[EM] Sincere Range and Approval
Forest Simmons
fsimmons at pcc.edu
Sat Nov 1 14:40:16 PDT 2014
Kris,
good points!
I hope I didn't give the impression that this definition of sincere Score
and sincere Approval is the only one possible.
The thing I like about it is that it has meaningful interpretations for
both (1) the sum over all ballots of the ratings for a candidate (the
expected number of voters that will be correctly represented on a random
issue of interest) and (2) the sum of the candidate ratings on one ballot
(the expected number of candidates that will correctly represent the voter
of that ballot on a random issue of interest).
Note that in the geometric example I gave in my answer to your other email,
the ratings were well defined by geometric proximity (opposite of distance)
rather than by probability.
Both of these approaches to cardinal ratings nullify the criticism so often
used against ratings that individual utilities are incapable of being added
or even compared.
Forest
On Sat, Nov 1, 2014 at 3:09 AM, Kristofer Munsterhjelm <km_elmet at t-online.de
> wrote:
> On 10/31/2014 03:35 AM, Forest Simmons wrote:
>
>> I have written before about how to convert sincere ratings into sincere
>> approval ballots.This time I want to step back and explain a way to
>> compute sincere ratings: when the meanings of the sincere ratings are
>> more evident, then the sincere approvals take on additional meaning, too.
>>
>>
>> Suppose that by examining the voting record of candidate X you see that
>> on a random issue of interest to you there is a probability p that she
>> would vote the same way you would vote if you had the opportunity to
>> vote in the representative body, i.e. there is a probability p that she
>> would correctly represent your wishes if she were your representative.
>>
>>
>> I will now explain why I consider this probability p to be a natural
>> choice for your sincere rating of candidate X.
>>
>>
>> In fact, if every voter V rated candidate X according to the
>> voter’ssubjective (if not calculated) probability of X correctly
>> representing V on a random issue of interest, then the sum of these
>> ratings would be the expected number of voters that would be correctly
>> represented by X on a random issue of interest.
>>
>> So with this definition of sincere ratings, the candidate with the
>> highest sum of ratings is by definition the candidate expected to
>> correctly represent the greatest number of voters on a random issue of
>> interest:i.e. the Range Winner maximizes the expected number of
>> correctly represented voters (as long as ratings are sincere).
>>
>
> It's an interesting definition, but by its definition, I think that many
> voters would not be voting sincerely since they might take the quality or
> experience of the candidate into account.
>
> Say there's an election for a general body. Voter X is considering either
> voting for (i.e. giving a high score to) A or B. A is very close to X but
> doesn't know the political apparatus all that well, or doesn't know how to
> implement the policies in question. On the other hand, B is somewhat
> further away but knows the political arena very well. Then the voter might
> rate A and B equal even though B represents X's views less correctly.
>
> Obviously, there's a limit to this. A left-wing voter would rather have an
> inexperienced left-wing candidate than an experienced right-wing one. He
> might in fact prefer an inexperienced right-wing candidate to an
> experienced one.
>
> I suppose you could integrate this into the rating, and say something
> like: A's sincere rating, from X's point of view, is the degree to which
> electing A would help X get the society that he prefers. But that may be
> objected against in similar ways to how one might criticize utilitarianism:
> that X most likely doesn't have the extreme calculating capacity or the
> full information to make this judgement, so with high probability, any
> rating will differ from the sincere one.
>
> Also, an interesting implication of this is that advertising, etc, would
> turn voters' votes less sincere by indirect effect, unless you consider
> such campaigns to actually alter the voter's opinion on policy rather than
> on which candidates are closest to him.
>
> This is not to say that your definition is bad. By using this definition,
> it should be possible to reason about rated methods and how to elect
> candidates properly under various settings (e.g. affine-transformed
> ratings). But it isn't complete.
>
> It would perhaps be more accurate for an electoral equivalent of the
> "advisory" system one could imagine happening under sortition: that is,
> when the representatives are randomly selected, their knowledge of
> implementing things will probably vary quite a lot, and so they would make
> use of advisors or advisory bodies to help them. In such a system,
> representation is the important thing, because quality or experience
> variance is dealt with by using advisory bodies. If an electoral body
> worked the same way, then the important matter to a voter would be whether
> the candidate represented him, not how much experience he had, and then
> your definition would work very well.
>
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