Rob LeGrand honky98 at gmail.com
Mon Oct 31 19:45:17 PDT 2016

Michael Ossipoff wrote:
> But pulling the candidate toward a particular final score reminds me of
> MJ. What makes XA do that more effectively than MJ? What's the main
> advantage that distinguishes how XA does that from how MJ does it, or the
> results, from the voters' strategic standpoint?

My dissertation is available at


One chapter describes a parameterized class of nonmanipulable ratings-
summarizing systems that includes plain median on one hand and chiastic
median (which we called Average-Approval-Ratings DSV) on the other.  We used
movie-ratings data from metacritic.com to find the parameters whose
corresponding system gave results nearest to averaging the inputs
(essentially minimizing the Bayesian regret).  So you can use real data to
help you decide on median, XM or something in between.

Here's one intuitive reason to favor XM over median:  Say the ratings of one
candidate are all at the extremes: [0, 0, 0, 100, 100].  The median is 0,
making 3 of the voters maximally happy and completely alienating the others.
The XM outcome is 40, perhaps more fairly reflecting the voters' wishes.  In
fact, when the voters' ratings are all at the extremes, XM always agrees
with the average rating.

> Say someone gives Jill 100, and Hillary 70. Is that voter reliably voting
> for Jill to beat Hillary? I guess if Jill only ends up with 60, and you've
> drawn Hillary up to 70, then you've helped Hillary beat Jill.

That's correct.  My dissertation also pointed out that basing a
multicandidate, single-winner voting system on a nonmanipulable
ratings-summarizing system such as median or XM does not give you a
nonmanipulable voting system.  I gave a specific example of manipulating an
election that used AAR DSV for each candidate (equivalent to chiastic
approval) and recommended instead using plain approval or approval DSV
(which I analyzed in a separate chapter).

Rob LeGrand
rob at approvalvoting.org

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