Elements of algebraic geometry and the positive theory of partially commutative groups

The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H * F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.

Foundations for contest success functions

In the literature the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions. In the first we analyze the implications of contestants' incomplete information concerning the "type" of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones. Keywords: Endogenous Contests, Contest Success Function. JEL Classification: C72 (Noncooperative Games), D72 (Economic Models of Political Processes: Rent-Seeking, Elections), D74 (Conflict; Conflict Resolution; Alliances).

Música i matemàtiques

Treball de recerca realitzat per una alumna d’ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l’any 2008. Existeix una relació entre la música i les matemàtiques i per demostrar-ho s’ha relacionat la música amb diferents matèries que avalen aquesta afirmació. Mitjançant una entrevista es situa el panorama musical en relació a les noves tecnologies en l’actualitat. Des d’una perspectiva teòrica, s’estudia la concepció de la música; seguidament s’aprofundeix en la figura de Pitàgores com a descobridor de les proporcions matemàtiques de l’escala musical, amb una introducció al llenguatge i la notació musical. Com a part pràctica, s’analitza una de les teories de Pitàgores sobre l’univers i la música per demostrar la certesa dels seus raonaments en base als coneixements actuals. D’una banda, es treballa el camp de les ones sonores, la formació de les diferents escales matemàticament i els models matemàtics emprats per diversos compositors a l’hora de realitzar les seves peces musicals. D’altra banda, es presenten els efectes que té la música sobre l’oïda, seguit d’un estudi exhaustiu de l’asimetria cerebral i les seves conseqüències en l’aprenentatge i l’execució musical. En relació a la cultura, es mostra la relació matemàtica de les diferents escales, modes i harmonies arreu del món. Aplicant aquests coneixements s’ha realitzat la composició d’una peça musical.

Bargaining one-dimensional policies and the efficiency of super majority rules

We consider negotiations selecting one-dimensional policies. Individuals have single-peaked preferences, and they are impatient. Decisions arise from a bargaining game with random proposers and (super) majority approval, ranging from the simple majority up to unanimity. The existence and uniqueness of stationary subgame perfect equilibrium is established, and its explicit characterization provided. We supply an explicit formula to determine the unique alternative that prevails, as impatience vanishes, for each majority. As an application, we examine the efficiency of majority rules. For symmetric distributions of peaks unanimity is the unanimously preferred majority rule. For asymmetric populations rules maximizing social surplus are characterized.

Linking conflict to inequality and polarization

In this paper we study a behavioral model of conflict that provides a basis for choosing certain indices of dispersion as indicators for conflict. We show that the (equilibrium) level of conflict can be expressed as an (approximate) linear function of the Gini coefficient, the Herfindahl-Hirschman fractionalization index, and a specific measure of polarization due to Esteban and Ray

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states.

The Causal effect of education on aggregate income

Empirical studies assume that the macro Mincer return on schooling is con- stant across countries. Using a large sample of countries this paper shows that countries with a better quality of education have on average relatively higher macro Mincer coeficients. As rich countries have on average better educational quality, differences in human capital between countries are larger than has been typically assumed in the development accounting literature. Consequently, factor accumulation explains a considerably larger share of income differences across countries than what is usually found.

El canvi climàtic a les Terres de l'Ebre

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit científic del Jovent l'any 2009. En aquest treball s’estudia sobretot l’augment de les temperatures a les Terres de l’Ebre. Amb les temperatures facilitades per l’Observatori de l’Ebre s’han pogut realitzar prediccions de temperatures mitjanes, màximes i mínimes, per a saber les temperatures d’aquí uns 100 anys. Un cop fetes les prediccions, s’han consultat les condicions climàtiques de les plantes més característiques de la zona amb els científics de l’Institut de recerca i tecnologia agroalimentària i així poder fer una predicció i veure fins quan podríem gaudir de les nostres plantes, o fins quan la seva producció seria fins com la d’avui en dia. A més a més, un altre tema que afecta sobretot aquestes terres és la pujada del nivell del mar, ja que tenim una costa molt vulnerable a aquesta situació. Per aquest fet hi trobareu mapes de la zona amb inundacions per cada metre que pugés el nivell del mar.

A Sensitivity analysis of poverty definitions

We conduct a sensitivity analysis of several estimators related to household income, to explore how some details of the definitions of the variables concerned influence the values of the common estimates, such as the mean, median and (poverty) rates. The purpose of this study is to highlight that some of the operational definitions entail an element of arbitrariness which leaves an undesirable stamp on the inferences made. The analyses use both a cross-sectional and a longitudinal (panel) component of the EU-SILC database.

