[EM] Advanced Math question

Forest Simmons fsimmons at pcc.edu
Tue Jan 7 16:43:57 PST 2003

Josh (as I understood him) was asking which mathematical disciplines would
be most useful for someone like him to study in order to better understand
the technical aspects of election methods.

My list omitted the most important of all: Game Theory, in particular,
N-Person Game Theory (if not differential game theory).

[Differential Game theory would be ideal for the continuous (joy stick)
version of the CRAB race method.]


On Thu, 2 Jan 2003, Dave Ketchum wrote:

> 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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