[EM] Part 2: Property-Requirements & Best Methods for Green scenario.

[Michael Ossipoff]

 When we no longer need FBC, then we can, instead, get some properties
valuable for the Green scenario:

1. Mutual Majority Criterion (MMC)
2. No chicken dilemma
3. Preferably, Condorcet Criterion

The combination of #1 & #2 is a powerful combination, one that allows
strategy-free sincere ranking for members of a mutual majority. ...the
otherwise elusive rank-balloting ideal.

#3 adds a considerable amount of strategic freedom to rank sincerely,
even for voters who are not in a mutual majority. Additionally, #3
avoids dis-satisfied majorites, thereby making the voting system
stable against replacement.

What methods possess properties #1, #2, and #3?

Benham and Woodall do.

Let me define them  here. I'll start with Benham, but it's necessary
to define IRV first, because Benham uses IRV:

IRV:

Determine which candidate tops fewest rankings. Delete hir from all
the rankings.

Repeat till only one candidate remains un-deleted. Elect hir.

[end of IRV definition]

Benham:

1. "X beats Y" means that the number of ballots ranking X over Y is
greater than the number of ballots ranking Y over X.

2, Do IRV until there is one un-deleted candidate who beats each one
of the other un-deleted candidates. Elect hir.

[end of Benham definition]

Woodall:

Do IRV till only one member of the initial Smith set remains
un-deleted. Elect hir.

The Smith set is the smallest set of candidates such that every
candidate in the set beat every candidate outside the set.

[end of Woodall definition]

Strictly speaking, Woodall is a little better than Benham. But not
importantly. They both always choose from the Smith set, but Woodall
is more particular which Smith member it chooses.

Benham is definitely good enough. It possesses the 3 properties that I
listed, and more (Smith Criterion).

Benham is  lot easier to define and propose, in comparison to Woodall,
because, though it always chooses from the Smth set, Benham's
definition definition doesn't require a definiion of the Smith set.

Benham is offered as one of the rank-counts at the Condorcet Internet
Voting Service. There, it's referred to as Condorcet-IRV.

A journal article by James Green Armyage discusses Benham, Woodall,
and a few others, and points out their better freedom from
strategy-need, in comparison to other methods.

to be continued...

Michael Ossipoff