Here is the link to my review of Saari and Valognes. It covers models of voting outcomes. thumpasery-reading-project1

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What immortal hand or eye / could frame thy fearful symmetry?

Posted by: **thumpasery** | December 6, 2008
## “Geometry, Voting, and Paradoxes”

Here is the link to my review of Saari and Valognes. It covers models of voting outcomes. thumpasery-reading-project1

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I like your choice of what to include in your project: you give the background and lead-up to the main theorem of the paper so it can be understood in context. I think you did a really good job of organising your thoughts in this project.

The question you are looking at leaves open lots of other interesting mathematical directions. Theorem 1 of the paper is very specific and we might muse as to its generalisations to lots of other situations (more items to rank, more types allowed, other than centrally distributed, etc.). You claim, along with the author, that geometry is a good approach to such questions, and Theorem 1 is a sort of showcase of the types of results that might be obtained. With your Math 152 powers, maybe you can use other polygons to get other theorems like this one!

I take issue a little bit with your last sentence, though. If Wine, Milk or Beer were actually elements of the group, you could multiply them together. What is Wine*Wine? Beer? I think what you mean is they are labellings and their permutations are a group S_3 (not Z_3), which relates to the triangle (as we’ve studied in Math 152).

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Prof. Kateon January 13, 2009at 11:05 am