# [Election-Methods] Another Lottery Method for the Record

Gervase Lam gervase.lam at group.force9.co.uk
Sun Jun 29 16:29:39 PDT 2008

```> Date: Sat, 28 Jun 2008 22:17:58 +0000 (GMT)
> From: fsimmons at pcc.edu
> Subject: [Election-Methods] Another Lottery Method for the Record

> A voter is chosen at random.
>
> This voter picks another voter to be eliminated, along with himself.
>
> One of the remaining voters is chosen at random, etc.
>
> If the number of voters is odd, the last voter left decides the election.
>
> If the number of voters is even, a coin is flipped to determine which of the last two voters decides the
> election.

The above post reminded me of a group of ballot association methods I
posted to the list a few years ago.  The aim of the "methods" was to
find multiple winners using ranked ballots.

I'll simplify my explanation by describing such a method in which there
needs to be just 2 winners.  The description is very loose (e.g. it is
possible for the 2 winners to be the same candidate, etc...).  But I
just want to give an idea of what is entailed in the method rather than
the detail.

(1) From all the ballots cast in the election, find the two ballots that
produce the greatest Kemeny distance score (i.e. find the two ballots
that are the most different from each other).  These are the seed
ballots.

(2) For the first of the seed ballots, from the remaining (unassociated)
ballots, find a ballot that has the least Kemeny distance to the first
seed ballot.  Associate this ballot with the first seed ballot.

(3) For the second of the seed ballots, from the remaining
(unassociated) ballots, find a ballot that has the least Kemeny distance
to the second seed ballot.  Associate this ballot with the second seed
ballot.

(4) Repeat steps (2) and (3) until all of the ballots have been
associated with either the first or second seed ballots.

(5) Find the first winning candidate by using the ballots associated
with the first seed ballot.  Since Kemeny has already been used, may be
Kemeny could be used to do this.

(6) Find the second winning candidate by using the ballots associated
with the second seed ballot.  Again, Kemeny could be used to do this.

Thanks,
Gervase.

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