[EM] RV comments

[Abd ul-Rahman Lomax]

At 11:00 PM 7/20/2007, Chris Benham wrote:
Can we please have an example of one of these "other scenarios" that 
shows that Mike Ossipoff's
>"claim  is false"?
>
>I think Warren Schudy put it well in a  July 2007 draft paper:
>
>"Range voting is a generalisation of approval voting where you can 
>give each candidate any score
>between 0 and 1. Optimal strategies never vote anything other than 0 
>or 1, so range voting
>complicates ballots and confuses voters for little or no gain."

Good. Since this is simple, clear, and false, we should be able to 
dispose of it quickly. I actually gave an example, and Benham 
dismisses it, for reasons that are ... simply obfuscation.

>>If I prefer A>B>C, and those are the only options, it's
>>clear that I optimize my expectation by voting A max, B min, but
>>where do I rate B? ...
>>
>>Where do I rate B? Well, if the B utility is midway between A and C,
>>we can define a "sincere" rating of B as 50%. If we have rated A max
>>and C min. However, that max and min rating is itself a full
>>disclosure of the utilities, the ratings have been normalized to the
>>election candidate set, causing loss of absolute utilities.
>>
>>It never hurts the voter personally to normalize in that way.
>
>That is only true (probabilistically) if  both the "B utility" is 
>*exactly* midway between A and C
>and  also  (as far 
>as  the  voter  knows)  both   A  and   C   are  equally  likely   to  win.

Since I was describing the normalization, which only deals with the 
extremes, Benham's comment is completely off, for the purpose of my 
comment about "it never hurts the voter personally...." was only 
about the votes for A and B. In other words, this was about the voter 
voting max for A and min for B.

In order to understand the rating for B, I must first consider the 
ratings for A and C, which are unique in being the most preferred and 
least preferred. If I rate them to the extremes, I give my overall 
vote maximum strength.

I hadn't yet stated what the optimum vote for B would be. I went on 
to do so, but Chris truncated my response.

To repeat, in what I was quoted above as writing, I did not yet give 
the optimum vote for B. I only stated what a "sincere" rating would 
be. I was not claiming, nor do I claim, that this "sincere" vote is 
optimum, and, yes, it can hurt the voter to vote that as a Range 
vote. To a degree.

>It  is obvious that in practice the voter in Abd's example could 
>be  "hurt personally" by not voting
>B max if  that causes C to win instead of B, or by not voting B min 
>if  that causes B to win instead
>of  A.

And I said exactly that, so why Benham thinks he is in some way 
refuting what I wrote is beyond me, except that I can speculate that 
he has concluded that I'm wrong, therefore he interprets what I write 
in a way as to make it wrong. And then he did not bother to read the 
next paragraphs, which went on to note that the optimum vote for B 
was exactly as he said, in the cases which I described in detail.

But then I noted that the optimum vote for B in the zero-knowledge 
case (where we must assume equal probability of election of all the 
candidates) was 50%, i.e., the sincere estimation of utility. And 
this is actually quite easy to prove, so easy that I won't even 
bother unless forced, and I'd prefer that someone else state the 
argument, I'm tired of belaboring the obvious....

Sure, a voter could, after the election, discover that their vote 
caused an undesirable outcome. But that is true for any voting 
method, and certainly it's true for Approval, where it can cause 
precisely this outcome, and where the voter does not have that option 
of an intermediate vote. So such "regret" is more likely, in fact.

I'll quote Schudy again:

>"Range voting is a generalisation of approval voting where you can 
>give each candidate any score
>between 0 and 1. Optimal strategies never vote anything other than 0 
>or 1, so range voting
>complicates ballots and confuses voters for little or no gain."

First of all, it is inaccurate to call Range Voting "a generalization 
of approval voting." Range was independently invented; however, 
because both methods sum votes, both methods belong to the same class 
of methods, and the general name for the class has become Range, with 
Approval being a specific method with the minimum range of possible votes.

It is also more general to state that Range allows the voter to give 
each candidate any score between 0 and N, and we frequently describe 
the scores in terms of percentage.

Now, to the core of Schudy's claim:

He uses the word "never," which is an absolute, making it trivial to 
refute his claim, all I have to show is a simple counterexample, and 
I already did that. The optimal vote in Range -- as in Approval -- 
depends on the estimated probabilities of election of each candidate. 
To repeat the argument, if I prefer A>B>C, with the A>B preference 
strength being equal to the B>C preference strength, then, in 
Approval, how I vote for B depends on my estimation of the election 
probabilities. If C is an irrelevant alternative (no chance of being 
elected), then I will not approve of B. If A is an irrelevant 
alternative, then I will approve of B. And if B is an irrelevant 
alternative, then it does not matter how I vote for B, it's moot.

(This example shows how "approval" is not a characteristic purely of 
the relationship between a voter and candidate, as some seem to 
pretend, but is also a function of context, at least when it comes to 
voting strategy. You cannot tell from my vote whether or not I 
actually "approve" of B, in ordinary terms; indeed, you can't tell 
from the vote if I approve of any of the candidates. I prefer not to 
use the term Approval for this very reason; rather I write about 
voting, and suggest that we simply count all the votes. And with 
Range, we are doing the same, counting all the votes, only every 
voter can cast up to N votes for each candidate.)

Now, in the Approval example, we have a crisis point. If I am 
considering which candidate is the frontrunner, between A and C, on 
which my choice turns, and as the relative probability of the 
election of C increases, there is a point where my vote for B 
suddenly flips from disapproval to approval. The discontinuity is a 
sign that there is something amiss.

If we look instead at this same context for a Range election, there 
would be no discontinuity. As the relative probability of the 
election of C increased, the optimum rating of B would increase, 
until, at some point, the rating of B would become maximum.

If A and C are equally likely to be elected, or we don't know which 
of them is equally likely, so we must assume equality, and given the 
initial condition that the preference strengths are balanced, it's 
clear that game theory would optimize our vote as 50% for B. This 
precisely balances the risk that our vote will elect B over A with 
the risk that our vote will fail to elect B over C.

In fact, it is usually a vanishingly small probability that our vote 
will actually turn the outcome, so for true game theory analysis I'd 
have to assume that there is no particular advantage to any 
particular vote, it is down in the noise; however, there remains the 
satisfaction of having clearly expressed one's opinion.

And that, of course, would be a sincere vote! And the more expression 
the method allows, the better it is for this purpose. This may, 
indeed, swamp other strategic considerations.... On the other hand, 
we could look at common strategy to be pursued in coordination by 
some subset of voters; I'm proposing to do similar by assuming that 
there are only three voters (thus we have three 'subsets' who will 
follow unified strategy).

And the actual matrix will have to wait for another day, it's too 
late to finish this now....




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