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Counter-example:<br>
Lets assume ballots represent sincere ratings.<br>
50%: A-100 B-70 C-0<br>
30%: B-100 C- 90 A-0 <br>
20%: C-100 A-10 B-0<br>
Average ratings: A-52 B-65 C-47<br>
Outcome: B wins<br>
Satisfaction: 30%<br>
A method delivering A as a winner would produce a 50% satisfaction
measure.<br>
<br>
I do not maximize social utility. But rather individual approbation.<br>
I compare the global result with the optimal result according to the
voter.<br>
The optimal result is defined as the elected representatives that
would be obtained if every other<br>
voters with the same opportunity than the reference voter had voted
like the reference voter.<br>
Maybe satisfaction is not the proper terminology.<br>
<br>
Stéphane<br>
<br>
Stéphane Rouillon a écrit :
<blockquote cite="midBAYC1-PASMTP124575B60DE568EA6B022C94D40@CEZ.ICE"
type="cite">
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Hi Kevin,<br>
<br>
the satisfaction criteria I proposed to evaluate multi-winner methods
is independant of PR measurement.<br>
It is a parallel criteria. For example two different electoral methods
could elect the same<br>
proportion of the political parties candidates (30 Cons and 70 Lib for
example),<br>
but not the same persons. Thus proportional analysis would produce the
same<br>
PR measure but satisfaction analysis could differ in result.<br>
<br>
I do not need to know the method. The goal is even to be able to<br>
evaluate a method without knowing wich one it is.<br>
All I need is a sincere set of the electorate will (it covers either
preference or approbation<br>
using this word) and the outcome. To be precise I need to know the
candidate set<br>
among which each elector can choose one or several representative (it
can be applied to single-winner method too).<br>
<br>
No I don't think average rating will always be optimal. I'll try to
build a counter-example.<br>
<br>
Yes I can build cases where pushing PR to optimality would decrease
satisfaction measurement.<br>
<br>
SPPA optimizes PR, and after, using this optimal seat distribution as a
constraint, optimizes<br>
satisfaction by choosing which candidate receives seats for each
political party.<br>
At the time, I was calling this maximizing individual approbation.<br>
<br>
Stéphane<br>
<br>
Kevin Venzke a écrit :
<blockquote cite="mid590774.29342.qm@web23303.mail.ird.yahoo.com"
type="cite">
<pre wrap="">Hi Stéphane,
--- Stéphane Rouillon <a class="moz-txt-link-rfc2396E"
href="mailto:stephane.rouillon@sympatico.ca"><stephane.rouillon@sympatico.ca></a> a écrit :
</pre>
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<pre wrap="">Hello Kevin,
these ratios are guesses I have for real elections.
But I am fed up with guesses so the goal is to build an objective method
able to
determine for a perticular set (method, ballots expressing sincere
preferences, outcome)
of one electoral data, the most satisfying method in the eye of all
voters.
</pre>
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<pre wrap=""><!---->
But if you assume sincerity, won't you end up finding "average rating" to
be the best method? Or are you mainly concerned with PR here?
If the latter, it seems interesting to me to ask whether "the most
satisfying method in the eye of all voters" might actually be incompatible
with proportionality?
Kevin Venzke
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