Kathy Dopp wrote:
James,
Your formulas below are only correct in the case that voters are
allowed to rank all the candidates who run for an election contest.
That may be true in Australia, but is not true in the US where
typically voters are allowed to rank up to only three candidates.
As a note: some methods (most discussed here, actually) also permit both
truncation and equal-ranking. If one takes that into account, the
formulas become more complex still.
Yet, on another level, this may not really matter. On the one hand, if
there'll ever just be a few candidates, the amount of information to
transmit is managable. On the other, setting a hard limit to, say, "no
more than 5 candidates may participate in this election" is rather
inelegant, and I would say, unfair, and if the potential number of
candidates can grow to any number, it doesn't matter what formula is
being used as long as it's superpolynomial (and so the values grow very
large very quickly). Truncation or no truncation, equal rank or not, the
number of unique orderings grow in that manner.
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