On the rule of K names

The rule of k names can be described as follows: given a set of candidates for office, a committee chooses k members from this set by voting, and makes a list with their names. Then a single individual from outside the committee selects one of the listed names for the office. Different variants of this method have been used since the distant past and are still used today in many countries and for different types of choices. After documenting this widespread use by means of actual examples, we provide a theoretical analysis. We concentrate on the plausible outcomes induced by the rule of k names when the agents involved act strategically. Our analysis shows how the parameter k, the screening rule and the nature of candidacies act as a means to balance the power of the committee with that of the chooser.employment by lotto, probabilistic mechanism, two-sided matching, stability

How to choose a non-controversial list with k names

Barberà and Coelho (2006) documented six screening rules associated with the rule of k names that are used by different institutions around the world. Here, we study whether these screening rules satisfy stability. A set is said to be a weak Condorcet set la Gehrlein (1985) if no candidate in this set can be defeated by any candidate from outside the set on the basis of simple majority rule. We say that a screening rule is stable if it always selects a weak Condorcet set whenever such set exists. We show that all of the six procedures which are used in reality do violate stability if the voters act not strategically. We then show that there are screening rules which satisfy stability. Finally, we provide two results that can explain the widespread use of unstable screening rules.NULL

On Marilda Sotomayor's extraordinary contribution to matching theory

Financial support the research grants ECO2012-31962, 2014SGR-142, and ICREA AcademiaWe report on Marilda Sotomayor's extraordinay contribution to Matching Theory on the occasion of her 70th anniversar

Understanding, evaluating and selecting voting rules through games and axioms

Consultable des del TDXTítol obtingut de la portada digitalitzadaLa tesis de doctorado "Understanding, Evaluating and Selecting Voting Rules Through Games and Axioms" de Danilo Santa Cruz Coelho está compuesta de cuatro capítulos. La introducción es el primero y describe brevemente el contenido de los capítulos siguientes. En el Capítulo 2, en el contexto de un modelo de votación probabilística propuesto por Rae (1969), el autor investiga las consecuencias de elegir reglas de votación según el criterio de maximin. En el modelo, una regla de votación es el número mínimo de votantes favorables necesarios a una propuesta para que esta sea aceptada. El autor demuestra que la regla de votación que satisface el criterio de maximin puede ser distinta de la mayoría simple que es la que maximiza la suma de las utilidades esperadas de los votantes. El autor proporciona una caracterización de las reglas de votación que satisfacen el criterio de maximin. En el Capítulo 3, dos juegos que pueden ser inducidos por la regla de los k nombres son propuestos y analizados. El autor proporciona para cada uno de los juegos una caracterización del conjunto de los resultados del equilibrio fuerte de Nash. Estas caracterizaciones permiten al autor discutir las preferencias de los jugadores sobre diferentes variantes de la regla de los k nombres. Una parte importante de la regla de los k nombres es el procedimiento utilizado para seleccionar los k nombres que son propuestos al individuo que toma la decisión final. Seis reglas diferentes de selección que son utilizadas en la realidad por diferentes cuerpos decisorios alrededor del mundo son documentadas. En el Capítulo 4, el autor estudia si estas reglas satisfacen la propiedad de estabilidad. Una regla cumple esta propiedad si esta siempre selecciona un conjunto Weak Condorcet y cuando exista un conjunto con esta característica. El autor demuestra que todas estas seis reglas violan esta propiedad si los votantes no actúan estratégicamente. El autor entonces propone dos reglas estables. Finalmente, él proporciona dos justificaciones para el uso extensivo de las reglas inestables.The dissertation entitled "Understanding, Evaluating and Selecting Voting Rules Through Games and Axioms" by Danilo Santa Cruz Coelho is composed of four chapters. The introduction is the first one and describes briefly the contents of the following chapters. In Chapter 2, in the context of a probabilistic voting model proposed by Rae (1969), the author investigates the consequences of choosing among threshold voting rules according to the maximin criterion. A threshold voting rule is given by the minimum number of votes needed to approve a proposal of change from the status quo. The author shows that the voting rules that satisfy the maximin criterion are different from the simple majority rule which is the one that maximizes the sum of voter's expected utilities. He provides a characterization of the threshold voting rules that satisfy this criterion as a function of the distribution of voters' probabilities to favour change from the status quo. In Chapter 3, two different game theoretical models that can be induced by the rule of k names are proposed and analysed. A characterization of the set of strong Nash Equilibrium outcomes of each of the games is provided. These characterizations enable the author to discuss the preferences of the players over different variants of the rule of k names. An important part of the rule of k names is the procedure used to screen out the k names to be proposed to the individual who takes the final decision. Six different screening rules which are used in reality by different decision bodies around the world are documented. In Chapter 4, he studies whether these screening rules satisfy stability. A screening rule is stable if it always selects a weak Condorcet set whenever such set exists. He shows that all of the six screening rules violate stability if the voters act not strategically. He then proposes two screening rules which satisfy stability. Finally, he provides two possible justifications for the widespread use of unstable screening rules

