[EM] Andy's Question

[Juho Laatu]

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, fsimmons at 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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