Consider say environmentalism or the earlier and more correct versions of supply-side economics, both innovations with small starts. But extremism makes us more innovative in bad ways too, and I would not wish to inject more American nutty extremism into Nordic politics.

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Perhaps the resulting innovativeness is worthwhile only in a small number of fairly large countries which can introduce new ideas using increasing returns to scale? By elevating persuasion over trading in politics at some margins, at least , we encourage centrist and majoritarian groups.

## Mathematics of Social Choice - Voting, Compensation, and Division

We encourage groups which think they can persuade others to accept their points of view. This may not work well in every society but it does seem to work well in many. It may require some sense of persuadibility, rather than all voting being based on ethnic politics, as it would have been in say a democratic Singapore in the early years of that country. In any case the relevant question is what kinds of preference formation, and which kinds of groups, we should allow voting mechanisms to encourage.

Addendum : On Twitter Glenn Weyl cites this paper , with Posner, which discusses some of these issues more. Alex Tabarrok Email Alex Follow atabarrok. Tyler Cowen Email Tyler Follow tylercowen. Webmaster Report an issue. Email Address. Toggle navigation. Recent work involves developing a general framework for understanding functor calculus that includes the calculus of homotopy functors and orthogonal calculus and provides a means for developing new calculus theories as well.

I have also worked with undergraduates on problems in knot theory, especially questions about intrinsically linked and knotted graphs.

### by Christoph Borgers

I work in the overlap of operator algebra theory and representation theory of Lie groups. These are subjects with roots in the mathematical foundations of quantum mechanics and in Fourier analysis. I am also interested in spectral theory, and analysis on finite and infinite graphs. My main research interests lie in the field of commutative algebra, with connections to algebraic geometry and homological algebra. Early in my career, my research was focused on the use of homological methods in commutative algebra.

More specifically, I studied Gorenstein dimensions of modules over commutative local rings. In recent years, my research has shifted directions to include problems concerning pairs of commuting nilpotent matrices. My interest in this project originates from my commutative algebra background and my algebraic geometry interests, while the nature of the study has invited the use of additional tools from algebraic combinatorics and representation theory.

My current research interest is in the general area of number theory with a particular interest in the theory of modular forms, quasi modular forms, and mock modular forms.

I am also interested in the various products of Eisenstein series and identities between Eisenstein series. I study algebraic topology, specifically unstable homotopy theory.

I started out by studying the unstable Adams spectral sequence, in a problem related to the Sullivan Conjecture on maps from projective spaces. I returned to the unstable Adams spectral sequence in two later papers on the infinite orthogonal group SO. Most of my recent work has to do with connections between the Goodwillie calculus and the Whitehead Conjecture proved by Kuhn and Priddy , along with the analogous connections between the orthogonal calculus and an unproved version of the Whitehead Conjecture for connective complex K-theory.

I study the historical development of math, astronomy and related subjects, mostly in Sanskrit, Arabic and Latin texts from before the twentieth century. Research travel takes me most often to India, where there are tens of thousands of manuscripts of little-known early scientific works that I use in piecing together this history. I have been teaching mathematics at Union College for over three decades. Prior to I published two books and 27 articles on various aspects of category theory.

From I served as Dean of Studies at the college, overseeing the curriculum and the academic lives of the entire student body. After resigning as Dean, I returned to the mathematics classroom with a renewed vigor and enthusiasm. Since I have regularly taught the First-Year Preceptorial, a required seminar on critical reading and writing. At the same time my attention has turned from mathematical research to writing. I have had a dozen publications mostly fiction appear in various literary journals.

My graduate training was in the field of mathematical logic, and I spent the first fifteen years of my career doing infinitary combinatorics. Most of my work involved ultrafilters on omega, ideals on uncountable cardinals, and partition theory including a bit of work with finite Ramsey theory. Here, I was primarily studying simple games.

For the past decade I have returned to set theory with somewhat of a focus on coordinated inference as captured by so-called hat problems. I work in number theory and function fields. While number theory is primarily concerned with integers, the area of function fields is primarily concerned with polynomials.

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One can add, subtract, and multiply polynomials just as one can with integers and this analogy can be extended in many directions. By exploiting this analogy we can better understand both worlds. Of particular interest to me are multizeta values.

## Mathematics of Social Choice: Voting, Compensation, and Division - Christoph Borgers - Google книги

It is not true that there are mathematical theories that are useful and others not. Rather, some have been used, and is a challenge to use those so far not been used.. Today mathematics is used in many areas of human endeavor, including music, art, criminology, cooking, etc. Then we give a short list of some applications of mathematics. The question is not where to apply mathematics. But rather, where there are no mathematics to create them.