[EM] serious strategy problem in Condorcet but not in IRV?

[Jobst Heitzig]

Just an idea...

"BANKS//APPROVAL":
Take the Banks set (that is, find the top elements of all maximal chains
(= acyclic complete subgraphs) of the graph of strict defeats), find the
element(s) with largest approval, break remaining ties by random choice.

This is pretty easy, seems to fulfil Condorcet, monotonicity,
cloneproofness and so on, and resolves at least the examples of
strategic voting James cited (at least I think so).

As the Banks set is a subset of the Schwartz set, the method is "in the
spirit" of Condorcet although it doesn't consider strengths of defeats.
Unfortunately, I can't remember whether the Banks set tends to be large
or small in case of many candidates...

When A wins in Banks//Approval, each argument "B is better than A" with
majority support can be shown to be ridiculous by pointing out a chain
of similar arguments leading back to A (since A is in the Schwartz set).
However, the latter defeats might of course be smaller. Thus, another
interesting variant could be the following:

"BANKS//WEAKLY IMMUNE//APPROVAL":
Find those elements A of the Banks set such that for all B defeating A
there is C defeating B by at least the same magnitude. Proceed with
approval.

Perhaps we focused on cycle breaking methods a bit too much?

Jobst