[EM] Yet Another Lottery Method

[raphfrk at netscape.net]

From: Simmons, Forest <simmonfo at up.edu>
>  This method makes use of ordinal information as well as approval 
information.

So each voter would rank the candidates and also select one candidate 
as
the threshold between approved and unapproved ?  All unranked candidates
being unapproved.

>
>1.  Eliminate each candidate X for which there is a candidate Y such 
that on
>each of more than half of the ballots Y is approved and X is not.

What about going direct to Condorcet here ?  Eliminate any candidate 
who is
not in the Smith (or Schwartz) set and then use random ballot.

I guess the problem being that voters who are going to lose might be 
willing
to force a tie which gives them a chance of getting their candidate 
elected
even though it also gives a lower preference a chance of being elected. 
 I am
not sure your method is immune from this.

>
>2.  Use random ballot among the remaining candidates to choose the 
winner.
>
>Note that if any candidate X is eliminated, then some candidate Y must 
have more
>than fifty percent approval, which makes her invulnerable to 
elimination.
>
>This method satisfies Monotonicity, Clone Independence, Independence 
from Pareto
>Dominated Alternatives, Strong Favorite Betrayal Criterion, etc.  In 
fact, as
>near as I can tell there is no incentive for any insincere order 
reversal or
>collapse.
>
>Of course, Random Ballot without step 1 satisfies all of those 
criteria, too,
>but it is a bit too promiscuous with the probability.

Assuming the votes are:

45:  A, B approved  ( B>A>>C )
40:  C approved ( C>>A>B )

The remaining 15 voters are of the opinion
A>C>B

if they approve A only:
C is eliminated ( 45+15 = 60 votes approve A and not C )

result is:
A: 40+15 = 55%
B: 45 = 45%
C: elim = 0%

OTOH, if they approve C (tactical voting)
A,B are eliminated ( 55% approve C and none other)

results is
A: elim= 0%
B: elim= 0%
C: 100% ( only remaining )

It is not clear to me that a 55% chance of your favorite and 45% chance
of your lowest choice is superior to a 100% chance of your middle 
choice.

This means that depending on the 15 voters relative preference 
strengths,
it might be in their interests to tactical vote and just approve C, 
even though
they prefer A to C.

If the ranked choice must be consistant with the approval choice, they 
could
just vote C approved and C first choice as a pure tactical vote.

>With this new method any united majority can eliminate any dangerous 
candidate
>from consideration.  This majority defense feature has a name, but I 
won't try
>to remember what it is.