[EM] “Monotonic” Binomial STV

[Forest Simmons]

Richard,

Here's an example of monotonicity failure in conventional single winner STV
as I understand it:

Original profile of ballots:

35 A>B>C
33 B>C>A
32 C>A>B

C eliminated and A wins.

New profile: two members of B faction defect to A faction:

37 A>B>C
31 B>C>A
32 C>A>B

Now B is eliminated and C wins.

How does Binomial STV avoid this monotonicity failure?

Thanks!

-Forest

El jue., 24 de feb. de 2022 10:36 a. m., Richard Lung <
voting at ukscientists.com> escribió:

>
> “Monotonic” Binomial STV
>
>
>
> I was told (hello Kristofer) that I could not say that binomial STV is
> “monotonic” unlike traditional or conventional STV. But I gave my reasons
> why I could say this, and they were not contradicted or even answered. It
> is not tabu or forbidden to say, and say again, what there is good reason
> to believe is true, whatever the prevailing view.
>
> In conventional STV, the transfer of surpluses, over a quota, to next
> preferences is monotonic. There is “later no harm” unlike the Borda count.
> The intermediate Plant report quoted a non-monotonic test example from
> Riker, to justify their rejection of STV. This was based solely on the
> perverse outcome of a different candidate being last past the post, for
> elimination.
>
> Riker made the unsupported claim that STV is “chaotic.” From a century of
> STV usage, he did not provide a single real case of this. The record is
> that STV counts well approximate STV votes, all things considered.
>
> A paper that tried to provide some doubt, of STV as a well-behaved system,
> drew not on a conventional STV election of candidates, but on NASA using
> STV for outer space engineers to vote on a set of best trajectories (I
> forget where).
>
> Traditional STV is not “chaotic”. It is not even wrong. It is just an
> initial or first approximation of binomial STV, a zero order binomial STV.
>
> Zero order STV is a uninomial count that does not clearly distinguish
> between an election count or an exclusion count. In 1912, HG Wells said of
> FPTP, we no longer have elections we only have Rejections. From first order
> Binomial STV, the two counts, election and exclusion counts, are clearly
> distinguished and both made operational.
>
> Binomial STV does not exclude candidates during the count. It uses an
> exclusion count, to help determine a final election. This exclusion count
> is exactly the same or symmetrical to the (monotonic) transfer of surplus
> votes in an election count.
>
> In both election and exclusion counts, Gregory Method or the senatorial
> rules are expressed in terms of keep values, which enable proper
> book-keeping of all preferences. Keep values can keep track of all the
> preference votes, including abstentions. So, no perverse results are
> possible from the chance exclusion of preferences from this or that
> candidate last past the post. This is also why binomial STV is one complete
> dimension of choice.
>
> Binomial STV has “Independence of Irrelevant Alternatives.” For instance,
> it makes no difference what level the quota is set, to the order of the
> candidates keep values, their order of election. It is just that bigger
> quotas raise the threshold of election.
>
> Regards,
>
> Richard Lung.
>
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