[EM] Mike Ossipoff: LRV properties

[fsimmons at pcc.edu]

Mike,

LRV is just another equivalent way of describing MMMPO. The are just MMPO with symmetric 
completion at the bottom level but not at the top.

In addition to FBC it satisfies MAP, KMBE, and U, but not LNHe.

> MAP means Mono-Add-Plump
> KMBE means Kevin's MMPO bad-example
> LNHe means Later-No-Help
> U means that a majority can be established unilaterally

LRV/MMPO goes beyond MAP to satsify mono-add-equal-top; if a new ballot ranks the old winner equal 
top, then the winner stays the same.

The FBC is a corollary of the following property.:

If (on a ballot) a candidate is moved up from a position above the winner or to a position that is not above 
the winner, then the winner either stays the same or is changed to the candidate that was moved up.

Now here's my attempt at Minimal Mutual Acquiescing Majority Top:

A ballot acquiesces to a set S of candidates if no candidate outside of S is ranked above any candidate 
inside the set S on the ballot in question.

A set S is a Mutual Acquiescing Majority set if a majority of ballots acquiesce to S.

A set with a certain property is minimal with respect to that property if it ceases to have that property 
when any of its members is removed.

A Minimal Mutual Acquiescing Majority set is a Mutual Acquiescing Majority set which would cease to 
be a Mutual Acquiescing Majority set if any of its candidates were removed.

Minimal Mutual Acquiescing Majority, Top method:

Of all the candidates that belong to some Minimal Mutual Acquiescing Majority set, elect the one rated 
top (or equal top) on the greatest number of ballots.

End of method definition.

Note that there is always a Minimal Mutual Acquiescing Majority set because if no proper subset of the 
candidates is such a set, then the entirre set of candidates is a Minimal Mutual Acquiescing Majority 
set.

Forest