On Dec 5, 2009, at 7:41 PM, Dave Ketchum wrote on: Election Goals &
Methods - a review:
Here I explore some possibilities based on using margins. Assuming
polling has given perfect knowledge as to the voting without strategy,
what change might a strategist propose for the one group of voters
that hears strategy gimmicks.
100 votes:
45A
5A,B - these 5 voters add in B as second choice. Effect is 31B
to 29 C and B winning.
11B
3B,A - effect is 48A to 44C and B winning (3 vote margin is less
than this 4 vote margin).
15B,C
3B - effect is 45A to 41C and B winning.
29C,B
6C,A - effect is 51A to 49B and A winning (hard to sell, since C
wins without strategy).
The pairwise defeats are as follows:
B beats A, 55 to 45 (55 winning votes, a margin of 10 votes)
A beats C, 45 to 44 (45 winning votes, a margin of 1 vote)
C beats B, 29 to 26 (29 winning votes, a margin of 3 votes)
Using the winning votes definition of defeat strength, the defeat of
B by C is the weakest, and the defeat of A by B is the strongest.
Using the margins definition of defeat strength, the defeat of C by
A is the weakest, and the defeat of A by B is the strongest.
Using winning votes as the definition of defeat strength, candidate
B would win under minimax, Ranked Pairs and the Schulze method, but,
using margins as the definition of defeat strength, candidate C
would win in the same methods.
If all voters give complete rankings of the candidates, then winning
votes and margins will always produce the same result. The
difference between them can only come into play when some voters
declare equal preferences amongst candidates, as occurs implicitly
if they do not rank all candidates, as in the example above.
Dave Ketchum
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