[EM] Beatpath question

[Rob LeGrand]

Jameson wrote:
> I can show (under reasonable strategic assumptions) that my delegated
> system SODA elects one of the candidates who beats all with a winning vote
> beatpath of length 2 or less, if there is any such candidate. "A beats B
> with a winning vote beatpath of length 2" means: there is some C such that
> the minimium of (votes for A against C, votes for C against B) is greater
> than votes for B against A.
> Obviously, if we allow any length of beatpath, and if there are no ties,
> there must be some beats-all winner. But is it possible that there is no
> winner with beatpaths of length 2 or less? Can anybody give an example of
> such an electorate?

If I understand you correctly, this electorate does what you want:

29:A>C>B>D
15:B>D>A>C
16:D>C>B>A

If beatpaths of all lengths are considered, as in the Schulze method, A
loses no beatpath comparisons.  In particular, the beatpath A>C>B>D is
stronger than D>A.  But A needs a beatpath that long to defeat D; the
beatpaths A>B>D and A>C>D are weaker than D>A.  Using only beatpaths of
length 2 or less, every candidate loses a beatpath comparison.

What would strategic SODA do in the above case?

--
Rob LeGrand
rob at approvalvoting.org