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

[Kristofer Munsterhjelm]

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.