[EM] MMPO objections

[fsimmons at pcc.edu]

The ordinary MMPO pairwise opposition matrix has blanks down the main diagonal.  If you put the 
respective disapprovals in those positions, then the Plurality problem goes away.

Filling in the diagonal elements with disapprovals is tantamount to incorporating a virtual Minimum 
Acceptable Candidate (MAC) as the approval cutoff.  The disapproval is simply the opposition by MAC. 

The simplest way to incorporate this feature is to use implicit approval.  Then the diagonal element in 
position (i, i) is simply the number of ballots on which candidate i is unranked (or unrated).

With this convention, when all ballots rate candidates only at the extremes, the method elects the 
approval winner.

In Kevin's example

49 A
01 A=C
01 B=C
49 B ,

the MAC opposition to C is 98, which is much larger than any other opposition, so the approval loser C 
is also the MMPO loser for this version of MMPO.

Now consider these facts:

1.  When there are complete rankings ordinary MMPO elects the same candidate as MinMax(margins).

2.  In case of incomplete rankings MinMax(margins) elects the same candidate whether or not the 
ballots are treated with symmetric completion.

3.  When incomplete ballots are treated with symmetric completion, regular MMPO elects the same 
candidate as MinMax(margins).

4.  Under MMPO with symmetric completion, exempting the equal top position from symmetric 
completion trades Condorcet Criterion compliance for FBC compliance.

5. This partial symmetric completion version of MMPO resolves Kevin's approval bad example (ABE).

6.  Introducing the virtual candidate MAC to this version of MMPO does not change this satisfactory 
resolution.

7.  If we limit the method to three slots (or four slots with MAC between the two middle slots), then the 
clone winner failure that MMPO shares with MinMax(margins) goes away.

In sum, I propose this version of MMPO.  The problem is how to package it for public approval.

I suggest calling it MaxAssentMinDissent.

People are familiar with the concept of decisions rendered by deliberative bodies like the supreme court 
being accompanied by a count of concurring votes, dissenting votes, and abstentions.

If we lump the concurring and abstentions together into the category of "assent," then our method 
maximizes the minimum assent and minimizes the maximun dissent from all of the pairwise decisions 
relative to the method winner.

If candidate X is elected there will be dissentions relative to each of the other candidates including MAC.

Suppose that the largest of these dissents is 43 percent, i.e. 43 percent of the ballots show a preference 
of some candidate Y over X.

The largest dissent against Y will be larger than this 43 percent dissent against X,  so Y has no better 
claim than X to be elected. 

Likewise the minimum assent for X would be 100-43=67, and this is greater than the minimum assent for 
Y.

Etc.

Thoughts?

Forest


In sum  MMPO with MAC and Bottom Symmetric Completion is the ri