# [EM] the "meaning" of a vote (or lack thereof)

fsimmons at pcc.edu fsimmons at pcc.edu
Sun Aug 28 16:44:56 PDT 2011

```> An example, due to Samuel Merrill (of Brams, Fishburn, and
> Merrill fame), simply normalizes the
> scores on each range ballot the same way that we convert a
> garden variety normal random variable into
> a standard one: i.e. on each ballot subtract the mean (of scores
> on that ballot) and divide by the
> standard deviation (of scores on that ballot). Once each ballot
> has been normalized in this way, elect
> the candidate with the greatest total of normalized scores (over
> all ballots).

Let's call the above version of range voting Merrill's method.  As I mentioned before it is strategy free in
the zero information case.  For the partial or complete info case we can make a "double range" version
(as Warren calls it) using Merrill's method as method X, or more simply ...

(1) Have the voters fill out two range ballots.

(2) From the first set of range ballots (the potentially strategic ones) extract a candidate A using Merrill's
method.

(3) Also from the first set, find the Smith set, and the random ballot Smith probabilities.

(4) Use the second set of range ballots to decide between the random ballot smith lottery and candidate
A.

(5) Elect A if more voters prefer A over random ballot Smith than vice versa.

(6) Else elect the Smith candidate rated highest on a random ballot (from the first set).

This method has the advantage of sincerity on both ballot sets under zero info conditions, and sincerity
on the second set under any conditions.  Furthermore it always elects from the Smith set when not
electing the sincere range winner.  It is monotone, clone free, satisfies the Condorcet Criterion, etc.
Yes, it relies on chance to a small degree, but doesn't actually pick the winner by chance unless there
is no Condorcet winner, and even then only when the expected utility of random Smith is greater than
the utility of the (potentially strategic) range winner, which would be rare.

```