[EM] Who comes "second" in Ranked Pairs?

[Scott Ritchie]

I'm writing a ranked pairs counter as practice for learning python, and
I realized I don't know the answer to this question.

Suppose I want to know who comes in second in a ranked pairs election.
Is it:

1) Run ranked pairs algorithm on the ballots, find that candidate A
wins, then purge A from all the ballots and rerun the algorithm to find
a new winner and call him the second place candidate OR

2) Run ranked pairs algorithm on the ballots, lock in all pairs in their
order that don't create cycles, then look at whom is second in the graph
(ie, whoever beats all but A)


Or will these two always be the same?  It'd be nice if I could see an
example where that's not the case.

It's also possible that there is no "official" way to calculate
second-place in ranked pairs?  Many single-winner methods face a similar
question.

Thanks,
Scott Ritchie