The Muller-Satterthwaite theorem states that social choice functions that satisfy unanimity and monotonicity are also dictatorial. Unlike Arrow’s theorem, it does not assume that the function produces a transitive social ordering. Wilson showed that a voting process under Arrow’s conditions can be interpreted as a strong and proper simple game—as defined by von Neumann and Morgenstern. We show ...

We introduce “embedding dimensions” of a family of generators of a finite von Neumann algebra when the von Neumann algebra can be faithfully embedded into the ultrapower of the hyperfinite II1 factor. These embedding dimensions are von Neumann algebra invariants, i.e., do not depend on the choices of the generators. We also find values of these invariants for some specific von Neumann algebras.

We prove that a finite von Neumann algebra A is semisimple if the algebra of affiliated operators U of A is semisimple. When A is not semisimple, we give the upper and lower bounds for the global dimensions of A and U . This last result requires the use of the Continuum Hypothesis.

The next generation of air traffic control will require automation in order to meet safety, reliability, flexibility, and robustness demands in an environment of steadily increasing air traffic density. Optimization, however, is an inadequate paradigm for the design of a cooperative distributed air traffic control system. The problem stems from a fundamental limitation of von Neumann-Morgenster...

Motivated by the need to reason about u t i l ities, and inspired by the success of bayesian networks in representing and reasoning about probabilities, we introduce the notion of ut i l i ty distr ibutions, in which uti l i t ies have the structure of probabilit ies. We furthermore define the notion of a bi-d istr ibut ion, a structure that includes in a symmetric fashion both a probabil i ty ...

Traditional accounts of decision-making under uncertainty have taken the Von Neumann and Morgenstern approach of Expected Utility Theory that considers how decisions under uncertainty should be made. This prescriptive model states that, when faced with a choice, a rational decision maker will pick the prospect that offers the highest expected utility. But as has been demonstrated by Kahnemann a...

In this paper I analyze a 3-person voting game in which players sequentially choose amendments to a bill and then vote sophisticatedly on the resulting agenda. This game differs from previous work on endogenous agenda formation in that the number of items on the agenda is not fixed. Players keep making proposals until they can do no better. I find that there is a nonempty set of minimax equilib...

Expected Utility (EU) theory is a technique developed by Von Neumann and Morgenstern (1944) to deal with situations of quantifiable risk. It requires preferences to exhibit two additional axioms of continuity and independence, which are somewhat controversial. Assume that states of nature can be indexed by an s = 1, ..., S, each with a probability of occurring of p1, ..., pS , which as probabil...

For choice with deterministic consequences, the standard rationality hypothesis is ordinality — i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann– Morgenstern utility function. For choice under risk, this implies a key independence axiom; u...

Zeno’s paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement is concerned. Parkinson’s Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements and using arguments similar to Zeno’...