# [EM] Some method definitions.

MIKE OSSIPOFF nkklrp at hotmail.com
Sun Apr 22 18:16:13 PDT 2001

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Someone requested some method definitions, but I was distracted by
other issues on the list and so I neglected to post the definitions.
So here they are:

Ordinary SSD:

The "current Schwartz set" is the Schwartz set based only on undropped
defeats.

1. If any candidate is unbeaten he wins.
2. Otherwise, calculate the current Schwartz set.
3. Drop the weakest defeat that's among Schwartz set candidates.
4. Go to 1.

[end of definition]

Cloneproof SSD:

[Cloneproof SSD differs from ordinary SSD only in its stopping rule]

1. Calculate the current Schwartz set.
2. If there are no defeats among that set's candidates, then they win.
3. Otherwise, drop the weakest defeat that's among that set's candidates.
4. Go to 1.

(Cloneproof SSD measures defeats by defeat-support (wv), and is
equivalent to BeatpathWinner(wv) ).

[end of definition]

Ranked Pairs(wv)

Same as Ranked-Pairs(m) except that strengths of defeats are measured by
defeat support, also called "winning votes" and abbreviated "wv".

If A beats B, then the defeat support of that defeat is the number
of voters who've voted A over B.

PC:

Anyone unbeaten wins. If no one is initially unbeaten, then:

Drop the weakest defeat. Repeat till there's an unbeaten candidate.

Smith//PC:

Use PC to choose from among the Smith set.

Smith set:

The smallest set of candidates such that every candidate in the set
pairwise beats every candidate outside the set.

SD:

Anyone unbeaten wins. If no one is initially unbeaten, then:

Drop the weakest defeat that's in a cycle. Repeat till there's an
unbeaten candidate.

CR:

Within a specified range of ratings values, each voter may give any
rating to any candidate. The winner is the candidate who, when his
ratings are summed over all the voters, has the highest sum.

BeatpathWinner:

1. A has a beatpath to B if either A beats B, or A beats someone who has
a beatpath to B.
2. Any sequence of defeats that, by itself, would make it possible to
say that A has a beatpath to B is called a beatpath that A has to B.
3. The strength of a beatpath is measured by the strength of the weakest
defeat in the sequence that is that beatpath.
3. If A has a stronger defeat to B than vice-versa, then A has a
beatpath win over B.
4. The winner is the candidate who has a beatpath win over each of the
other candidates.

[end of definition]

(It's been shown that, without pairwise ties or equal defeats, there
is always a unique winner).

Mike Ossipoff

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