[EM] Proposal: Majority Enhanced Approval (MEA)

[Chris Benham]

Forest,

This MEA method you have suggested would nearly always give the same winner as 
Smith//Approval (ranking), one of the methods I endorse.

Where they do give different winners, would it be the case that the Smith//Approval winner
is the more approved?  But outside the Uncovered set?

What is the most "realistic" example you can give of the two methods giving different winners?

A feature of both methods that I am going off is that voters can be punished for failing to truncate
their least preferred of the viable candidates.

49: A1>A2
24: B
27: C>B>A1

A1 is uncovered and most approved, so both methods elect A1. But the presence of the weakly
pareto-dominated clone A2 on the ballot caused the C supporters to not truncate A1. If they had
done so then B would have won.

This type of example is what motivated me to recently propose that a candidate's 'biggest gross
pairwise score in a pairwise victory over an uncovered candidate' be used as a quasi-approval score.
B then wins whether the C voters truncate A1 or not.

(The other motivation was that I was looking for something that used nothing but the normal gross
pairwise matrix.)

I recognize that this can cause failure of mono-raise, but probably only in a complicated not very
likely example.

Chris Benham



Forest Simmons wrote (8 May 2010):

I have a proposal that uses the same pairwise win/loss/tie information that Copeland is based on, along with 
the complementary information that Approval is based on.  It’s a simple and powerful Condorcet/Approval 
hybrid which, like Copeland, always elects an uncovered candidate, but without the indecisiveness or clone 
dependence of Copeland.

I used to call it UncAAO, but for better name recognition, I’m changing the name to Majority Enhanced 
Approval (MEA).

The method is extremely easy to understand once you get the simple concept of covering.  Candidate X 
covers candidate Y if candidate X pairwise beats both Y and every candidate that Y beats pairwise.

MEA elects the candidate A1 that is approved on the greatest number of ballots if A1 is uncovered. 
Otherwise it elects the highest approval candidate A2 that covers A1 if A2 is uncovered.  Otherwise it elects 
the highest approval candidate A3 that covers A2 if A3 is uncovered.  Otherwise, etc. until we arrive at an 
uncovered candidate An, which is elected.

MEA satisfies Monotonicity, Clone Independence, Independence from Pareto Dominated Alternatives, and 
Independence from Non-Smith Alternatives, as well as all of the following:

1.  It elects the same member of a clone set as the method would when restricted to the clone set.

2.  If a candidate that beats the winner is removed, the winner is unchanged.

3.  If an added candidate covers the winner, the new candidate becomes the new winner.

4.  If the old winner covers an added candidate, the old winner still wins.

5.  It always chooses from the uncovered set.

6.  It is easy to describe:  Initialize L to be an empty list.  While there exists some alternative that covers 
every member of L,  add to L the one (from among those) with the greatest approval.  Elect the last 
candidate added to L. 

What other deterministic method (based on ranked ballots with truncations allowed) satisfies all of these 
criteria?

Forest