[EM] Re: IRV letter

[Chris Benham]

Bart,
In response to me writing:

> 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". 

You replied:

>I don't mean to nitpick, but B has only 49 first preferences, while C
>has 97 non-last preferences.  While the hypothetical method may not
>guarantee Plurality compliance, the above doesn't appear to be an
>example of failure.
>  
>
CB: Oops! You are right, I didn't count  the 49 B>C>A  ballots as 
non-last votes for C. In this example, Plurality Criterion only says
"not A".  I probably shouldn't  have even mentioned Plurality.  It is 
not one of my fundamental criteria.  
I prefer  Mono-add-top, and  my point about that remains valid. Of 
 course the method you describe doesn't  even meet
Mono-add-Plump.

Chris Benham


>  
>