# [EM] "Possible Approval Winner" set/criterion (was "Juho--Margins fails Plurality. WV passes.")

Juho juho4880 at yahoo.co.uk
Tue Mar 13 22:55:45 PDT 2007

```On Mar 13, 2007, at 18:35 , Chris Benham wrote:

>> The definition of the criterion contains a function that can be
>> used to evaluate the candidates (also for other uses) - the
>> possibility and strength of an approval win. This function can be
>> modified to support also cardinal ratings.
>>
>> In the first example there is only one entry (11: A>B) that can
>> vary when checking the Approval levels. B can be either approved
>> or not. In the case of cardinal ratings values could be 1.0 for A,
>> 0.0 for C and anything between 0.0001 and 0.9999 for B. Or without
>> normalization the values could be any values between 0.0. and 1.0
>> as long as value(A) > value(B) > value (C). With the cardinal
>> ratings version it is possible to check what the "original utility
>> values" leading to this group of voters voting A>B could have been
>> (and if the outcome is achievable in some cardinal ratings based
>> method, e.g. max average rating).
> This concept looks vulnerable to some weak irrelevant candidate
> being added to the top of some ballots, displacing a candidate down to
> second preference and maybe thereby causing it to fall out of the
> set of  "possible winners". It probably has other problems
> regarding Independence
> properties, and I can't see any use for it.

It seems, as usual, that you discuss more strategy resistance and
criteria and I discuss more behaviour with sincere votes and achieved
utility. Nothing wrong with that. Both are needed.

I didn't yet find out a scenario where the difference between rating
and Approval style evaluation would lead to strategic problems. Let's
see if I can find scenarios that would demonstrate some essential
differences.

In general I'd still say that the two criteria bring almost identical
results. My motivation was just to present the (about) same criterion
in a way that directly links to some well known social utility
function and thereby give some "sincere vote behaviour" beased
explanation to why some elections could decide to use the PAW criterion.

The strategic problems of Range / ratings based methods are not
problematic here since one talks only in theory "what kind of
outcomes would be possible (with sincere votes)".

I don't see any strong need to use the PAW criterion (or
corresponding ratings variant) for strategy resistance or for
"election target" reasons but they seem possible. They add
complexity, but if justified for some reason, then why not. I'll try
to think more and come back if needed.

Juho

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