A Decision Maker (DM) must choose at discrete moments from a finite set of actions that result in random rewards. The environment is complex in that she finds it impossible to describe the states and is thus prevented from application of standard Bayesian methods. This paper presents an...

This paper contributes to the program of numerical characterisation and classification of simple games outlined in the classical monograph of von Neumann and Morgenstern (1944). One of the most fundamental questions of this program is what makes a simple game a weighted majority game. The...

In voting theory, bribery is a form of manipulative behavior in which an external actor (the briber) offers to pay the voters to change their votes in order to get her preferred candidate elected. We investigate a model of bribery where the price of each vote depends on the amount of change that...

The goal of this paper is to examine the incentives to vote insincerely, other than those created by rounding, faced by voters in the systems of proportional representation (PR). We rigorously investigate two models of voter behaviour. The first model assumes that a voter is primarily interested...

We find conditions on the order on subsets of a finite set which are necessary and sufficient for the relative ranking of any two subsets in this order to be determined by their extreme elements relative to an abstract convex geometry. It turns out that this question is closely related to the...