[EM] Markus: RP & BeatpathWinner/CSSD

[Steve Eppley]

On 10 Mar 2003 at 12:27, Markus Schulze wrote:
-snip-
> However, according to Steve Eppley, there is a merit
> difference. Steve, who uses the term "MAM" for Ranked Pairs

It is more reasonable to use the term MAM as a variation of 
Ranked Pairs than as a synonym for Ranked Pairs.  MAM is 
monotonic, whereas Zavist-Tideman's Ranked Pairs 1989 is 
not (nor is the "winning votes" variation of Ranked Pairs 
1989).  MAM satisfies strong Pareto and clone independence, 
whereas Tideman's Ranked Pairs 1987 does not.  And, being a 
"winning votes" variation, MAM satisfies some criteria 
(Minimal Defense, Non-drastic Defense and Truncation 
Resistance) that "margins" variations of Ranked Pairs do 
not satisfy.  Given its satisfaction of these criteria, MAM 
seems to be the best variation of Ranked Pairs.

> and the term "PathWinner" for the beat path method, writes:
>
>> MAM may be preferable to PathWinner for a couple of reasons:
>>
>> 1. MAM (but not PathWinner) satisfies immunity from majority
>> complaints (IMC), immunity from second-place complaints (I2C)
>> and other criteria described in the document Immunity from
>> Majority Complaints.
>>
>> 2. Computer simulations using randomly generated profiles of
>> voters' orderings suggest the alternative chosen by MAM will
>> beat pairwise the alternative chosen by PathWinner more often
>> than vice versa, and that over the long run more voters will
>> prefer MAM winners over PathWinner winners than vice versa.

Also, MAM satisfies Peyton Young's criterion "local 
independence of irrelevant alternatives (LIIA), and 
BeatpathWinner does not.  

   Call a subset X of the alternatives "contiguous"
   if no alternative outside X is socially ordered 
   equal to or between any alternatives in X.

   LIIA:  For all subsets X of the alternatives, 
   if X is contiguous then the alternatives in X 
   must be socially ordered, relative to each other,
   the same as they would be if all alternatives 
   outside X were deleted from the votes. 

LIIA is weaker than Immunity from Majority Complaints, both 
described in my web pages.  

Young wrote in "Equity: In Theory and Practice" that LIIA 
is a "slight weakening" of Arrow's IIA, and on that basis 
argued for the Kemeny-Young method.  But clearly "LIIA + 
Clone Independence" is even less of a weakening of IIA, so 
Young ought to have argued for a method like MAM that 
satisfies both LIIA and Clone Independence.  Personally, I 
don't think Young's justification of LIIA is as significant 
as Young thinks, but some readers may consider LIIA 
satisfaction to be another significant advantage MAM has 
over BeatpathWinner. (It may also help in a campaign to 
reform the voting method if one can cite Young's desire for 
LIIA compliance and point out the proposed voting method 
satisfies it.)

Mike Ossipoff wrote that another MAM advantage is its 
briefer definition, but since that kind of thing tends like 
beauty to be in the eye of the beholder, I didn't make that 
claim in my web pages.  Mike seems to like to minimize word 
count even if that reduces clarity, whereas I think clarity 
is more important than brevity. 

* *

In a recent message I erred when I said Mike Ossipoff 
considers MAM best in both committees and public elections, 
judging by his recent messages in EM that say he thinks 
it's better in public elections but not in committees.

I must have misunderstood the implications of some of his 
comments in private email, or maybe he's changed his mind 
again.  Maybe I'll find time to reread his private email, 
and time to argue with him over his claim that the 
BeatpathWinner algorithm is really briefer or more elegant. 
These can depend on the language in which the algorithm is 
written.  For instance, languages that include "sorting" as 
a high level instruction make MAM much briefer and more 
elegant than languages that demand the programmer implement 
a sorting routine using low level instructions.  

To see a fairly brief yet complete MAM algorithm written in 
"structured English", follow the link to "MAM procedure 
definition" from "www.alumni.caltech.edu/~seppley".  

MAM's definition and algorithm can be significantly 
shortened for public elections, since in that context it is 
reasonable to ignore the unlikely occurrence of two or more 
majorities that are exactly the same size, and pairings 
that are tied.  

The definition and algorithm can also be shortened in the 
committee context if, instead of using Random Voter 
Hierarchy to construct a tiebreaking ordering of the 
alternatives, we use for the tiebreaking ordering the 
chronological order in which the alternatives were 
nominated.  This variation doesn't completely satisfy the 
Neutrality criterion, but rewarding the early alternatives 
when breaking ties seems a reasonable and slight relaxation 
of Neutrality.  This variation might also not completely 
satisfy Clone Independence--I won't have time to check this 
for awhile--but, if not, probably provides enough clone 
independence.

-- Steve Eppley