[EM] New Condorcet/RP variant

[Steve Eppley]

Hi,

Markus S wrote about Paul Crowley's proposed voting method:
> your Condorcet/RP variant sounds like Steve Eppley's
> "minimize thwarted majorities" (MTM) method.

I think of the name MTM as an old name for MAM, which stands 
for "maximize affirmed majorities."  To my ear, "maximize 
affirmed majorities" has a more positive sound than "minimize 
thwarted majorities." (I'm open to suggestions for a better 
name, although so much has already been written about MAM 
that changing the name again will be problematic.)  I don't 
recall which tiebreaking technique I defined for it back 
in those days, years ago.  I may have posted more than one 
tiebreaker as the method evolved, and may even have left 
tiebreaking undefined initially.  If he thinks it matters, 
hopefully Markus will tell us which MTM tiebreaker he has 
in mind.

The tiebreaking in Paul's method sounds different than MAM's.  
But I'd appreciate seeing examples to clarify each case Paul 
wrote about.  I got the impression his tiebreaker is not 
independent of clones, but I'm not confident I understand 
what he intended.

I'd appreciate if Paul would elaborate on why he thinks its 
tiebreaking is "fairer" and "cleaner" than MAM's.  Are there 
any criteria we can use to more clearly define "fairer" 
and/or "cleaner?"

What I want from a tiebreaker is for it to be as simple as 
possible, but without sacrificing any criteria that people 
consider important.  Even though my principal concern is with 
public elections, where it's unlikely any pairing will be a tie 
and unlikely two majorities will be the same size, I think 
it's important that the tiebreaker behave well in small group 
voting.  That's because I expect the public will be reluctant 
to accept a voting method for public elections that hasn't been 
thoroughly tested by many organizations. (A couple of months 
ago in the discussion of the Kemeny-Young method, I didn't find 
the time to mention this connection between public elections 
and small group voting.  K-Y's failure of clone independence 
is likely to cause problems if K-Y is used by small groups 
voting on propositions and amendments, since clone amendments 
cannot refuse to be nominated, and the participants typically 
won't know at nomination time whether or not there will be
any pairwise ties or same-size majorities.  Clone nominations 
might also be a simple way to make K-Y fail the minimal defense 
criterion, but I haven't looked at this.)

There's also the issue of execution time.  There's no inherent 
upper bound on the number of alternatives in an election 
(particularly when voting on propositions).  I don't want to 
have to defend a voting method from attacks by "hired gun" 
academics who argue that its worst case execution time blows up 
as the number of alternatives increases.  Election reform is 
tough enough already; there's no reason to unnecessarily 
give ammo to the enemy, who'll be able to afford much more 
media time.  I spent months trying to develop a quick algorithm 
to implement MTM before finally finding one.  Then I recognized 
that algorithm was equivalent to Tideman's top-down algorithm 
that had been posted in the EM list a year earlier--except 
using "winning votes" instead of margins, and the open issue of 
tiebreaking.  So then I got ahold of Tideman's 1987 paper and 
Zavist-Tideman's 1989 paper.  I misinterpreted Zavist's 
tiebreaker when I copied it for MAM, but that turned out 
to be good luck since my version provides monotonicity but 
Zavist's does not. (I don't mean to imply I think monotonicity 
is important.  To me monotonicity is just another unimportant 
"consistency" criterion.  I only care about monotonicity 
because people have been known to criticize methods that 
aren't monotonic.)

It's common for small groups to use voting methods that violate 
neutrality and anonymity.  The basic Robert's Rules method, 
a pairwise single-elimination method, resolves the top cycle 
(if there is one) based on the order in which amendments are 
proposed, thus violating neutrality.  Ties are typically 
broken by appealing to the chairperson or the agenda order, 
thus violating anonymity or neutrality.  So, if a group 
wants to eliminate randomness by trading away anonymity or 
neutrality, they can do so by favoring the alternatives 
nominated earlier--status quo treated as first--and/or 
a seniority order of the voters. (But I haven't checked 
whether using the nomination order satisfies a criterion 
weaker than clone independence: independence from all clones 
except the earliest.  Although weaker, its satisfaction 
would seem to be sufficient.) 

If he hasn't already done so, Paul might want to look at 
the section entitled "MAM2, a voting rule equivalent to MAM" 
in the following webpage:
www.alumni.caltech.edu/~seppley/MAM%20formal%20definition.htm
Here's an excerpt from that section:

   MAM2 finds the social orderings which "maximize affirmed
   majorities" and elects an alternative which tops such an
   ordering.  This is similar to the Kemeny-Young "maximum
   likelihood estimation" voting rule, except MAM2 uses a
   leximax comparison of the possible social orderings while 
   Kemeny-Young scores each of the possible social orderings 
   by adding the sizes of the majorities it agrees with.

MAM2 is completely equivalent to MAM due to the way it
handles tiebreaking.

--Steve