Squeezing equivalence of quantum harmonic oscillators under different frequency jumps

In their studies on the squeezing produced by a sequence of sudden frequency changes of a quantum harmonic oscillator, Janszky and Adam [Phys. Rev. A {\bf 46}, 6091 (1992)] found the following equivalence: a harmonic oscillator, under a sequence of two sudden frequency jumps, from $\omega_0$ to $\omega_1$ and back to $\omega_0$ (after a time interval $\tau$), exhibits, for $\tau=k\pi/\omega_1$ ($k\in\mathbb{N}$), exactly the same squeezing parameter as the harmonic oscillator whose frequency would remain constant [specifically, $r(t>\tau)=0$]. In the present paper, we show an extended version of this equivalence, demonstrating how to set up different sequences of two sudden frequency jumps, so that, despite having different intermediate frequencies during a time interval $\tau$, they result in a same value $r(t>\tau)\neq0$ (and, consequently, in the same physical quantities that depend on it) after the jumps cease. Applied to a particular situation, our formulas recover the equivalence obtained by Janszky and Adam.Comment: 10 pages, 6 figure

Exact solution of a time-dependent quantum harmonic oscillator with two frequency jumps via the Lewis-Riesenfeld dynamical invariant method

Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency $\omega_0$, that undergoes a sudden jump to a frequency $\omega_1$ and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis-Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when $\omega_1<\omega_0$. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.Comment: 11 pages, 12 figure

Branding cultural: um estudo exploratório sobre o universo que conecta a cultura com marcas

O branding cultural existe como teoria há quase duas décadas e, ainda assim, possuí pouco estudo aprofundado, provavelmente devido à sua complexidade de entendimento, análise e aplicação, que faz com que o conceito não seja tão atrativo para o mundo moderno. Porém, ainda que seja tão complexo, seu potencial contemporâneo é inestimável e incalculável. Este trabalho busca entender o universo do branding cultural, explorando, de maneira introdutória, a origem do conceito e o seu funcionamento como uma ferramenta de gestão. Além disso, este estudo prevê a análise do conceito perante a realidade da cultura e mercado brasileiros. Inicialmente, a pesquisa contextualiza o tema abordado e fundamenta o mesmo diante dos universos da cultura e do branding. A discussão principal discorre em torno do conceito apresentado em 2004, por Douglas B. Holt, em seu livro “Como as marcas se tornam ícones”, ao mesmo tempo em que procura expandir o entendimento acerca do tema, além de encontrar suas limitações. A pesquisa também traz uma análise contextualizada de duas marcas brasileiras que surgem em momentos históricos semelhantes e cujas trajetórias se aproximam do conceito através de estratégias culturais e da inovação cultural consequente. Como resultado, o estudo mostra que há a possibilidade de se utilizar o branding cultural, mesmo em um contexto menos globalizado e de baixo investimento, como é a realidade de grande parte do mercado nacional