Classify simple games into sixteen "types" in terms of the four conventional axioms: monotonicity, properness, strongness, and nonweakness. Further classify them into sixty-four classes in terms of finiteness (existence of a finite carrier) and computability. For each such class, we either show...

It was shown earlier that the class of algorithmically computable simple games (i) includes the class of games that have finite carriers and (ii) is included in the class of games that have finite winning coalitions. This paper characterizes computable games, strengthens the earlier result that...

This paper investigates algorithmic computability of simple games (voting games). It shows that (i) games with a finite carrier are computable, (ii) computable games have both finite winning coalitions and cofinite losing coalitions, and (iii) computable games violate any conceivable notion of...

We study a restricted version of Shannon's General Purpose Analog Computer in which we only allow the machine to solve linear differential equations. This corresponds to only allowing local feedback in the machine's variables. We show that if this computer is allowed to sense inequalities in a...

Shannon's General Purpose Analog Computer (GPAC) is an elegant model of analog computation in continuous time. In this paper, we consider whether the set G of GPAC-computable functions is closed under iteration, that is, whether for any function f(x) 2 G there is a function F(x; t) 2 G such that...

For infinite societies, Fishburn (1970), Kirman and Sondermann (1972), and Armstrong (1980) gave a nonconstructive proof of the existence of a social welfare function satisfying Arrowfs conditions (Unanimity, Independence, and Nondictatorship). This paper improves on their results by (i) giving...