[EM] Proof idea that IRV can't be summable

Richard Lung voting at ukscientists.com
Thu Dec 3 12:33:48 PST 2020

On 03/12/2020 14:01, Richard Lung wrote:
> Droop proportionality fails, because it is the minimally proportional 
> election. That means that candidates may be elected on statistically 
> insignificant majorities -- whether single member majorities (like 51 
> out of 100) or multi-member majorities, (like two winners with 34 
> votes each out of 100). The Droop quota superseded the Hare quota for 
> historical reasons. But there is also logical reason for its 
> democratic short-comings: in the most extreme case, a single member 
> requires all the votes, to be elected, which could only be achieved by 
> a completely deferential electorate. That is why the first of my four 
> averages, in FAB STV, is (my innovation of) the harmonic mean quota, 
> V/(S + 1/2), as the harmonic mean of the Hare and Droop quotas. The 
> use of the HM quota does imply multi-member constituencies, of at 
> least 4 or 5 members, but that is what democratic diversity requires.
> Your last paragraph of democratic skepticism is in contrast to the 
> view that there is a right and a wrong way to do voting method. In 
> this respect, I follow the tradition of Hare, Mill, Wells, Hoag and 
> Hallett, and Lakeman. and many other estimable people, up against 
> "current constraints."
> Richard L.
> On 03/12/2020 10:20, Kristofer Munsterhjelm wrote:
>> On 03/12/2020 08.31, Richard Lung wrote:
>>> Of course, all that learning won't alter what John Stuart Mill knew over
>>> 150 years ago that maiorocracy is not democracy. The fixation on single
>>> winner methods, (the monarchism hang-over) is candidate-centred not
>>> voter-centered or politician-based not people-based.
>> I have a hunch that anything that passes Droop proportionality must fail
>> strong summability: that it's impossible to find a Droop-proportional
>> multiwinner method where you can construct an array of numbers
>> polynomial in the number of candidates, and then later use that array to
>> find the outcome for any number of seats. The same approach could
>> possibly be used to prove this, although it would be a lot harder.
>> Proving multiwinner STV non-summable would not be too much harder than
>> what I did in the post you replied to. There's nothing there that has to
>> necessarily be single-winner. It's not clear whether the corresponding
>> regions should be of candidates, or councils, though. (E.g. do we
>> consider the region "A is on the council" as some analog of a win-or-tie
>> region for A, or should the region be "the two-seat council is AB"?)
>> If told to create something democratic without concern to current
>> constraints, I'd probably just skip right to sortition. This would not
>> just invalidate single-winner methods, but voting altogether; except,
>> possibly, the method the assembly itself uses to decide.
>> -km

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