[EM] Grouping/bifurcation elimination methods

[Roy]

Does anyone know whether the theorem that all elimination methods
suffer failure of monotonicity applies to one-at-a-time elimination
only, or would include any kind of elimination?

I am, in particular, interested in knowing whether bifurcation can be
used to find candidates' rankings. I have proposed median elimination
as one method, which would eliminate all candidates whose median rank
is not in the top half (this could alternatively be seen as grouping
candidates, if a complete ranking was desired -- then each grouping
could be further median-cut, until a complete ranking was determined).

A similar method could be used for evaluating ranked pairs: It seems
clear that the top contenders in RP are going to be the ones with
victories against the most opponents, so a grouping could be done
based on that: all candidates who beat three candidates are in one
group, those who beat two are in a separate, lower-ranked group, etc.
Then, within each group, the contests that include candidates not in
the group are discarded, and the candidates are re-grouped based on
victories against each other.

In this situation, it seems clear to me that lowering a candidate's
position, if it changes anything, can only result in his moving into a
lower group, or that that elevated candidate moves into a higher
group, both of which would "eliminate" the lowered candidate. Thus, no
failure of monotonicity.