CSSE = Simmons' Method ?

Forest Simmons fsimmons at pcc.edu
Mon Feb 18 20:52:39 PST 2002

```Correction: Borda Seeded Bubble Sort does not satisfy the Reverse Symmetry
Criterion.

It can be fixed by just Bubble sorting down to the lowest seeded
candidate with above average Borda count.

The winner would still be a member of the Smith set, so it would still
satisfy the Condorcet Criterion and have the other mentioned advantages.

I want to emphasize that I don't believe in pure preference ballots for
public elections.  This method is mainly to show how to improve Borda in a
way that competes with Black in utility while reducing the potential for
manipulability somewhat.

Further sacrifice of utility buys increased resistance to manipulation if
the MinMax candidate is chosen.  Also sacrificed are Reverse Symmetry and
Smith set property, although the Condorcet Criterion is retained.

It seems that there has to be a utility/manipulability trade off.

Forest

On Thu, 14 Feb 2002, Forest Simmons wrote:

> The more I think about it the more I prefer Borda Seeded Bubble Sort as a
> simple, high utility, hard to manipulate, method satisfying the Condorcet
> Criterion, when limited to pure ranked preference ballots where
> truncation, Yes/No, NOTB, etc. are not allowed or provided for.
>
> The Borda order is sorted down to the bottom seeded candidate Z by
> (recursively) bubble sorting all of the candidates above candidate Z
> before percolating Z upward until Z is defeated in a pairwise comparison.
>
> This method is easy to describe (even without the simplicity of
> recursion), always picks a winner from the Smith set, is monotonic (I
> believe), satisfies the Reverse Symmetry Criterion, and encourages
> insincere ranking of candidates even less than Borda Seeded Single
> elimination.
>
> In a nut shell here's why I think it gives less incentive for insincere
> ranking:
>
> Suppose you prefer X to Y but you are told that X might spoil Y's chance
> of winning without X going on to victory (because Y has a better chance
> according to the polls).
>
> In both methods (Bubble and Single Elimination) you could say, "To heck
> with the polls, if X gets a higher Borda count than Y, then I say X has a
> better chance.  I don't trust those polls anyway."
>
> But after you vote X ahead of Y you begin to worry.  What if X is seeded
> below Y, and then (in single elimination) over-takes and defeats Y, and
> then goes no further, dashing Y's hopes of winning without having the
> steam to keep going?
>
> This could never happen in Bubble Sort.  If X is seeded below Y, then Y
> has already risen to its apogee before any possible challenge from X.
> Candidate X cannot hurt Y from below in Bubble Sort.
>
> The Borda Seeding should give the method near maximal Social Utility for a
> method based on pure ranked preference ballots (no Approval marker, etc.)
> and satisfying the condition of always picking from the Smith set.
>
> Forest
>

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