[EM] “Monotonic” Binomial STV

[Richard Lung]

Thank you, Forest,

Your example is the kind of example that Riker gave.

Here the quota equals 50 = 100/[1+1].

Original profile:

Election Keep value is quota/candidate vote:

for A  50/35

B:  50/33

C:   50/32

Exclusion keep value = quota/candidate reverse vote:

for A:  50/33

B:   50/32

C:  50/35

Final (geometric mean) keep values, divide election keep value by 
exclusion keep value.

(This is equivalent to multiplying by the inverse exclusion keep value, 
as a make-shift second opinion election keep value.)

for A:  50/35 x 33/50. And take their square root ~ ,971

for B: 50/33 x 32/50.  As above, gives ~ .9847

for C:  50/32 x 35/50. ... gives ~ 1.0458

Keep values below unity are technically electable. A wins, with lowest 
keep value.

New profile:

Election divided by exclusion keep values:

A: 50/37 x 31/50. Take square root of 31/37, for ~ .9153

B: 50/31 x 32/50. As above, ~ 1.016

C:  50/32 x 37/50. As above, ~ 1,075

Again, A is elected as before, and with a yet lower keep value, as the 
extra preferences for A warrant.

Regards,

Richard Lung.


On 26/02/2022 01:30, Forest Simmons wrote:
> 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.
>
>     ----
>     Election-Methods mailing list - see https://electorama.com/em for
>     list info
>
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