[EM] Ballot design (new simple legal strategy to get IRV)

[Juho Laatu]

> On 11 Oct 2015, at 15:26, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> 
> On 10/11/2015 02:23 PM, Juho Laatu wrote:
>>> On 11 Oct 2015, at 15:11, Kristofer Munsterhjelm
>>> <km_elmet at t-online.de> wrote:
>>> 
>>> On 10/11/2015 01:06 AM, Juho Laatu wrote:
>>>> 
>>>> Bias-lessness is achieved in Finland by inviting representatives
>>>> of
>>> all parties to take part in the vote counting process. I guess the 
>>> tradition is to not to even start making biased interpretations.
>>>> 
>>>> STV is unfortunately not as summable as e.g. Condorcet. One may
>>>> lose also some privacy and introduce some risk of coercion and
>>>> vote buying by recording and distributing ranked votes to the
>>>> central authority (and who knows even publishing them). I have no
>>>> good foolproof solution for that right now. Risks to be estimated
>>>> and appropriate protective measures to be taken (or just stay in
>>>> some simpler methods).
>>> 
>>> That brings to mind what I'd call a great open question: is the
>>> Droop proportionality criterion compatible with summability? I
>>> suspect not, and I suspect that a proof would make use of a
>>> pigeonhole principle. I don't have much beyond that hunch, though.
>> 
>> Do you mean Droop proportionality with ranked votes? I'm thinking
>> about a voter who votes A>B>C>D>E, where candidates A, B, C and D can
>> not win. To pass the vote to E, the vote probably has to be stored as
>> it is.
> 
> Yes, I was thinking of ranked ballot DPC. But it's a bit harder than
> that because the single-winner analog, mutual majority, is compatible
> with summability even though (if I recall correctly) inferring the whole
> mutual majority set isn't. That is, summable methods can pass mutual
> majority, but they can't let you know the whole minimal mutual majority set.

That may mean that summable methods that meet mutual majority do some sort of an overkill. I mean that having mutual majority depends on the actual votes in the same way as vote transfer did in my A>B>D>C>E example. You can get the same matrix with votes where some mutual majority exists or it doesn't exist. If this is the case, some vote sets that do not have mutual majority will be handled as if they had mutual majority since the (summed up) matrix can not tell us if there was a mutual majority or not.

Juho