[EM] Brief comments about Clone-Independence and Reversal Symmetry

[Michael Ossipoff]

Clone-Independence:

With Clone-Independence, Kristofer has shown one special particular
thing that won't deter sincere ranking in Beatpath..When clone A2 is
added to A, then A's initial preferrers can divide their vote between
A>A2 and A2>A, without a split-vote problem that makes {A,A2} lose,
_provided that all of the other voters vote A and A2 as clones_ (which
of course is necessary in order to call A2 a clone of A).

But, in general, in Beatpath, if you rank X over Y, then you're
helping to make Y beaten (instead of winning as CW) , and you're
adding to one of Y's defeats, which could strengthen a beatpath to Y
from someone outside {X,Y}.

So, if it's a u/a election, and if X and Y are acceptables, then you'd
better top-rank them both--except that a few people doing so, instead
of ranking X>Y, could allow Y to pairbeat X, changing a CW win for X
to a cycle in which someone much worse, outside of {X,Y} wins.

That's why I say that Beatpath, and TUC in general, is a strategic mess.

With an Improved Condorcet method, such as ICA, ICT, or SICT,
top-ranking both X and Y, instead of ranking X>Y, won't allow Y to
beat X, or prevent the winner from coming from {X,Y}.

Approval, Score, and Improved Condorcet methods have a known u/a
strategy, unlike Beatpath and other TUC methods. And their optimal
strategy could never involve favorite-burial. Neither of those things
can be said for Beatpath.

Reversal-Symmetry:

Kristofer said that violation of Reversal-Symmetry is saying that the
same candidate who is the best is also the worst. That depends on the
unsupported and unwarranted assumption that reversing the rankings
amounts to an election for worst. And that depends on the assumption
that a reversed ranking says the exact opposite of what it said before
reversal.

But that isn't true, as I showed in my earlier posting, entitled "A
few more words about Reversal-Symmetry".

Mike Ossipoff