# [EM] favorite betrayal and 2-party domination in Condorcet(wv, =); and about DMC

Warren Smith wds at math.temple.edu
Mon Sep 5 18:47:40 PDT 2005

```To recount some recent history.  I at first had this idea that all
Condorcet methods would lead to 2-party domination.
I in fact produced a "proof" of that (well, a proof of a related statement, anyhow)
and put it on the CRV web site.  Then one of the attacks on my proof (by Adam Tarr) was that
my proof was only about "margins" Condorcet with "full rank orderings only" as votes.
If equal rankings are permitted, my proof still worked (after slight amendment)
so that was not an issue.  But with =permitted AND winning-votes THEN my
proof was no longer useable.

So it was then argued that Condorcet(ww, =permitted) voting methods perhaps can
escape 2-party domination - and definitely could escape my proof.

However, I now point out, following Kevin Venzke, that Condorcet(ww, =permitted) voting
methods STILL DO suffer from "favorite betrayal" in 3-candidate elections.  An
example (and it does NOT involve any "ties", unlike my last example) is at
http://math.temple.edu/~wds/crv/VenzkeFBC3.html
and this now again makes it plausible that even these Condorcet methods (and hence
ALL condorcet methods) will lead to 2-party domination.   As has been pointed
out by Suter and myself, 2-party dominance is an experimental question,
so we don't really *know*, but anyhow this example at least suffices to
make it a plausible worry - just how plausible depends how common such
examples are, which I have no idea of beyond that it is between 0.0001 and 1.

Meanwhile, range and approval voting do not suffer from favorite-betrayal.

So.  from the point of view of US third parties,
1. all Condorcet methods plausibly lead
to 2-party domination, though we cannot be sure,
2. all are more complicated
than range voting, and
3. range voting apparently does NOT lead to 2-party domination.

Therefore, US third parties should push range voting in preference
to all Condorcet methods.   (Doing the reverse would be idiotic/suicidal, name

------

Also, concerning the elegant hybrid Condorcet-Approval method DMC.
Simmons wanted to push it as sort of best of breed.   I am coming to agree with him.
I had attacked DMC as apparently leading to 2-party domination, while Condorcet(wv, =)
would not be - but as we see the latter part of that attack is now somewhere
between questionable & false.
I also had noted Heitzig was pushing DFC not DMC despite being named as DMC's inventor.
However, Heitzig is denying paternity.  Also, while I admire the idea of "lottery methods"
such as DFC, I suspect none of them are acceptable for practical use because too
many people will protest too greatly the notion of chance playing such a big role.
I think, however, that lottery methods should still be studied, and if I ever get around
to making my humongo-comparative-sim study ride again - which could happen faster if
some programmer want to help... - I would like to include some of them.

-wds

```