[EM] Ranked Pairs

[Kevin Venzke]

Hi Colin,

> Michael - I don't think I understand everything you're saying. I was
> referring to RP (margins), which I believe is the form in which Tideman
> specified it, and I assumed that truncation was a mixture of laziness
> and ignorance.

I would note, there's another motivation reachable by a simulation, which is quite
reasonable with such methods. Suppose an election is believed to be primarily
between two frontrunners. Then voters might want to resist ranking the worse
frontrunner over anyone else, for the reason that they might be assisting that
candidate, which clearly shouldn't be able to occur if only two candidates are
contenders.

(With WV such truncation solves the issue for the voter. With margins, the savvy
voter cannot conclude truncation is the optimal (or even safe) way to achieve the
same result, and actually this is meant to be a selling point. Though I would argue
that this uncertainty invites the savvy voter to play a dangerous game.

The likely response to my view is that the savvy voter doesn't have enough
information to play the dangerous game. And that's completely right, he doesn't. Yet
he still has to make a decision. Supposedly we should trust that the savvy voter
just votes sincerely and risks handing an advantage to the worse frontrunner. But
that's not at all obvious to me. Something I've said before is that my own
inclination to vote sincerely in a margins Condorcet election would have an inverse
relationship to how robust the method has proven to be in practice.)

> (Actually the simulation I referred to assumed mandatory
> truncation, which I think is common in the US.) I don't hold any brief
> for RP; on the contrary I much prefer minimax (also margins).

I have to say, if a real entity were to enact margins Condorcet with mandatory
truncation, I would find it baffling. One of the few arguments that can be made for
margins is the truncation item above, that a savvy voter can't conclude they should
use it. But with mandatory truncation all voters literally must use it.

> [earlier]
> I notice that RP is the only election method mentioned by name in the
> Virginia agenda.
> 
> A while ago I ran some simulations on elections with truncated ballots.
> Something I noticed was that the presence of RP in the list of methods
> made the software unacceptably slow. I didn't look into the cause, but
> there's a natural explanation, which is the fact that RP is known to be
> NP-complete when it deals correctly with tied margins, i.e. by
> exhausting over all their permutations. Presumably if some candidates
> are unpopular and ballots are extensively truncated, then tied margins
> are much likelier than with complete ballots.
> 
> I gather that practical implementations of RP choose a random
> permutation rather than exhausting. This seems to me to bring a danger.
> The presence of a few vanity candidates (truncated off almost all
> ballots) may lead to ties, and this may lead to a comfortable winner
> looking as though he owes his victory to a coin-toss. Obviously this
> undermines the legitimacy of his win.

I guess that a real election can tolerate a slow calculation, more than simulations
would want to.

The coin-toss concern is legitimate to me. It might suggest using Schulze instead,
but only on the practical matter, or for transparency (no issues of permutations of
defeats), given that Schulze can still have ties in the final result.

Needless to say, methods should be designed so that vanity candidates (including
even a weak third candidate) don't affect the outcome. The outcome of the most
important single question of the election should be "locked" as quickly as possible
to prevent mischief.

Kevin
votingmethods.net