[EM] “Monotonic” Binomial STV

[Richard Lung]

“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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