Regular distributive efficiency and the distributive liberal social contract.

We consider abstract social systems of private property, made of n individuals endowed with non-paternalistic interdependent preferences, who interact through exchanges on competitive markets and Pareto-efficient lumpsum transfers. The transfers follow from a distributive liberal social contract defined as a redistribution of initial endowments such that the resulting market equilibrium allocation is, both, Pareto-efficient relative to individual interdependent preferences, and unanimously weakly preferred to the initial market equilibrium. We elicit the global structure of the set of Pareto-efficient allocations: its relative interior is a simply connected smooth manifold of dimension n-1, homeomorphic to the relative interior of the unit-simplex of ℝn . The property obtains under three suitable conditions on the partial preordering of Pareto associated with individual interdependent preferences, which essentially state that: the social utility functions built from weighted sums of individual interdependent utilities, by means of arbitrary positive weights, exhibit a property of differentiable non-satiation and some suitably defined property of inequality aversion; and individuals have diverging views on redistribution, in some suitable sense, at (inclusive) distributive optima. The set of market equilibrium allocations associated with the transfers of the inclusive distributive liberal social contracts consists of the allocations that are unanimously weakly preferred to the initial market equilibrium and that maximize, in the set of attainable allocations, weighted sums of individual interdependent utilities derived from suitable vectors of positive weights of ℝn ++. Its relative interior is a simply connected smooth manifold of dimension n-1 whenever the initial market equilibrium is not Pareto-efficient relative to individual interdependent preferences.Walrasian equilibrium; Pareto-efficiency; liberal social contract; individual social preferences; allocation; distribution.

Voting Power in the EU Council of Ministers and Fair Decision Making in Distributive Politics

We analyze and evaluate the different decision rules describing the Council of Ministers of the EU starting from 1958 up to date. All the existing studies use the Banzhaf index (for binary voting) or the Shapley-Shubik index (for distributive politics). We argue that the nucleolus can be considered an appropriate power measure in distributive situations and an alternative to the Shapley-Shubik index. We then calculate the nucleolus and compare the results of our calculations with the conventional measures. In the second part, we analyze the power of the European citizens as measured by the nucleolus under the egalitarian criterion proposed by Felsenthal and Machover (1998), and characterize the first best situation. Based on these results we propose a methodology for the design of the optimal (fair) decision rules. We perform the optimization exercise for the earlier stages of the EU within a restricted domain of voting rules, and conclude that Germany should receive more than the other three large countries under the optimal voting rule.

Voting over piece-wise linear tax methods

We analyze the problem of choosing the most appropriate method for apportioning taxes in a democracy. We consider a simple theoretical model of taxation and restrict our attention to piece-wise linear tax methods, which are almost ubiquitous in advanced democracies world- wide. We show that if we allow agents to vote for any method within a rich domain of piece-wise linear methods, then a majority voting equilibrium exists. Furthermore, if most voters have income below mean income then each method within the domain can be supported in equilibrium.voting, taxes, majority, single-crossing, Talmud

Sharing Variable Returns of Cooperation

A finite set of agents jointly undertake a project. Depending on the aggregate of individual agent characteristics the project runs losses or profits, which have to be shared. This paper adopts the mechanistic view and concentrates on devices that a contingent planner may use in order to share the net profits. The Moulin and Shenker (1994) representation theorem is used to show that additive mechanisms with the constant returns property relate 1 to 1 to rationing methods. Refinements are discussed dealing with monotonicity and equity properties that relate to the dispersion of shares. The second part introduces the notion of a consistent solution. Each rationing method induced by a consistent mechanism is consistent. If such mechanism is continuous as well, then the corresponding rationing method is parametric in the terminology of Young (1998) and Moulin (2000). Most prevalent mechanisms (average, serial, Shapley-Shubik) are consistent as member of the class of incremental mechanisms. Each interval consistent incremental mechanism is shown to be a composition of marginal mechanisms and the average mechanism. Immediately the average mechanism is the unique strongly consistent solution. Finally a characterization of mechanisms within the general class is discussed using super-additivity.

Axiomatic Cost and Surplis-Sharing

The equitable division of a joint cost (or a jointly produced output) among agents with different shares or types of output (or input) commodities, is a central theme of the theory of cooperative games with transferable utility. Ever since Shapley's seminal contribution in 1953, this question has generated some of the deepest axiomatic results of modern microeconomic theory.More recently, the simpler problem of rationing a single commodity according to a profile of claims (reflecting individual needs, or demands, or liabilities) has been another fertile ground for axiomatic analysis. This rationing model is often called the bankruptcy problem in the literature.This chapter reviews the normative literature on these two models, and emphasizes their deep structural link via the Additivity axiom for cost sharing: individual cost shares depend additively upon the cost function. Loosely speaking, an additive cost-sharing method can be written as the integral of a rationing method, and this representation defines a linear isomorphism between additive cost-sharing methods and rationing methods.The simple proportionality rule in rationing thus corresponds to average cost pricing and to the Aumann-Shapley pricing method (respectively for homogeneous or heterogeneous output commodities). The uniform rationing rule, equalizing individual shares subject to the claim being an upper bound, corresponds to serial cost sharing. And random priority rationing corresponds to the Shapley-Shubik method, applying the Shapley formula to the Stand Alone costs.Several open problems are included. The axiomatic discussion of non-additive methods to share joint costs appears to be a promising direction for future research.

From Quantum Metalanguage to the Logic of Qubits

The main aim of this thesis is to look for a logical deductive calculus (we will adopt sequent calculus, originally introduced in Gentzen, 1935), which could describe quantum information and its properties. More precisely, we intended to describe in logical terms the formation of the qubit (the unit of quantum information) which is a particular linear superposition of the two classical bits 0 and 1. To do so, we had to introduce the new connective "quantum superposition", in the logic of one qubit, Lq, as the classical conjunction cannot describe this quantum link.Comment: 138 pages, PhD thesis in Mathematic

Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?

In this work, we attempt to characterize the main theoretical difficulties to prove the existence of competitive equilibrium in infinite dimensional models. We shall show cases in which it is not possible to prove the existence of equilibrium and some others in which, however the existence of equilibrium can be proved, the equilibrium prices seem not to have natural economic interpretation. Nevertheless in pure exchange economies, most of these difficulties may be avoided by mild restrictions on the model. In productive economies new specifics problem appear, for instance non convexity of the production sets or non boundedness of the feasible allocation sets. To prove the existence and the efficiency of the equilibrium in productive economies we need some strong hypothesis about the technological possibilities of each firm.

Fairness Behind a Veil of Ignorance: A Welfare Analysis for Automated Decision Making

We draw attention to an important, yet largely overlooked aspect of evaluating fairness for automated decision making systems---namely risk and welfare considerations. Our proposed family of measures corresponds to the long-established formulations of cardinal social welfare in economics, and is justified by the Rawlsian conception of fairness behind a veil of ignorance. The convex formulation of our welfare-based measures of fairness allows us to integrate them as a constraint into any convex loss minimization pipeline. Our empirical analysis reveals interesting trade-offs between our proposal and (a) prediction accuracy, (b) group discrimination, and (c) Dwork et al.'s notion of individual fairness. Furthermore and perhaps most importantly, our work provides both heuristic justification and empirical evidence suggesting that a lower-bound on our measures often leads to bounded inequality in algorithmic outcomes; hence presenting the first computationally feasible mechanism for bounding individual-level inequality.Comment: Conference: Thirty-second Conference on Neural Information Processing Systems (NIPS 2018