# [Election-Methods] RE : Smith + mono-add-top?

Diego Santos diego.renato at gmail.com
Tue Jan 1 04:21:18 PST 2008

```Happy new year to all!

Perhaps my previous definition was not enough clear, for the possible
confusion between "potential winner" and "winner" on its final. Then, I
reformulated it:

"Some candidate X is eliminated if a) exists Y that beats X and b) the
margin of Y against X is greater than the greatest margin of another
candidate against Y. The winner is the Condorcet winner among non-eliminated
candidates".

An example (from http://www.mcdougall.org.uk/VM/ISSUE6/P4.HTM):

5:a>d>c>b
5:b>c>a>d
8:c>a>b>d
4:d>a>b>c
8:d>b>c>a

Notation:
Candidate X(minimax score of X): Candidate Y(margin of Y against X, minmax
score of Y):

a(12): c(12,4)           eliminated
b(4): a(4,12), d(4,6)
c(4): b(4,4), d(4,6)
d(6): a(6,12)

d beats either b and c, then d is elected.

Another example (from Markus' paper):

3:a>d>e>b>c>f
3:b>f>e>c>d>a
4:c>a>b>f>d>e
1:d>b>c>e>f>a
4:d>e>f>a>b>c
2:e>c>b>d>f>a
2:f>a>c>d>b>e

a(5): c(1,5), d(1,3), e(1,9), f(5,7)
b(7): a(7,5), d(1,3)                           eliminated
c(5): b(3,7), e(5,9)
d(3): c(3,5)
e(9): b(1,7), d(9,3)                           eliminated
f(7): b(7,7), c(1,5), d(1,3), e(1,9)

c beats a, d and f, then c is elected.
________________________________
Diego  Santos
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