[Election-Methods] Correction of false statements by Ossipff & Schudy about range voting.

[Peter Barath]

>>"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."
>>
>>Ossipoff: Warren Schude's statement was correct

>--CORRECTION: optimal strategies can vote other than 0 and 1, and
>voting 0 or 1 can be suboptimal.

Seems you were not so assiduous as to actually read the footnotes
in Warren Schudy's paper, which in this particular case (footnote
number 1) reads: "As long as the population is sufficiently big
and uncertain."

And in that case we may nicely agree, I guess.

I think Michael Ossipoff's analysis:

"Suppose that the method is 0-10 RV...
Now, suppose that you consider the points that you're awarding 
one-at-a-time, as if it were a series of 10 Approval elections...
We're assuming that it's a public election, so that there are so many 
voters 
that your own votes have no significant effect on the probabilities.
Your Approval strategy is based on two things: The candidates' utility 
to 
you, and the probabilities that you estimate...
Your utilities don't change during that series of 10 Approval 
elections that 
you vote. The probability estimates don't change either...
If you give to a candidate any points at all, you give hir 10 points."

is informal, but fully correct. (Which doesn't mean I agree with
him in everything else.) And those who refer to linear
programming essentially say the same thing. If the field is big
enough, a small part of it may be considered as having linear
probability-distribution (or whatever) functions, so the optimum
lies somewhere on the border. So if you started to go to a
direction you have to stay on that course.

So, they say if the number of voters goes toward infinity, the
probability of a case where Approval-style voting is suboptimal
goes toward zero.

The counterexamples? most of them have extremally small number
of votes. And even which does not so, uses the less-then infinite,
non-linear attributes or simply wrong.

http://beyondpolitics.org/Range2Utility.htm

when shifts from Range(0,1,2) to Approval, calculates like those
"odd number" cases would simply vanish. And vanishing some good
vote value, the average worsens when Approval becomes the method.
But those cases don't vanish. The logical statistic assumption is
that they evenly distribute themselves among the neighboring cases.
And some of previously irrelevant cases become relevant cases, so
the probability of decisive vote rises. This rise exactly compensates
for the loss of utility rise. As for

http://rangevoting.org/RVstrat5.html

it's more reality, but only by using the three-candidate-tie event,
attributed with a T probability. If T=0, the classic case happens:
giving the in-between B candidate max or min is optimal, or all
the same. And if the number of voters goes toward infinity, T
goes toward zero.

So, please, don't infer "which graduation is best for range voting"
type statements from these calculations. We can go back to the
consensus (used even in your simulations) that _essentially_
a strategic Range vote is an Approval vote.

Which doesn't decide which one is better. Valid arguments exists
on both sides. Range voters can choose from more possibilities, but
is this choice a pleasant one? I can be a "sucker" or a "cheater",
maybe I would be more glad without it.

I think they are so close that even their fans can be close and
fight side by side. I'm looking for the future when TV-personalities
as well as people at the coffee machine dispute about whether
Approval or Range is better method.

Peter Barath

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