On Strategy-proofness and symmetric single-peakedness

We characterize the class of strategy-proof social choice functions on the domain of symmetric single-peaked preferences. This class is strictly larger than the set of generalized median voter schemes (the class of strategy-proof and tops-only social choice functions on the domain of single-peaked preferences characterized by Moulin (1980)) since, under the domain of symmetric single-peaked preferences, generalized median voter schemes can be disturbed by discontinuity points and remain strategy-proof on the smaller domain. Our result identifies the specific nature of these discontinuities which allow to design non-onto social choice functions to deal with feasibility constraints.

The Disadvantage of winning an election

This paper analyzes the problem that an incumbent faces during the legislature when deciding how to react to popular initiatives or policy proposals coming from different sources. We argue that this potential source of electoral disadvantage that the incumbent obtains after being elected can jeopardize the reelection possibilities of the incumbent. We analyze the decision of the incumbent when facing reelection and we characterize the conditions under which the advantages that the incumbent obtains can overcome the disadvantages. Finally, we use the results of this analysis to discuss some implications of the use of mechanisms of direct democracy like referenda and popular assemblies on electoral competition.

Work values, endogenous sentiments and redistribution

We examine the interactions between individual behavior, sentiments and the social contract in a model of rational voting over redistribution. Agents have moral "work values". Individuals' self-esteem and social consideration of others are endogenously determined comparing behaviors to moral standards. Attitudes toward redistribution depend on self-interest and social preferences. We characterize the politico-economic equilibria in which sentiments, labor supply and redistribution are determined simultaneously. The equilibria feature different degrees of "social cohesion" and redistribution depending on pre-tax income inequality. In clustered equilibria the poor are held partly responsible for their low income since they work less than the moral standard and hence redistribution is low. The paper proposes a novel explanation for the emergence of different sentiments and social contracts across countries. The predictions appear broadly in line with well-documented differences between the United States and Europe.

Preference intensities and risk aversion in school choice: a laboratory experiment

We experimentally investigate in the laboratory two prominent mechanisms that are employed in school choice programs to assign students to public schools. We study how individual behavior is influenced by preference intensities and risk aversion. Our main results show that (a) the Gale-Shapley mechanism is more robust to changes in cardinal preferences than the Boston mechanism independently of whether individuals can submit a complete or only a restricted ranking of the schools and (b) subjects with a higher degree of risk aversion are more likely to play "safer" strategies under the Gale-Shapley but not under the Boston mechanism. Both results have important implications for the efficiency and the stability of the mechanisms.

Longer-term impacts of mentoring, educational services, and incentives to learn: evidence from a randomized trial in the United States

This paper is the first to use a randomized trial in the US to analyze the short- and long-term educational and employment impacts of an afterschool program that offered disadvantaged high-school youth: mentoring, educational services, and financial rewards with the objective to improve high-school graduation and postsecondary schooling enrollment. The short-term hefty beneficial average impacts quickly faded away. Heterogeneity matters. While encouraging results are found for younger youth, and when the program is implemented in relatively small communities of 9th graders; detrimental longlived outcomes are found for males, and when case managers are partially compensated by incentive payments and students receive more regular reminders of incentives.

Strategic mass killings

Since World War II there have been about fifty episodes of large-scale mass killings of civilians and massive forced displacements. They were usually meticulously planned and independent of military goals. We provide a model where conflict onset, conflict intensity and the decision to commit mass killings are all endogenous, with two main goals: (1) to identify the key variables and situations that make mass killings more likely to occur; and (2) to distinguish conditions under which mass killings and military conflict intensity reinforce each other from situations where they are substitute modes of strategic violence. We predict that mass killings are most likely in societies with large natural resources, significant proportionality constraints for rent sharing, low productivity and low state capacity. Further, massacres are more likely in a civil than in an interstate war, as in the latter group sizes matter less for future rents. In non polarized societies there are asymmetric equilibria with only the larger group wanting to engage in massacres. In such settings the smaller group compensates for this by fighting harder in the first place. In this case we can talk of mass killings and fighting efforts to be substitutes. In contrast, in polarized societies either both or none of the groups can be ready to do mass killings in case of victory. Under the "shadow of mass killings" groups fight harder. Hence, in this case massacres and fighting are complements. We also present novel empirical results on the role of natural resources in mass killings and on what kinds of ethnic groups are most likely to be victimized in massacres and forced resettlements, using group level panel data.