[EM] Notes on a few Later-no-harm methods

[Kristofer Munsterhjelm]

On 02.06.2022 19:10, Richard Lung wrote:
> 
> On 02/06/2022 11:28, Richard Lung wrote:
>>
>>
>> Sometimes the keep value quotient, in binomial STV, does not help to
>> decide an election. It may even make the contest less decisive. Never
>> the less, the quotient is an extra source of rational information, to
>> that provided by the quota, as to the decision or indecision of the
>> public.
>>
>> The simple plurality method generally implies, representatively, that
>> it should not be in a single-member system, but at least in a two
>> member system, and often in a three or four member system.
>>
>> Likewise, I recommend a minimum of a 4 or 5 member system for binomial
>> STV, for sufficiently representative elections, to produce decisive
>> results.
>>
>> The draft Scottish constitution recommended a minimum of four member
>> STV constituencies. The Irish constitutional convention recommended a
>> minimum of five-member STV constituencies.
>>
>> The McAllister report on the Welsh Parliament cited an academic
>> consensus on four to seven member constituencies for sufficient
>> diversity of representation.
>>
>> Four Welsh reports have recommended the single transferable vote.
>>
>>  
>>
>> Thus, a lack of decisiveness, in single-member binomial STV, is not
>> necessarily a problem of BSTV but it is a problem of single, double
>> and even triple member constituencies. The insistence on a decisive
>> election winner is a presumption of social choice theory.

I'm not sure what you're referring to, but the Duggan-Schwartz theorem
states that for deterministic ranked multi-winner methods, unless the
method always returns the set of every voter's first preferences as the
outcome, there will exist elections where strategic voting pays off.

So a multi-winner method has to be very tie-prone if it's to be
unmanipulable.

>> The incompleteness theorem of Kurt Gödel is not an insistence on the
>> “Impossibility” of deductive science. It took the theorem of Kenneth
>> Arrow to assert that for logical democracy. (The assertion, that no
>> election method is perfect, is not a scientific statement, and can be
>> disregarded as such.)

Gödel's incompleteness theorem is a good example. It may not be a
practical problem that the mathematical system can't prove every fact
about itself. (Usually one gets around this by just creating a more
powerful system to prove things with.)

But it shows that some property that would really simplify things is
unattainable. Similarly with voting methods: it may not be a practical
problem that strategy is possible, but the lack of an unmanipulable
deterministic method means we have to pick our poison about which kind
of strategy to allow (that hopefully does the least harm).

Or sidestep the question by looking at the greater context (analogous to
creating a more powerful system) and use something like sortition
instead of elections.

>> Thus, the impossibility theorem insistence on decisive results amounts
>> to an imperative for an administrative decision, and not necessarily
>> popular representation. But the United Statesis a republic, a thing of
>> the people, not a thing of Administration, or a “rebureau.”

What's a rebureau?

-km