The axioms underlying Arrow's impossibility theorem are very restrictive in terms of what can be used when aggregating preferences. Social preferences may not depend on the menu nor on preferences over alternatives outside the menu. But context matters. So we weaken these restrictions to allow for context to be included. The context as we define describes which alternatives in the menu and which preferences over alternatives outside the menu matter. We obtain unique representations. These are discussed in examples involving markets, bargaining and intertemporal well-being of an individual. Proofs are constructive and insightful.
The von Neumann-Morgenstern axioms are uncontroversial desiderata for individual decision making. We say that a bargaining solution is rational, if it can be interpreted as the most preferred alternative under these axioms. Yet, we find that neither the Nash nor the Kalai-Smorodinsky bargaining solution is rational in this sense. We formalize two consequences of rationality, namely that one can neither be strictly better off nor strictly worse off from randomizing over different actions. These two axioms, together with other standard axioms, characterize the relative utilitarian bargaining solution. We then implement this bargaining solution in sub-game perfect equilibrium.
Work in Progress
Consumer Search in Service Markets.
Axiomatizing Preferences over Varying Time Horizons