[EM] “Monotonic” Binomial STV

[Kristofer Munsterhjelm]

On 28.02.2022 02:59, Richard Lung wrote:
> 
> Kristofer,
> 
> Your reasoning is perfectly right. But the point is that neither of the 
> B candidates nearly reach the Droop quota. In fact splitting the B votes
> further removes the B party from the quota. it is true I haven't said
> that here. But in your first example, several weeks ago, the winner A
> missed the quota by half a vote, which is statistically insignificant.
> More-over, in that former example, candidates B and C, technically with
> marginally better keep values, had votes that completely failed the
> standard deviation test for distance from the quota.

This is pretty hard to parse - you're using your personal terminology
that I'm not familiar with. But I would imagine that the candidates who
are close to the quota would merit election; and, if you're doing a
statistical test, it should elect the candidates who are above the quota
rather than below it. In the example I provided, the Bs are below the
quota and A is above it, yet A is not elected. The distance that B is
below the quota just acts as further evidence that B should not be elected.

> Here the same must apply if the sample size of the total vote is big
> enough. Take the square root of 100 votes times probability of success
> and corresponding probability of failure or 1/2 in both cases out of a
> unit total probability. So sq rt of 100 x 1/2 x 1/2 gives one standard
> deviation of 5 votes.  Two standard deviations are significant to a 95%
> probability  that the B vote is not in the region of the quota as a
> chance fluctuation from the quota. in fact, Bo is over 3 SDs adrift from
> the quota, which yields about one chance in a thousand that the Bo vote
> is is just a random departure from the quota, of no significance.
> 
> This example is even more helpful than your previous one, because it
> makes clear to me that statistical rules of representation by average
> and significant dispersion must be observed, in conjunction with
> elevating exclusion to the same rational status as election.

I don't understand your reasoning. Are you saying that flipping a 60-40
outcome merely by fielding additional candidates is okay? Or is the
method missing a rule that disqualifies candidates far below the quota?

If it's the latter, could you do my example again, demonstrating that rule?

-km