[EM] RCV Challenge

[Kevin Venzke]

Hi Forest,

Does IACC give different results from TACC? Off the top of my head it seems that
in a three-candidate cycle both methods will elect whichever candidate beats the
approval loser.

For myself, here's a short list of ideas.

1. As you initially described this challenge (with UD, monotonicity, clone
independence) the bar seemed very high, making me think only a few methods would
be worth mentioning.

One of them is River. If I'm not mistaken River's resolution process can be
explained and executed very easily.

Say that each candidate "has" a set of candidates, which initially contains only
the candidate himself.

Evaluate the propositions from strongest to weakest.

When you consider "A beats B," ask simply whether B is still in his original
set. If so, then move every candidate in B's set into whichever set A currently
occupies. Otherwise do nothing.

(If A is in B's original set, it's the same result to move or to not move.)

After considering all the propositions, elect from among the candidates who
remain in their original set.

If I deviate from the criteria:

2. Condorcet//Approval with implicit approval is probably the simplest Condorcet
method that I like. I think with three slots it's best, though. It's very simple
to understand, and burial strategy has high risk.

3. I am still intrigued by the "BTP" method from a year ago, in which voters
basically acquiesce to every candidate who "Beats or Ties" each candidate
"Preferred" to them on that ballot. I'm still unsure what pitfalls this method
may have.

It is a strange quirk to see, for example, Gore prevail over Bush with
acquiescence interpreted to come not from the Nader voters, but from the Bush
voters.

4. Not quite a Condorcet method, but I like Approval-Elimination Runoff in which
we eliminate the least-approved candidates until there is a majority favorite.

5. My "King of the Hill" method. Between the first preference winner and the
candidate with the most first preferences who is involved in a majority-strength
pairwise contest with the FP winner, elect the winner of that contest, if there is
such a contest.

This is based on the intuition that a high first preference count indicates
viability, and that respecting a full majority among such candidates should at
least ensure the winner comes from the "correct" side of the spectrum. This
method also admits no burial strategy.

Kevin