[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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