# [EM] GSA

Forest W Simmons fsimmons at pcc.edu
Wed Jan 17 15:43:52 PST 2007

```This method is based on ranked ballots that (at least) allow truncation.

The candidate with the fewest truncations (i.e. the one that is ranked
on the greatest number of ballots) is designated c0.

Let c1 be the candidate (among those that cover c0) against which c0
scores the smallest opposition.

Let c2 be the candidate (among those that cover c1) against which c1
scores the smallest opposition.

Let c3 be the candidate (among those that cover c2) against which c2
scores the smallest opposition.

etc.

Keep going until an uncovered candidate cN is reached.

This candidate cN is the winner.

Clarification on the meaning of "cover" in this context:  X covers Y
iff  X  defeats every candidate that  Y  defeats INCLUDING the
(artificial) "truncation candidate."

To "defeat the truncation candidate" simply means to be ranked on more
than fifty percent of the ballots, just like defeating the "approval
cutoff candidate" would mean being approved on more than fifty percent
of the ballots.

In the current context this entails that if  c0 is ranked on more than
fifty percent of the ballots, then each of c1, c2, etc. must also be
ranked on more than fifty percent of the ballots.

For wont of a better name I call this method  Guided Steepest Ascent or
GSA for short, because each step in the path from c0 to cN is as
"steep" as possible under the guy wire constraints of the covering
requirement.  This covering requirement constrains the sideways motion
of the path to keep it from spiraling or cycling around the center, so
in a way it "guides" the upward path.

Obviously there are other versions of GSA that pick c0 by different
criteria.  For example, if the ballots have an approval cutoff, then we
can choose c0 by greatest approval.  Alternatively, c0 could be the
Equal Rankings or Range Ballot version of the Bucklin winner.

For a non-deterministic version, just choose c0 by random ballot.

More ideas?

Forest

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