[EM] Strong FBC Can Be Satisfied By Ranked Methods! (sort of)
asmall at physics.ucsb.edu
Thu Oct 31 14:43:13 PST 2002
I just figured out a ranked method that sort of satisfies strong FBC:
Any positional method that assigns equal points to your first and second
choices satisfies Strong FBC. By positional method I mean any method that
assigns points to candidates based on rankings, and the candidate with the
most points wins.
Plurality is a positional method that gives 1 point to your favorite and
zero to all others. Borda gives zero to your bottom choice, 1 to your
second-last, 2 to the next higher choice, etc.
So, a method that assigns one point each to your favorite and second
favorites and zero to all lower choices in races with 3+ candidates (and
is defined to be plurality in 2-way races) will satisfy strong FBC. This
isn't a very satisfying answer on strong FBC, since it essentially treats
your first and second choices equally. However, formally it is a ranked
method that satisfies strong FBC.
If you want something more satisfying, I can think of two paths.
1) Define "Stronger FBC": Regular FBC with the added condition that
"There will exist situations in which a different result is obtained if
all voters interchange their first and second choices." A method that
gives 1 point each to your first and second choices, and zero to all
others, does not satisfy this.
2) Ask if strong FBC is compatible with the majority criterion: If a
candidate is the first choice of a majority of the voters then he will
That's all for now, folks. I don't know that I want to continue on this
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