[EM] Versions of Ranked-Pairs

[Michael Ossipoff]

 By "Ranked-Pairis", I refer to the general method:

Disregard every defeat that contradicts stronger non-disregarded defeats.

[end of RP definition]

I've heard that Niklaus Tideman first proposed RP. More recent
versions allow equal-ranking and truncation, and measure
defeat-strength by winning-votes (wv).

These more recent versions differ in how they deal with ties--equal
defeats and pairwise-ties.

Steve Eppley's MAM, when there is/are one or more ties, randomly
selects a voter's ranking, and uses it to solve the ties, where they
occur.

That's probabaly the bests solution when it's necessary to elect one
person, or choose one alternative.

To avoid randomness during the count, the Condorcet Internet Voting
Service's CIVS-RP, when there are two or more equal defeats, equally
qualifying for being skipped (disregarded) instead of kept, in the
same cycle, keeps all of those equally-skip-qualified defeats. It may
then return a tie, but its need for randomness occurs only for
choosing from among several tied winners. Ideally that choice would be
by random choice of a voter's ranking.

Eppley pointed out that if X>Y>Z>X, and if X>Y is the strongest, and
if Y>Z and Z>X are equal, then CIVS-RP would keep all the defeats, and
return a 3-way tie for winner.

He pointed out that MAM would, instead, deterministically disqualify y
from winning,

But what if we, instead, _disregard_ those two equally-skip-qualified
defeats? Then the method determistically returns a y-z tie for winner.

When it isn't necessary to a unique winner, whee it isn't necessary
act on a winner, as by choosing an organizational officer, or choosing
an alternative--which could be the case for a purely informational
poll, for example, maybe the equal-defeats solution described in the
previous paragraph would be good, if a deterministic (even if tied)
answer is desired.

I'll call that equal-defeats solution "Disregard Equal Defeats" (DED).

Eppley proposed another deterministic tie-solution:

Use the alternatives' order-of-nomination to solve ties when there are
equally-skip-qualified defeats, or pairwise-ties. Maybe that's better,
but of course it might not always be applicable.

For example, in many polls, many, most, or all of the alternatives
were simultaneously nominated by the person who started the poll.

And, in meetings, that rule could just result in eveyone
simultaneously raising their hands to nominate first.

But, where applicable, it's a good solution. Order-of-nomination is
sometimes used to determine the voting-order in Seqential-Pairwise,
the popular show-of-hands method for meetngs.

What's said here about RP likewise applies to River.

Michael Ossipoff