Social Choice: Information, Power, Collective Rationality, Indeterminacy and Chaos

We will consider social welfare functions (SWFs) for N individuals(voters) and M alternatives. Those are functions which associate to every rofiles of individual order preference-relations on the alternatives, a social preference relation. We will discuss, power, aggregation of information, collective rationality, indeterminacy and chaos in the context of social choice. For this we will consider several properties of social welfare functions and the connections between them. The first property is well known (Condorcet and Arrow).

Rationality of Purity and Danger

Abstract: Mary Douglas, who has died recently, developed her Group / Grid theory based upon her field reseach in West Africa and a deep study of the Old Testament. The gist of her argument: Rationality is not universal, it is culture-dependent. And Culture, understood here as a way-of-life or a sort of Habitus, is a mix of values, behaviour and patterns of organisaion. Culture is shaped by 2 forces, Group and Grid. I intend to elaborate an these, and show how fruitful the theory has been in various empirical fields.

EFFICIENT, STRATEGY-PROOF AND ALMOST BUDGET-BALANCED ASSIGNMENT

Abstract Call a Vickrey-Clarke-Groves (VCG) mechanism to assign p identical objects among n agents, feasible if cash transfers yield no deficit. The efficiency loss of such a mechanism is the worst (largest) ratio of the budget surplus to the efficient surplus, over all profiles of non negative valuations. The optimal (smallest) efficiency loss

PURE SECRET CORRELATION AND FINITE AUTOMATA (JOINT WORK WITH OLIVIER GOSSNER)

AbstractIn this paper we study the conditions in which a team guarantees a successful coordination against a similar opponent. We consider a dynamical situation of a 3-players game in which each player is iden- tied by his ability to implement strategies. If the team payo is the opposite to its opponent one, the optimal coordination is character- ized by the value in correlated strategies of the zero-sum game. The ability of each player i is related to the number of states of thesmall-est machine which implements a strategy of player i, i.e.: mi.

EVOLUTION AND REPEATED GAMES (JOINT WORK WITH D. FUNDERBERG)

Abstract:We characterize the set of payoffs that are evolutionarily stable in two-player, symmetric repeated games when there is a small but positive probability that a player will make a mistake and a small but positive discount rate.

UNCOUPLED AUTOMATA AND PURE NASH EQUILIBRIA

Abstract: We study the problem of reaching a pure Nash equilibrium in multi-person games that are repeatedly played, under the assumption of uncoupledness: every player knows only his own payoff function.We consider strategies that can be implemented by finite-state automata, and characterize the minimal number of states needed in order to guarantee that a pure Nash equilibrium is reached in every game where such an equilibrium exists.

Marvels and Misconceptions of Insurance Production

AbstractHow does insurance work? What is the relative advantage of the insurance firm in bearing risks? In the literature of business, mathematics and economics these questions are answered by ‘risk pooling'and the law of large numbers (LLN). The popular argument is: by selling many contracts LLN helps predicting fairly accurately the loss. Because the risk of insolvency is real and troubling, enhanced confidence in its underwriting results affords the competing larger firm an advantage that ought to be reflected in lower prices.

AGREEING TO DISAGREE: THE NON-PROBABILISTIC CASE

Abstract: A non-probabilistic generalization of Aumann's (1976) agreement theorem is proved. Early attempts at such a theorem were based on a version of the sure-thing principle which assumes an intrapersonal-interstate comparison of knowledge. But such comparisons are impossible in partition structures.

Optimal Use of Communication Resources with Partial Monitoring

Abstract:Communication enables players to exchange information and thus bridge the optimality gap resulting from asymmetric information.

QUALITY OF LIFE: A SYSTEMIC DEFINITION, PARTIAL-ORDER MEASUREMENT, AND DATA ANALYTIC STRUCTURES

Abstract. The concept of happiness, not unlike happiness itself, is evasive. Renaming it human well-being or human quality of life (QOL) has been of little help. Yet, it is a key concept in evaluating the actual utility of actions taken in personal life as well as in national life.A top-down systemic theory is presented, yielding a structured generic set of QOL components that, under simple assumptions, are argued to be exclusive and exhaustive.

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