[EM] Non-monotonicity and Incompleteness

[Richard Lung]

On 19/04/2023 09:44, Richard Lung wrote:
>
> The British Labour Party Intermediate Plant Report (betimes on their 
> website) cited Riker for non-monotonicity of STV.
>
> When an election has no more surplus votes to transfer, the trailing 
> candidate is eliminated to redistribute their vote to next preferences.
>
> A scenario can be imagined, in which a contender for election receives 
> more votes, but this results in the elimination of a less favorable 
> candidate, with an adverse, instead of a positive, effect on the 
> contender.
>
> In theory, conventional STV is indeed non-monotonic. In practise, STV 
> elects mainly first preferences, especially with more seats, in the 
> multi-member constituency. This robustness may be explained because 
> the Riker test example, for instance, is not a typical STV election 
> with surplus transfers. Rather it is a purely eliminative count of 
> candidates with the least first preferences.
>
> This consideration also suggests, in my personal opinion, that STV 
> could be made monotonic, if the irrational method of elimination were 
> discarded. It would be possible to use quota election, with surplus 
> transfer, also for an “exclusion quota,” by conducting exactly the 
> same (symmetrical) count, but with the preferences counted in reverse 
> order. This “Binomial” STV (a bi-nomial count) would be a (consistent) 
> one-truth system, which satisfies the truth, that one voters 
> preferences may be another voters unpreferences, and therefore cannot 
> logically be treated differently.
>
> Polarising candidates might win both an election quota and an 
> exclusion quota. This would be a case of what Forest Simmons calls 
> “Schrödinger’s candidate” (after Schrödinger’s cat, deemed, in quantum 
> theory, to be both alive and dead!) The result could be settled, one 
> way or the other, by a Quotient of the exclusion quota to the election 
> quota.
>
> The relative importance of election or exclusion, to the voters, could 
> be measured by the counting of abstentions. This might cause one seat, 
> or more, to remain unfilled. This greater use of preference 
> information would satisfy the fundamental principle of the 
> conservation of information, which is breached by candidate 
> elimination rules.
>
> “Binomial STV” thus conforms to the Incompleteness theorem. “Godel 
> showed that mathematics could not be both complete and consistent…” 
> (James Gleick “The Information.” Fourth estate, 2012. Chapter 7.)For, 
> Binomial STV election and exclusion of candidates follows a consistent 
> count. But its counting of abstentions may leave an incomplete 
> election to all the seats. Whereas, practically all conventional 
> election methods seek to completely fill all the seats, but use 
> variously inconsistent election and exclusion rules.
>
> Regards,
>
> Richard Lung.
>
>
>
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