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math.stackexchange.com

Q&A for people studying math at any level and professionals in related fields

arxiv.org

A system of non-tradable credits that flow between individuals like karma, hence proposed under that name, is a mechanism for repeated resource allocation that comes with attractive efficiency and fairness properties, in theory. In this study, we test karma in an online experiment in which human subjects repeatedly compete for a resource with time-varying and stochastic individual preferences or urgency to acquire the resource. We confirm that karma has significant and sustained welfare benefits even in a population with no prior training. We identify mechanism usage in contexts with sporadic high urgency, more so than with frequent moderate urgency, and implemented as a simple (binary) karma bidding scheme as particularly effective for welfare improvements: relatively larger aggregate efficiency gains are realized that are (almost) Pareto superior. These findings provide guidance for further testing and for future implementation plans of such mechanisms in the real world.

projecteuclid.org

I review recent work in the statistics literature on instrumental variables methods from an econometrics perspective. I discuss some of the older, economic, applications including supply and demand models and relate them to the recent applications in settings of randomized experiments with noncompliance. I discuss the assumptions underlying instrumental variables methods and in what settings these may be plausible. By providing context to the current applications, a better understanding of the applicability of these methods may arise.

mathworld.wolfram.com

A connected graph G is distance-regular if for any vertices x and y of G and any integers i,j=0, 1, ...d (where d is the graph diameter), the number of vertices at distance i from x and distance j from y depends only on i, j, and the graph distance between x and y, independently of the choice of x and y. In particular, a distance-regular graph is a graph for which there exist integers b_i,c_i,i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly c_i...

ams.org

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math.mit.edu

the official website for the department of mathematics at mit

math.uchicago.edu

the department of mathematics at the university of chicago