[EM] Notes on a few Later-no-harm methods

[Kevin Venzke]

Hi Richard,

> Binomial stv is a statistical count that doesn't apply for very small
> numbers. For that, there is non-parametric statistics. There is no hard
> and fast rule. I'd say about 32 votes minimum. but that's just a
> minimum. There is a law of large numbers for better approximations.

Do you say it doesn't apply to very small numbers because you seek to avoid
divisions by zero in the math? I don't think there is any minimum number of voters
that will guarantee that.

> I forget the meaning of truncated, kindly explained to me.

It's the omission of a candidate from a voter's ranking.

> If a voter is really stuck between two candidates, he or she can toss a
> coin for it, and there will be no over-all bias.

This does bring to mind to a suggestion which would *not* satisfy Later-no-harm:
Suppose that BSTV automatically splits the voter into two when they omit the last
two candidates:

480: A      <-- These voters omit B and C
405: B>C>A
115: C>A>B

So BSTV would automatically split them into two blocs to achieve the following
ballots:

240: A>B>C  <-- half of the bloc
240: A>C>B  <-- the other half
405: B>C>A
115: C>A>B

BSTV elects A.

But now, suppose that the 480 voters had actually decided that they felt that B is
better than C, so they instead voted like this:

480: A>B>C  <-- different vote
405: B>C>A
115: C>A>B

Now BSTV elects B. The A>B>C voters do not prefer that outcome, so they were
better off omitting the lower rankings.

That can never happen in ordinary STV, so we say STV satisfies Later-no-harm.

Kevin