Majority Support? (was Re: Lowest Majority loser tie breaker)

[Steve Eppley]

DEMOREP1 wrote:
>I repeat again the absolute necessity that the winner have majority
>"positive" support. 

And on 7-8-96 Demorep submitted this response to the EM single-winner
poll (and hasn't amended it):
>My SW vote--
>1. A mixture of rank voting, majority yes (approval), Condorcet for
>  the majority yes candidates, limited approval tie breaker (limited
>  combined choices). See---- Subj:  Single Person Elections 6/27/96
>  Date:  Fri, Jun 28, 1996 12:20 AM EDT 
>2. Approval with rankings (dropping the last ranked choice- such as
>  having 5 candidates- only top 4 choices of a voter would count-
>  highest majority candidate wins) 
>3. Instant Run-Off (a.k.a. MPV)
>
>A majority winner must occur in view of the SW competitors of plain
>approval voting, top 2 runoff and instant run-off.

Since Instant Runoff doesn't allow the voters to express approval or
disapproval of candidates, it does NOT meet Demorep's standard; the
final sentence above is not true of IR.  IR's so-called majority
winners shouldn't be deemed "true" majority winners any more than 
the winners in Soviet-style one-candidate elections.  

IR performs worse than Condorcet on this standard, I believe.  Here
are examples where Condorcet beats IR.  (I'm using the character '|'
to show the voters' "None of the Rest" dividing lines between
approvals and disapprovals.)

   46: RM|L
   20: M|
   34: LM|R
and one which is slightly more complex, to mollify Donald:
   23: R|ML
   23: RM|L
   20: M|
   17: LM|R
   17: L|MR

   Only M is majority-approved.  

   Plain Condorcet, which ignores the |s, elects M.  (Condorcet+| 
   also elects M, no matter how the |s are tallied, since only M 
   pairwise-beats |.)  

   Plain IR, which ignores the |s, elects R.  Demorep's claim that
   IR satisfies "Majority Support" is disproved.

I'd like to see a countervailing example showing plain IR performing
better than Condorcet, using ranked ballots which include the voters'
dividing lines between approval and disapproval.  As above, when 
tallying the ballots using plain IR, the tally must ignore the 
dividing lines since plain IR doesn't really allow these enhanced 
ballots.

Demorep's support of plain IR is a remarkable inconsistency.  
To be consistent, Demorep should amend #3 to:

   3. a mixture of rank voting, majority yes (approval), 
      Instant Runoff for the majority yes candidates, limited 
      approval tie breaker, etc. 

And since none of these three new methods is likely to be among the
methods actually proposed due to their complexity, I suggest that
Demorep extend the response so it ranks some additional methods 
like Condorcet+NOTB, Approval, Smith//Condorcet, Condorcet, and
Instant Runoff, and maybe in this order to be consistent with how 
well they satisfy "majority support".  However, plain Approval's 
strategy problems cause it to perform poorly on this standard when
you examine it closely, since voters have the LOE dilemma when 
deciding whether to express approval of a compromise choice:
approval of a compromise can defeat one's favorite, and 
disapproval of a compromise can allow a greater evil to win.  
So I wouldn't recommend ranking Approval that high unless you don't
care about the "Sincere Voting", LOE, and "No Spoilers" standards
and have only a limited view of the majority rule standard.
(Apologies to Bruce for discussing standards instead of rigorous 
criteria.  But we can go rigorous later, if necessary, and standards 
provide useful introductions.)

---Steve     (Steve Eppley    seppley at alumni.caltech.edu)