# [EM] Strong FBC Can Be Satisfied By Ranked Methods! (sort of)

Alex Small 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
win.

That's all for now, folks.  I don't know that I want to continue on this
quest.

Alex

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