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. > > >