[EM] Ranked pairs summable?

[Kristofer Munsterhjelm]

As far as I understand, Ranked Pairs and MAM need a tiebreaker to
properly pass clone independence. The recommended tiebreaker is random
ballot or random voter hierarchy. But is that tiebreaker summable? It
seems you'd need to know the full ranking of the voter you choose for
the random ballot, and you can't know what voter (or which voters)
you're going to choose in advance.

Is there a way to make random ballot or RVH summable?

Even if you were to choose beforehand a lucky voter from each district
and transmit that voter's preference ordering along with the district
magnitude, you'd run into problems if a district's voter didn't rank
every candidate.

The two options to try to solve that would be to do random voter
hierarchy with every district's predetermined lucky voter, or to do
random voter hierarchy for each district so that the "composite lucky
ballot" always fully specifies every candidate. But either choice would
seem to alter the distribution. In the former case, you can't complete
one district's voter's ballot with a ballot from the same district, and
in the latter case, you can't complete one district's voter's ballot
with a ballot from another district. Unrestricted random voter hierarchy
can do both.

Maybe this is not a problem and either of the completion strategies will
work for clone independence purposes, but in that case, summable Ranked
Pairs or MAM with multiple districts differs from summable Ranked Pairs
or MAM in only one district. Or maybe I'm missing some easy way of
making random ballot or RVH summable, in which case it'd be interesting
to hear how to do so :-)

-km