[EM] Test of elimination counts versus proportional counts.

[Richard Lung]

Test of elimination counts versus proportional counts.

The elimination count may be described as the possibility of replacing 
one less prefered candidate than another. This is especially the basis 
of so-called Instant Run-off Voting, where the idea is that some 
candidates may have more general support than another, after the 
run-off. This system is also known as the Alternative Vote (AV).

By convention, AV is generally reserved for the single-member 
constituency or system case. And the single transferable vote is 
confined to multi-member constituency elections. This means that STV is 
a broken-backed system, because it does not apply to all constituency 
systems, single-member and multi-member constituencies. By the same 
token, AV is no more than a special case. It has never gained 
multi-member currency, beyond a short lived trial, for instance in 
British Columbiain the nineteen fifties. It has its very occasional 
reform advocate for a “bottom-up” election system. That is to say for 
rank choice in a multi-member elimination count system.

As Enid Lakeman, in How Democracies Vote, pointed out, the lack of a 
proportional count means that the overall majority voters may win in not 
just a single constituency seat, but in every seat in a multi-member 
constituency.

  Contrast this by how a proportional count can make the single 
transferable vote applicable, not only in multi-member constituencies 
but also single-member constituencies. STV, unlike IRV (alias AV), can 
be made a consistently proportional count, whereas IRV/AV cannot 
maintain a majority count, by elimination methods, in more than a single 
seat constituency.

The general rule, to apply beyond the study of election methods, is to 
introduce a one-truth condition to any election system.

The worlds existing election systems are two, or more, truth systems. I 
won’t attempt to say how many conflicting “truths” the Additional 
Members System (alias MMP) stands for. But ad hoc hybrid election 
methods are a bad idea, for this reason. (Tho these doubly safe seat 
systems may be an inspiration to career politics.)

Given that the elimination count does not produce even a bare overall 
majority in multi-member constituencies as well as single-member 
constituencies, that leaves the proportional count alternative to 
attempt a single-member count as well as a multi-member count.

It is the case of course that there cannot be proportional 
representation in single-member constituencies. (Not always appreciated 
by politicians, terrified, for their jobs, of any reform in the voting 
system.)

It is rightly appreciated, that with a proportional count, the voters 
for any candidate who has won votes in surplus of the quota (here, of 
one half the voters) cannot have the surplus transferable to the voters 
next preferences, because, by definition, there is no other vacant seat 
in the constituency.

Nevertheless, a transferable surplus in a single-member constituency is 
a measure of that candidates popularity. (It is the “keep value” in Meek 
method multi-member elections.)

Now here is the novelty. Use Meek method of surplus transfers in 
elections, also as the means of excluding candidates, applied to the 
voters reversed preferences. Then, invert the exclusion preferences, so 
you have a makeshift second-opinion election. You can legitimately do 
this, because one persons preference is another persons reverse 
preference. In other words, Meek surplus transfer is as logically 
legitimate as an exclusion count as it is as an election count.

Now you have two sets of keep values, election keep values and exclusion 
keep values, inverted, to be second opinion election keep values. Hence 
their (exclusion count over election count) ratio serves as an average 
keep value (actually, the square of their geometric mean).

These average keep values can serve as the election criterion of from 
one to many candidates. That is to say this “binomial” count of both 
rational election and rational exclusion is consistently applicable to 
single member and multi-member constituencies.

There are other considerations, such as the need to count all the 
abstentions, to-weigh the relative importance, to the voters, of 
electing and excluding candidates, and what to do with any “Schrödinger 
candidate” [Forest Simmons] both elected and excluded.

However, STV would be no longer a broken backed system but, for the 
first time, a one -truth election system. And this is a criterion that 
elimination counts, and official elections in general, fail to meet.

Richard Lung.

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