# [EM] Request for criticism

Rob LeGrand honky1998 at yahoo.com
Tue Mar 6 19:35:00 PST 2001

```Howdy all,

I've developed a program that simulates voters and elections to compare
methods, and I'd like some feedback on my approach.  For now I'm only
trying to measure how well a method reflects the true preferences of
sincere voters, so the results will not reflect the manipulability of
the methods.  (At this point I'm only interested in comparing methods
that have been shown to meet desirable criteria.)  The numbers followed
by (*) in the description below are values I picked; let me know if you
think different values would be better.

Since I'm assuming sincere votes, Ratings is the method by which the
others are judged.  Each of the 10000(*) "voters" rates the 25(*)
candidates individually with a number from 0 to 5(*), generated
randomly.  These are added up across the voters to determine the
candidate that "should" win the election.  I picked 5 as my estimate of
how fine people's preferences really are.

Each voter's candidate ratings are used to construct his sincere ranked
ballot.  For example, if a voter rated A 4, B 2, C 0, D 5 and E 2, his
ballot would be D>A>B=E>C.  The ranked ballots are compiled into a
pairwise matrix, P, which each method can use to determine a winner.
Pij is the number of voters who ranked candidate i strictly higher than
candidate j.  P is used to calculate the pairwise matrices M, W and T:

Mij = Pij - Pji   if Pij > Pji, and
0           otherwise;
Wij = Pij         if Pij > Pji, and
0           otherwise;
Tij = Pij         if Pij >= Pji, and
0           otherwise.

Each of three procedures (beatpath, Tideman, Condorcet) are applied to
each of the four matrices, giving the following 11 methods (with what I
believe to be their equivalences to the right):

beatpath(M)    Blake Cretney's Path Voting
beatpath(W)    Mike Ossipoff's Cloneproof SSD
beatpath(T)    Schulze's Method
beatpath(P)    Norm Petry's interpretation of Schulze
Tideman(M)     Tideman's Ranked Pairs
Tideman(W)     Steve Eppley's Majoritarian Tideman
Tideman(T)
Condorcet(M)   Blake's Minmax
Condorcet(W)   "Plain Condorcet"
Condorcet(T)
Condorcet(P)

(Note that Tideman(P) is left out; it's equivalent to Tideman(T).)

I also use P to find the Copeland and Borda winners. Overall I simulate
9999* elections and record how many times the 14 methods match each
other's results in a 14x14 array. The Ratings column reports how "well"
each method did at giving the public what it wants.

I'd like to have my approach criticized before I post any results.  Thanks!

=====
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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