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

Forest Simmons fsimmons at pcc.edu
Thu Oct 31 17:44:40 PST 2002

```Alex, it seems to me that if only the first two ranks get points, then in
a close race among several candidates if your favorite isn't among the top
three contenders with near equal chances, you may want to give the top to
slots on your ballot to your preferred among the top three contenders.

To be more specific, suppose that A,B, and C are approximately equal in
the polls, and way ahead of everybody else including your favorite F, and
that your true preference order is

F>A>B>...>>C

Wouldn't it be better strategy to vote

A>B>F>... ?

Forest

On Thu, 31 Oct 2002, Alex Small wrote:

> 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
>
>
> ----