# [EM] A Majoritarian, Clone Free, High Efficiency, Sincere Ratings Lottery

fsimmons at pcc.edu fsimmons at pcc.edu
Wed Jan 6 11:56:23 PST 2010

```The method I have in mind is inspired by Jobst's T3ASR, which I have copied to
the end of this message for comparison.  The only improvement is that this new
method is clone free, while T3ASR fails clone loser because (under T3ASR) if the
candidate with the most approval loses, one of his clones is sure to win,
provided that he has at least two of them.

In this new method voters are allowed three ballots ...  an approval ballot, an
ordinal preference ballot, and a cardinal (range style) ratings ballot.

1. The approval winner A is determined from the approval ballots (or approval
cutoff on ordinal ballots).

2. The ordinal ballots are used to determine the set  S  of candidates that
cover the approval winner A.  [Candidate C covers A   iff   every candidate that
pairwise beats C also pairwise beats A.]

3. The same ordinal ballots are used to determine the winning probabilities for
the lottery L(S) that uses random ordinal ballot to choose from S.

4. The range ballots are used to choose between A and L(S).

5.  If L(S) wins in step 4, then the winner is the member of S that is ranked
the highest on an ordinal ballot picked at random from those submitted.

Note that this method satisfies Independence from Pareto Dominated Alternatives
(IDPA), is monotone, clone free, and majoritarian in the sense that a majority
can ensure the election of any candidate by bullet voting on the first two
ballot types, i.e. on the strategic ballots.  In fact, if the approval winner A
is also the majority winner, then A is the only member of S.

It has high efficiency because it takes a well liked candidate to cover the
approval winner.  Geometrically speaking, candidates that cover  A are between A
and the "median voter."

And since there is always a chance for the set S to not be trivial, it is to the
rational advantage of voters to fill out honest range ballots.

Forest

P.S.

Here's Jobst's T3ASR:

Method "Top-3 approval sincere runoff" (T3ASR)
==============================================

1. Each voter separately supplies
a "nomination" approval ballot and a "runoff" range ballot.

2. From all "nomination" ballots, determine
the options A,B,C with the top-3 approval scores a>b>c.

3. Let p be the proportion of nomination ballots
which approve of C but not of B.

4. If on at least half of all "runoff" ballots we have a rating
r(A) > p*r(C) + (1-p)*r(B), then option A wins.

5. Otherwise draw a "nomination" ballot.
If it approves of C but not of B, C wins, otherwise B wins.

Most of the time, this will elect one of the top-2 approval options, and
only rarely the 3rd placed.

One can then also compute and publish some kind of "index of sincerity"
by comparing the submitted approval and range ballots.

The method is majoritarian, since any majority can rule by bullet voting
on both ballots.

```