The Relation between Monotonicity and Strategy-Proofness

The Muller-Satterthwaite Theorem (Muller and Satterthwaite, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller and Satterthwaite (1977) as well as private goods economies. For private goods economies we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller-Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new "Muller-Satterthwaite domains" (e.g.,Proposition 3).Muller-Satterthwaite Theorem; restricted domains; rich domains; single-peaked domains; strategy-proofness; unilateral/Maskin monotonicity

The relation between monotonicity and strategy-proofness

The Muller-Satterthwaite Theorem (J Econ Theory 14:412-418, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller-Satterthwaite (J Econ Theory 14:412-418, 1977) as well as private goods economies. For private goods economies, we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check preference domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked preference domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller-Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new "Muller-Satterthwaite preference domains” (e.g., Proposition 3

Maximal Domains for Strategy-proof or Maskin Monotonic Choice Rules

Domains of individual preferences for which the well-known impossibility Theorems of Gibbard-Satterthwaite and Muller-Satterthwaite do not hold are studied. First, we introduce necessary and sufficient conditions for a domain to admit non-dictatorial, Pareto efficient and either strategy-proof or Maskin monotonic social choice rules. Next, to comprehend the limitations the two Theorems imply for social choice rules, we search for the largest domains that are possible. Put differently, we look for the minimal restrictions that have to be imposed on the unrestricted domain to recover possibility results. It turns out that, for such domains, the conditions of inseparable pair and of inseparable set yield the only maximal domains on which there exist non-dictatorial, Pareto efficient and strategy-proof social choice rules. Next, we characterize the maximal domains which allow for Maskin monotonic, non-dictatorial and Pareto-optimal social choice rules.Strategy-proofness; Maskin monotonicity; Restricted domains; Maximal domains

Essays in applied economic theory

This thesis consists of three essays, all of which use the tools of economic theory to analyze specific situations in which multiple strategic agents interact with each other. The first chapter studies the strategic transmission of information between an informed expert and a decision maker when the latter has access to imperfect private information relevant to the decision. The main insight of the paper is that the access to private information of the decision maker hampers the incentives of the expert to communicate. Surprisingly, in a wide range of environments, the decision maker's information cannot make up for the loss of communication and the welfare of both agents diminishes. The second chapter presents a model of electoral competition between an in- cumbent and a challenger in which the voters receive more information about the quality of the incumbent. If the incumbent can manipulate the information received by the voters through costly effort, the model predicts an incumbency advantage, even though the two candidates are drawn from identical symmetric distributions, and the voters have rational expectations. It is also shown that a supermajority re-election rule improves welfare, mainly through discouraging low-quality politicians from manipulating the information. Finally the third chapter uses a mechanism design approach to characterize the class of social choice functions which cannot be profitably manipulated, when the individuals have symmetric single-peaked preferences. Our result allows for the design of social choice functions to deal with feasibility constraints

O Problema da Alocação de Tarefas sob o Aspecto da Escolha Social: uma Análise Arroviana de Sistemas Multirrobô.

A pesquisa em sistemas multirrobô é uma área fértil, que tem recebido muita atenção nas últimas décadas. Com os avanços de hardware e software, como o desenvolvimento do Robot Operating System - ROS, a aplicação real desses sistemas tem se tornado cada vez mais factível. Porém, novos desafios emergem, principalmente, a coordenação dos robôs e a alocação de tarefas para o correto cumprimento de uma missão. Apesar das muitas propostas apresentadas na literatura, a alocação de tarefas ainda não é um assunto esgotado, tanto em aplicações quanto em teorias. Assim, este trabalho propõe uma visão do problema de alocação de tarefas em sistemas multirrobô baseada na Teoria da Escolha Social, mais especificamente, na estrutura proposta por Kenneth J. Arrow em seu famoso Teorema da Impossibilidade. As condições impostas por Arrow visam criar um mecanismo agregador de preferências padrão por meio da análise axiomática. Essa análise é transportada para o domínio multirrobô. Classes de problemas com robôs mono-tarefa e algumas arquiteturas são analisadas desse ponto de vista. Além disso, é discutida a comparação de utilidades cardinais entre robôs e as vantagens da utilização de preferências ordinais. Também são propostos e analisados algoritmos para a agregação de preferências ordinais

The Relation between Monotonicity and Strategy-Proofness

The Muller-Satterthwaite Theorem (J Econ Theory 14:412-418, 1977) establishes the equivalence between Maskin monotonicity and strategy-proofness, two cornerstone conditions for the decentralization of social choice rules. We consider a general model that covers public goods economies as in Muller-Satterthwaite (J Econ Theory 14:412-418, 1977) as well as private goods economies. For private goods economies, we use a weaker condition than Maskin monotonicity that we call unilateral monotonicity. We introduce two easy-to-check preference domain conditions which separately guarantee that (i) unilateral/Maskin monotonicity implies strategy-proofness (Theorem 1) and (ii) strategy-proofness implies unilateral/Maskin monotonicity (Theorem 2). We introduce and discuss various classical single-peaked preference domains and show which of the domain conditions they satisfy (see Propositions 1 and 2 and an overview in Table 1). As a by-product of our analysis, we obtain some extensions of the Muller-Satterthwaite Theorem as summarized in Theorem 3. We also discuss some new "Muller-Satterthwaite preference domains" (e.g., Proposition 3)