[email protected] wrote:
If we abandon the Euclidean metric, then we also abandon Voronoi Polygons; the corresponding idea for more general metrics is that of a Dirichlet region.
That's strange. The Wikipedia article on Voronoi diagrams mention diagrams based on L_1 and Mahalanobis distance. Is the article being incorrect when it uses the term "Voronoi diagram" for these?
It would be amusing to see Yee diagrams based on L_1 and L_infinity metrics
Warren made at least one, where he argued that since Range kept its L_2 form when people voted according to L_1 distance, but Condorcet did not, Range was superior to Condorcet. See the bottom of http://rangevoting.org/BlackSingle.html .
To my knowledge, L_inf is just L_1 rotated.
Think of the Huntington Hill method of apportionment that is used in this country after every census. How many voters understand its details? Less than one in a thousand, but that doesn't matter; they understand the proportionality goal of apportionment, and they are willing to let the experts take care of the details.
In that case, I think letting the experts decide produced the wrong outcome, and that Webster should have been used instead. But so it goes.
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