[EM] Re: IRV letter

[Chris Benham]

Bart, interested participants,
A correspondent has brought to my attention that I erred when (on 
Tue.Apr.27) I wrote:

"IRV  meets  Mutual Majority (what Woodall calls "Majority"). It implies 
Majority Favourite and Condorcet Loser (which of course
implies Majority Loser)."

(M) Majority does imply Majority Favourite and Majority Loser, but not 
Condorcet Loser.
It is possible for there to be  a "profile"  where there is a Condorcet 
Loser, and yet MM says  "pick any candidate".
The example I was given:

>25 ABDC
>27 BCAD
>24 CADB
>24 DBCA
>
>Mutual Majority says the winner must be one of ABCD, but D is the Condorcet
>Loser.
>
>  
>
Here is an example from Adam Tarr (posted Tues.Apr.27,03) of   
whole-votes Bucklin failing Condorcet Loser:

>1% A=B=C
>33% A>B=D
>33% B>C=D
>33% C>A=D
>
>D loses 34%>33% pairwise to each candidate, yet D wins GB/MCA in the second 
>round with 99% approval.
>
Here again, MM  just says "pick any candidate". (BTW, Weighted Median 
Approval also stumbles in this example).

You wrote (Sun.May 9):

>Can someone tell me whether the following hypothetical method meets
>Mutual Majority?
>
>1. Voters submit ranked ballots.
>2. While no surviving candidate has a top-choice majority:
>      Eliminate the candidate with the greatest plurality of
>first-choice votes.
>(End definition)
>
>Example:
>3  A > B > C
>49 B > C > A
>48 C > B > A
>
>Round 1: No candidate has 50% + 1, so B is eliminated.
>Round 2: C wins with a 97% 'majority'.
>
>The method does appear to meet Majority Favorite and Condorcet Loser.
>
CB: Yes it does. But it fails two other Woodall criteria that are met by 
IRV,  "Plurality" and  Mono-add-top.
His Plurality criterion says that if  candidate A has more first-place 
votes than candidate B has non-last-place votes, then
B cannot be elected. In your example, B has more first preferences than 
C has non-last preferences, so  the Plurality Criterion
says  "not C".

Chris Benham