# [EM] Help naming a new method

Rob LeGrand honky1998 at yahoo.com
Sun Apr 3 12:30:54 PDT 2011

```Andy wrote:
> I have a new voting method and I think I need some help naming it.  Let
> me say, first of all, that I admit it may be too complicated for use by
> the general public.  It's a score aggregating method, like Score
> Voting.
>
> Each voter scores each candidate on a scale of 0-100.  Each candidate's
> votes are aggregated independently, with their societal score given by
> finding the largest number, x, such that x percent of the voters gave
> that candidate a grade of x or higher.
>
> So a candidate where 71% of the people gave a grade of 71 or higher
> (but the same can't be said of 71+epsilon) will get a final score of
> 71.
>
> It shares a strategy-resistance property with the median that any voter
> whose score was above the societal score, if he were allowed to change
> his vote, could do nothing to raise the societal score.  (Also, a voter
> whose score was below the societal score could do nothing to lower the
> societal score.)  This means that if you're only grading one candidate
> (e.g. choosing an approval rating for the sitting president), then
> there is a strong incentive for everyone to submit an honest vote.
>
> It can be generalized to "find the largest number, x, such that F(x)
> percent of the voters gave the candidate a grade of x or higher," for a
> non-decreasing function F.   F(x)=50, for example, is basically
> equivalent to "find the median".  But anything more complicated than
> F(x)=x is probably hopeless for explaining to people.  And the diagonal
> function F(x)=x has some nice properties.  For example, one voter can
> never unilaterally move the output by more than 100/N, where N is the
> number of voters.
>
> I thought of this method about three years ago.  I've been sitting on
> it since then, proving things for my doctoral thesis, which I finished
> last fall.  I did present this method at the Public Choice Society
> meeting about a year ago.  And I told Drs. Balinski and Laraki about it
> some time ago.  They make mention of it in their recently published
> book "Majority Judgment".
>
> I'd like to publish some things in a journal, but I'm thinking I may
> need a better name for the method.  So far, I've called it "the linear
> median" and "the diagonal median".  I've considered "the consensus
> median" or "the consensus score", but that may be misleading,
> associating it with consensus societies.

Hi Andy,

Please see chapter 3 of my dissertation:

http://www.cse.wustl.edu/~legrand/dissertation.pdf

It motivates and describes a rating system I call AAR DSV (Average-
Approval-Ratings Declared-Strategy Voting) that is equivalent to the
system applied to each candidate in your "linear median" method.  The
motivation is based on how rational voters would vote to try to pull the
outcome of a Average-based rating system as close to their ideal point as
possible.  The chapter also outlines a continuous range of rating systems
that includes both the standard AAR DSV and Median systems (including the
generalized ones you mention), interpolating between them using a two-
dimensional parameterization, and uses data from Metacritic.com to find
the "best" rating system in that range.  I prove that, if all voters are
only interested in moving the outcome as close to their ideal point as
possible, all of these systems are nonmanipulable.  This
nonmanipulability of course disappears when these systems are applied to
each candidate in a single-winner election.  My recent research has dealt
with generalizing these rating systems to higher-dimensional voting/
outcome spaces of various shapes; I haven't considered applying them to
electing a single winner from a discrete set of candidates in a while.

I presented a paper on AAR DSV called "Approval-rating systems that never
reward insincerity" at the 2nd International Workshop on Computational
Social Choice (COMSOC-2008):

http://www.csc.liv.ac.uk/~pwg/COMSOC-2008/

I'd like to see a copy of your doctoral thesis as well.

--
Rob LeGrand
rob at approvalvoting.org

```