[EM] “Monotonic” Binomial STV

[Kristofer Munsterhjelm]

On 27.02.2022 14:04, Richard Lung wrote:
> 
> Thank you, Kristofer,
> 
> 
> for first example.
> 
> The quota is 100/(1+1) = 50.
> 
> Election keep value is quota/(candidates preference votes)
> 
> for A: 50/51
> 
> B: 50/49
> 
> C: 50/0  Which, of course is infinite. It may be convenient, for tidy
> book-keeping, that small elections require that each candidate votes for
> themself. Then the keep value maximum simply equals the quota.
> Generally, it is not necessary to make this stipulation, for large scale
> elections, because no candidate, however miserable, ever gets no votes.

Another option is to just let infinities be worse than any alternative.
Since not every candidate can have a zero last preference count, at
least one candidate must have a finite value and so would be considered
better than every candidate with an infinite value.

> Exclusion keep value equals quota/(candidates reverse preference vote):
> 
> A: 50/1
> 
> B: 50/0
> 
> C: 50/99
> 
> Geometric mean keep value ( election keep value multiplied by inverse
> exclusion keep value):
> 
> A:  50/51 x 1/50  ~ 0,0196
> 
> B: 50/49 x 0/50 = 0/49 is indeterminate. The closest determinate
> approximation gives 1/49, not quite as low a keep value as 1/51 for A,
> who is therefore the winner.

Is 0/49 indeterminate? Shouldn't it just be zero? 0/x = 0 for x not
equal to zero, and the square root of zero is zero.

But let me in any case revise my example. Who wins in this one?

50: A>B>C
47: B>A>C
  2: B>C>A
  1: A>C>B

My calculations are as follows:

The quota is 50.

Election keep value is quota/candidate preferences:

A: 50/51
B: 50/49
C: infinity

Exclusion keep value equals quota/candidates reversed first preferences:

A: 50/2
B: 50/1
C: 50/97

Geometric mean:

A: square root of (50/51 x 2/50) ~ 0.198
B: square root of (50/49 x 1/50) ~ 0.143
C: ~= infinity (or very high)

So B wins, having the lowest keep value. Is this correct?

(You seem to have omitted the square root in your calculations, but it
shouldn't make a difference. Without the square root, A and B's values
are 0.0392 and 0.0204 respectively.)

-km