[EM] "Best voting systems" 3-part math paper by Warren D. Smith

[Warren Smith]

It unfortunately keeps getting longer and more subvided.
As of now there are 3 parts to the paper.  I'm going to submit it to a
journal pretty soon.

Part I:  http://rangevoting.org/BestVrange.html
Develops Bayesian Regret theory, finds BRs as closed formulas for a
lot of voting systems, proves range voting
superior to all rank-order voting systems (measured by BR) in
3-candidate elections under the RNEM (random normal elections model).
Also finds the best ratings-based voting system for honest voters in
3-candidate elections (which is
better than range voting, albeit only if over 91% or so of the voters
are honest). Unfortunately about 50 pages long, but concisely
summarized in table and plot.

Part II: http://rangevoting.org/Best4.html
Covers elections with more than 3 candidates.
Shows range voting superior to all rank-order voting systems (measured
by BR) in N-candidate elections under the RNEM (random normal
elections model) for all numbers N with 3<=N<=9, for all
honest+strategic voter mixtures.   Again there is a table and plot
which go a long way toward communicating the results even if you fail
to read the rest of the paper.

Part III: http://rangevoting.org/BestVot2.html
Goes beyond the RNEM to consider other underlying
probabilistic/political/utilities models, in particular
"D-dimensional politics models," and based on either binary or
continuum "issues."
In the particular models discussed:
 *  we can prove range voting is "optimal" in the binary model with
honest voters,
while various other voting methods are suboptimal
 *  in the continuum model we can prove Condorcet methods are
asymptotically optimal
and superior to range voting.
However (warning) all these results seem to depend sensitively on the
precise definition of the underlying model; in contrast the results in
parts I and II had been "robust."

No previous paper was able to identify "best voting systems," using a
valid measure (BR), in any reasonable underlying model.  So in that
sense, these papers are a breakthrough.

Please email any comments / questions / etc to warren.wds AT gmail.com.

-- 
Warren D. Smith
http://RangeVoting.org  <-- add your endorsement (by clicking
"endorse" as 1st step)
and
math.temple.edu/~wds/homepage/works.html