[EM] RP vs BeatpathWinner, committee clarification

[Steve Eppley]

Mike Ossipoff wrote (14 Mar 2003):
-snip-
>                                        I agree that RP(wv)is
> _slightly_ better than BeatpathWinner, when it comes
> to pure merit. But I also believe that the merit
> difference between RP(wv) and BeatpathWinner/CSSD isn't
> significant, and so my choice of which to recommend
> or propose is based on which can be more easily proposed
> to a particular group, or would be better accepted by
> that group. So I go by proposability & acceptability
> rather than by pure merit, when the merit difference
> is so slight.

Something to consider is that it will help in public acceptability if 
a method has already been used successfully.  This is an argument 
that can be interpreted in two opposite ways: If Mike is right that 
he/we can persuade small organizations to adopt BeatpathWinner but 
not MAM, then in the long run BeatpathWinner may be more readily 
accepted by the public, after years of its use within small 
organizations.  But if he's wrong, meaning he/we can persuade small 
organizations to use MAM if he/we try, then that would make it easier 
in the long run to achieve public acceptability of a voting method 
that meets the criteria he/we consider most important. (Minimal 
defense, clone independence, maybe a few others, if I'm not 
mistaken.) 

My own experiences explaining the merits of MAM to laypeople are only 
anecdotal (as I assume is the case with all of us regarding all 
methods) but I haven't yet found any particular sticking points with 
MAM.  After teaching how multiple majority preferences exist when 
there are more than two alternatives, it is natural to explain 
affirming the majority preferences, one at a time from largest to 
smallest, that don't conflict with those already affirmed. (It was 
natural enough that Condoret also came up with the idea.) 

There's a second, equivalent definition of MAM--find the ordering of 
candidates that minimizes the largest "thwarted" majority--that some 
people may find appealing. (That's yet another kind of "minimax", or 
more precisely a "minileximax," and is the definition I used when I 
developed MAM, originally called "Minimize Thwarted Majorities," or 
MTM.  Only later did I realize it's equivalent to affirming the 
majority preferences, one at a time from largest to smallest, that 
don't conflict with those already affirmed.)

> I also agree of course that MAM is better, when it
> comes to criterion compliances, than the RP(wv) version
> that I propose. The RP(wv) proposals differ in how they
> deal with equally strongest unconsidered defeats. MAM
> uses random ordering to solve those midcount ties, while
> my proposal, which has been called "deterministic#1"
> avoids random tiebreaking except if the method returns
> more than 1 winner.

It is misleading to say MAM uses a random ordering.  MAM uses an 
ordering constructed by the Random Voter Hierarchy procedure (RVH, a 
generalization of Random Dictator) and this is not a random ordering. 
For instance, an RVH ordering ranks clones together and satisfies 
strong Pareto, whereas a random ordering may rank non-clones between 
clones and may rank Pareto-dominated alternatives over their Pareto-
dominatrices.  Also, an RVH ordering satisfies a variation of 
monotonicity, in that upranking a candidate increases its chance of 
being ranked higher in the RVH ordering, whereas the candidate's 
chance is unaffected in a random ordering. 

> I don't deny that MAM is better than deterministic#1,
> but, again, my proposal choices are governed by
> what will be most easily accepted. I'm not even claiming
> for sure that deterministic#1 is more likely to be
> accepted than MAM is--it's just my subjective impression
> that it might be.

My hunch is that many people will accept the opinions of trusted 
experts, who are likely to distinguish on the basis of technical 
merit (that is, criteria compliance).

> How deterministic#1 deals with equally strongest unconsidered defeats:
> 
> Call those defeats the tie defeats.
> 
> A tie defeat is "qualified" if it isn't in a cycle
> consisting only of itself and some already-kept defeats.
> 
> Keep each qualified defeat that isn't in a cycle
> in which every defeat is either qualified or already-kept.
> 
> [end of instruction]
> 
> Deterministic#1 is more likely to return more than
> 1 winner than some other versions, and I don't know if
> it always meets Monotonicity & ICC. But it doesn't bother
> me if it violates them only if there are several equally
> strongest unkept defeats.

I seem to recall that when I looked at "Deterministic#1" a couple of 
years ago, it violated monotonicity.  I don't remember checking for 
clone independence.  It must have had some flaw that I thought 
significant at the time, or I would have dumped MAM in its favor.  

I'd be interested in seeing the demonstration that D#1 is more likely 
to return more than one winner.  Was it a proof or the result of 
simulations?  It would strike me as odd that some people would accept 
increased overall randomness to avoid "midcount" randomness.

It's reasonable to neglect those flaws in large public elections, 
since they can't occur without equally strong majorities and that 
would be very rare in large public elections. In fact, I don't see a 
compelling reason to talk about tiebreaking in that context, just as 
Instant Runoff advocates don't talk about tiebreaking when two or 
more candidates have the same equally smallest vote count in some 
iteration.  Have they encountered problems due to IRV's occasional 
need to resolve "midcount ties?"  Depending on how they break those 
ties, IRV might not be completely independent of clones.  For 
instance, if they eliminate all candidates having equally smallest 
vote count, that would lose clone independence.

But in small committees the flaws could occur more frequently, and 
flaws like clone dependence might be exploitable.

>From my observations of committee voting, they don't seem to mind 
using a chairperson's vote as a tiebreaker.  So some organizations 
might find it appealing to use the chairperson's vote as the tiebreak 
ordering used by RP and other methods.

-- Steve Eppley