearer. Vote A=100, B=99, C=1,
>D=0 obviously is not based on the sincere
>ratings only.

Probably not. But that does not make the vote insincere. It means 
that it has probably been cast by considering who the frontrunners 
are. But what about this vote: A,B 100, C, D 0. Is that "not based on 
sincere ratings.?

Why not? A and B could be clones, as far as the voter is concerned, 
likewise C and D. And if that vote is possibly based on sincere 
ratings, why not the one stated above? Clones with a discernable difference.

The transformation from ratings, as well, might be linear but 
truncated (the intermediate region simply was not populated with candidates).