[EM] Advanced Math question

Dave Ketchum davek at clarityconnect.com
Wed Jan 1 23:35:25 PST 2003


On Tue, 31 Dec 2002 17:46:56 -0800 (PST) Forest Simmons wrote:

> Linear algebra, graph theory, probability, statistics, measure theory,
> metric spaces, combinatorics, piecewise linear topology, linear
> programming, multivariate calculus, mathematical logic and set theory,
> theory of algorithms, etc. are all good for the tool box.
> 
> Most of the minimization can be done without multivariate calculus, but
> that's where most folks get a good feel for minimization with constraints
> and for geometry with more than two dimensions.
> 
> The linear algebra "stuff" may go past what you learned in the first
> semester of linear algebra.
> 
> For example, moving a candidate from "Candidate Space" into "Voter Space"
> is most naturally done with the help of the "Singular Value Decomposition"
> of the matrix whose rows represent the voters and whose columns represent
> the candidates.
> 
> Was the SVD part of your linear algebra course?
> 
> [By the way, the lambdas that represent the eigenvalues in the SVD are the
> same lambdas that represent Lagrange multipliers in multivariate
> maximization with constraints; the similarity of notation is no accident.]
> 
> I like this election methods field because it seems to be at the cross
> roads of all the fields of mathematics that I enjoy.  Even intuitions from
> differential equations and digital filtering have helped me from time to
> time.
> 
> We need people with all different kinds of backgrounds to help us find new
> ways of looking at these election methods.
> 
> Forest


I see three divisions:
      To analyze methods anything, such as described above, goes.
      The actual method had better stay with simple operations the average 
voter can understand.
      For near ties, such as Condorcet cycles, a bit more complexity is 
tolerable - but the more understandable to voters with minimum requirement 
for mathematical understanding the better.

-- 
  davek at clarityconnect.com    http://www.clarityconnect.com/webpages3/davek
   Dave Ketchum    108 Halstead Ave, Owego, NY  13827-1708    607-687-5026
              Do to no one what you would not want done to you.
                    If you want peace, work for justice.

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