Andy Jennings' question is a good question.
The original votes were
20 AC
20 AD
20 AE
20 BC
20 BD
20 BE
Let's decrease the support of A and B a bit (20 approvals reduced from both of
them).
20 C
20 AD
20 AE
20 C
20 BD
20 BE
Would {A,B,C} be a good choice now? It is not good if reduction of approvals
makes A and B winners. And adding those reduced approvals back shouldn't make A
and B losers.
One psychological problem in the original question is that we tend to assume
that the wide support of A and B (50% of the voters) can not be as strong as
the more focused support of C, D and E (33% support).
One question is if the target of this election is to treat all voters equally
or to treat all voters as well as possible. If we elect A, B and C (with the
original votes), then The C supporters (with 2 favourites approved) may be
happier than those A and B supporters that did not support C (1 favourite
approved). If we elect C, D and E instead, all voters are probably equally
happy, which may thus be a positive thing in some elections even though we can
assume that nobody became happier with the change. The criterion of equal
treatment could thus mean also that we should reduce the happiness level of
some voters in order to treat all equally. My answer to this last question is
that the chosen policy should depend on what one wants to achieve in that
election (i.e. the targets of the society for this election). I guess it is a
more common approach to allow the happiness level of some voters to increase if
that does not cause the happiness level of any voter to decrease.
With these votes that only display the approvals we may assume that the fact
that others may be jealous tho those that got 2 of their favourites elected
will not decrease their happiness. And we may assume that the support of A and
B is not any milder than the support of C, D and E. But if these assumptions do
not hold, then the happiness of some voters may decrease if we elect A or B.
Juho
On 31.7.2011, at 0.15, fsimm...@pcc.edu wrote:
> I think that Andy's question about who the PR winners should be in the three
> winner (approval) scenario
>
> 20 AC
> 20 AD
> 20 AE
> 20 BC
> 20 BD
> 20 BE
>
> needs more consideration.
>
> As was pointed out {C, D. E} seems the best, even though PAV would say the
> slates
>
> {A,B,C}, {A,B,D}, and {A,B,E} are tied for best.
>
> For those that lean towards {C, D, E}, would you go so far as to say it is
> the best solution for the
> scenario
>
> 40 ABC
> 40 ABD
> 40 ABE ?
>
> If not, then how do we decide? If so, then how about
>
> 40 C>A1>A2>A3(at 90%)>>>(all others)
> 40 D>A2>A3>A1(at 90%)>>>(all others)
> 40 E>A3>A1>A2(at 90%)>>>(all others)
>
> Should {A1, A2, A3} win? or should we continue with {C, D, E} ?
>
> If I understand it, STV would elect {C, D, E}, while RRV (sequential or not)
> would elect {A1, A2, A3}.
>
> How would Warren's three district connection solve this problem?
>
> I'm not saying that these scenarios are likely, but I think we need a clearer
> idea of what we want in these
> extreme cases when we are designing and evaluating practical methods. "The
> exceptional cases test
> the rule," which is the original meaning of the aphorism, "The exception
> proves the rule."
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