# [EM] Yet Another Lottery Method

raphfrk at netscape.net raphfrk at netscape.net
Sat Jun 24 08:33:52 PDT 2006

```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.

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.

```