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

[Juho Laatu]

> On 11 Oct 2015, at 21:42, Kristofer Munsterhjelm <km_elmet at t-online.de> wrote:
> 
> On 10/11/2015 03:59 PM, Juho Laatu wrote:
>>> 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.
> 
> Right. My point is that one could imagine this to be the case for Droop
> proportionality as well. A person who thinks that you can have both DPC
> and summability could say that there might exist methods out there that
> elects a candidate from a Droop solid coalition and also elects that
> candidate in a case with the same matrix but no Droop coalition. If
> knowing the full mutual majority set is incompatible with summability
> yet electing from it is compatible with summability, then that might be
> the case for a Droop set too.
> 
> I don't think so; but because of the equivalence, the proof can't just
> be that you don't have enough space to encode that the vote has to be
> transferred to E. If it were, it would also prove that electing from the
> mutual majority set is impossible because IRV is non-summable.

Ok, I think I got the point, or at least some part of it.

That led me to playing with the following votes
50: A>B>C
50: C>B>A
In the (typical) matrix all three candidates are identical, but A and C should be elected if there are two seats. The summing process can thus hide quite a lot of information.

What should we learn from this?

Juho