This work provides a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists and examples that show that rates of convergence can strongly depend on the metric chosen.Expand

My friend’s dilemma was a practical question that mathematics could answer, both elegantly and constructively. He and his housemates were moving to a house with rooms of various sizes and features,… Expand

Author’s note: This paper was originally written for my Minor Thesis requirement of the Ph.D. program at Harvard University. The object of this requirement is to learn about a body of work that is… Expand

The Shapley value of tree games is considered and a biological interpretation is suggested, a counterpart to Shapley’s original theorem on the larger class of cooperative games.Expand

This work provides two proofs of the following conjecture: a non-constructive proof introducing the notion of a pebble set of a polytope, and a constructive proof using a path-following argument.Expand

Examples of situations where sets model preferences and develop extensions of classical theorems about convex sets that can be used in the analysis of voting in "agreeable" societies are given.Expand

It is shown how the procedure eliminates envy by compensating envious players, establishes envy-freeness with minimal resources, and demonstrates its application to a wide class of fair-division problems.Expand

This paper aims to explore how the deeply human themes that drive us to do mathematics can be channeled to build a more beautiful and just world in which all can truly flourish.Expand