Hi Forest,

Unfortunately I don't find this to be monotone with "MMPS." The issue is that a winning
candidate B may wish for a candidate they defeat, A, to have a certain number of votes
against B, so that A is the initial chain head that B then defeats. So when B gains some
votes at the expense of A, a different candidate D becomes initial chain head and wins:

0.328: D>B
0.253: A>C
0.204: A>B  <-- changes to B>A
0.140: C>D>B>A
0.074: B

I calculate in the "before" scenario the MMPS order is ADBC, B alone covers A, no one covers
B. Then in the "after" scenario the order is DBAC, and no one covers D.

Yes, MMPS does seem to satisfy the weak FBC. But the strong FBC compliance (i.e. what I
normally just refer to as "compromise incentive") is worse than Bucklin or C//A. So I guess
if the legislature enacts MMPS it should make sure not to forget to allow equal ranking.

I am thinking you got lucky with the first draft of MGAscent being monotone. (To be honest
it makes me question my own result there. Why should the max gross score version work and
nothing else? Not sure.)

Kevin
votingmethods.net

Kevin,

The funny thing is that in the Round Robin sports tournament context the
MMPS method for picking the winning team seems to be monotone ... one team
can get more points against another without affecting any other pairwise
scores ... in the pairwise matrix only one entry changes.

Maybe we could call that Tournament Monotonicity.
a
How about the Chicken Defense and MMPS?

Thanks,

Forest

On Sun, Jan 15, 2023, 5:42 AM Kevin Venzke stepjak@yahoo.fr wrote:

Hi Forest,

MMPS alone is monotone. It's the chain-building process to find an uncovered winner which
will break it.

This question turned out to be complicated. Two really big issues here.

1. The CD criterion seems to suppose that if the fragmented majority were to cooperate, then
   they would win, and be rewarded for not defecting from each other. However, MMPS doesn't
   satisfy mutual majority, so the reward can't be promised.

(Is FPP a "good CD method"? I think it's not in the spirit of it at all.)

This should mean that there is even more incentive to just use favorite betrayal (or have
one candidate drop out). But in MMPS we don't have to use full order reversal as we have
equal ranking and weak FBC. So that leads to the next issue.

2. Can a method that allows equal ranking (and allows it to do something useful, as with a
   weak FBC promise) be considered to satisfy "CD" at all? This creates a separate, likely way
   for the fragmented majority to win, where many voters still defect. That really seems to
   undermine the mechanism that's supposed to be working here.

That is, either faction can reason "We can defect, and force the other faction to use equal
ranking to save the win and elect our guy."

Kevin
votingmethods.net

Thanks for clarifying some important points.

In the tournament context the covering finish order enhancement should work
for MMPS like it does for Approval because in that context (unlike in the
ballot based context) raising just one candidate (winner or not) moves it
up the finish order without disturbing the relative order of the other
candidates.

What I call tournament monotonicity is preserving the winner when any or
all entries in the winner's row of the pairwise matrix are increased while
keeping all of the other rows constant.

We could make use of that version of monotonicity in pairwise election
methods if voters had more control over the process of converting their
ballots to the precinct summable pairwise matrices. Maybe too complicated
for the ordinary voter, but could be used in conjunction with Eppley's VPR
idea.

If you knew that raising X from X<Y to X=Y would by default zero out m(Y,X)
... and would rather have both it and m(X,Y) equal to one, there should be
a way of accomplishing that. Then tournament monotonicity could have some
benefit in the pairwise election method context.

On Tue, Jan 17, 2023, 4:27 AM Kevin Venzke stepjak@yahoo.fr wrote: