The Combinatorial World (of Auctions) According to GARP

Revealed preference techniques are used to test whether a data set is compatible with rational behaviour. They are also incorporated as constraints in mechanism design to encourage truthful behaviour in applications such as combinatorial auctions. In the auction setting, we present an efficient combinatorial algorithm to find a virtual valuation function with the optimal (additive) rationality guarantee. Moreover, we show that there exists such a valuation function that both is individually rational and is minimum (that is, it is component-wise dominated by any other individually rational, virtual valuation function that approximately fits the data). Similarly, given upper bound constraints on the valuation function, we show how to fit the maximum virtual valuation function with the optimal additive rationality guarantee. In practice, revealed preference bidding constraints are very demanding. We explain how approximate rationality can be used to create relaxed revealed preference constraints in an auction. We then show how combinatorial methods can be used to implement these relaxed constraints. Worst/best-case welfare guarantees that result from the use of such mechanisms can be quantified via the minimum/maximum virtual valuation function

Gerir a diversidade: contributos da aprendizagem cooperativa para a construção de salas de aula inclusivas

The action-research we have held at the primary education, in a school placed near the town of Tomar, in 2009-2010, under the master's degree in Special Education, was the starting point for writing this article. The research had as main objective to promote the successful learning of a heterogeneous group of students, where a child considered with longstanding special educational needs is included – diagnosis of galactosaemia and cognitive impairment. Starting from the educational context of a particular classroom of 2nd and 3rd grades, where we were working as special education teacher, we had created an inclusive learning environment for each student in the class. Through effective collaboration between fellow teachers, we generated changes in methodologies, breaking with some traditional practices in the classroom, when regular teachers and special education are in the same learning space. By a systematic implementation of cooperative learning strategies among students, and applying qualitative data gathering techniques of research, before and after the intervention – interview, naturalistic observation, sociometry and documental research –, we have increased the quality and quantity of learning and promoted another way of ‘looking to’ the difference

GSP with General Independent Click-Through-Rates

The popular generalized second price (GSP) auction for sponsored search is built upon a separable model of click-through-rates that decomposes the likelihood of a click into the product of a "slot effect" and an "advertiser effect" --- if the first slot is twice as good as the second for some bidder, then it is twice as good for everyone. Though appealing in its simplicity, this model is quite suspect in practice. A wide variety of factors including externalities and budgets have been studied that can and do cause it to be violated. In this paper we adopt a view of GSP as an iterated second price auction (see, e.g., Milgrom 2010) and study how the most basic violation of separability --- position dependent, arbitrary public click-through-rates that do not decompose --- affects results from the foundational analysis of GSP (Varian 2007, Edelman et al. 2007). For the two-slot setting we prove that for arbitrary click-through-rates, for arbitrary bidder values, an efficient pure-strategy equilibrium always exists; however, without separability there always exist values such that the VCG outcome and payments cannot be realized by any bids, in equilibrium or otherwise. The separability assumption is therefore necessary in the two-slot case to match the payments of VCG but not for efficiency. We moreover show that without separability, generic existence of efficient equilibria is sensitive to the choice of tie-breaking rule, and when there are more than two slots, no (bid-independent) tie-breaking rule yields the positive result. In light of this we suggest alternative mechanisms that trade the simplicity of GSP for better equilibrium properties when there are three or more slots

Can the evolution of music be analyzed in a quantitative manner?

We propose a methodology to study music development by applying multivariate statistics on composers characteristics. Seven representative composers were considered in terms of eight main musical features. Grades were assigned to each characteristic and their correlations were analyzed. A bootstrap method was applied to simulate hundreds of artificial composers influenced by the seven representatives chosen. Afterwards we quantify non-numeric relations like dialectics, opposition and innovation. Composers differences on style and technique were represented as geometrical distances in the feature space, making it possible to quantify, for example, how much Bach and Stockhausen differ from other composers or how much Beethoven influenced Brahms. In addition, we compared the results with a prior investigation on philosophy. Opposition, strong on philosophy, was not remarkable on music. Supporting an observation already considered by music theorists, strong influences were identified between composers by the quantification of dialectics, implying inheritance and suggesting a stronger master-disciple evolution when compared to the philosophy analysis.Comment: 8 pages, 6 figures, added references for sections 1 and 4.C, better mathematical description on section 2. New values and interpretation, now considering a bootstrap metho

The effect of discrete vs. continuous-valued ratings on reputation and ranking systems

When users rate objects, a sophisticated algorithm that takes into account ability or reputation may produce a fairer or more accurate aggregation of ratings than the straightforward arithmetic average. Recently a number of authors have proposed different co-determination algorithms where estimates of user and object reputation are refined iteratively together, permitting accurate measures of both to be derived directly from the rating data. However, simulations demonstrating these methods' efficacy assumed a continuum of rating values, consistent with typical physical modelling practice, whereas in most actual rating systems only a limited range of discrete values (such as a 5-star system) is employed. We perform a comparative test of several co-determination algorithms with different scales of discrete ratings and show that this seemingly minor modification in fact has a significant impact on algorithms' performance. Paradoxically, where rating resolution is low, increased noise in users' ratings may even improve the overall performance of the system.Comment: 6 pages, 2 figure

The Influence of Strategic Patenting on Companies’ Patent Portfolios

This paper analyses whether strategic motives for patenting influence the characteristics of companies’ patent portfolios. We use the number of citations and oppositions to represent these characteristics. The investigation is based on survey and patent data from German companies. We find clear evidence that the companies’ patenting strategies explain the characteristics of their patent portfolios. First, companies using patents to protect their technological knowledge base receive a higher number of citations for their patents. Second, the motive of offensive – but not of defensive – blocking is related to a higher incidence of oppositions, whereas companies using patents as bartering chips in collaborations receive fewer oppositions to their patents

More light and less heat Mirowski on economics and the energy metaphor

I initially approached More Heat than Light with some apprehension. This is not because I suspected that I would disagree with its main thesis but because I feared that I would find the book anticlimactic. Over the past few years, Phil Mirowski has served us a number of delightful appetizers’-so many in fact that I suspected I might tire of the taste before the main entrée appeared. These concerns were wholly unfounded. The main entrée has finally arrived and is of such depth and complexity that it makes the appetizers, well, just appetizers. Mirowski’s central thesis is that neoclassical economics-initially developed during the 1870s and currently the dominant paradigm in economic theory-amounts to little more than a &dquo;brazen daylight robbery&dquo; (p. 4)2 of nineteenth-century energy physics. Motivated by the desire to achieve the status and prestige of the physical sciences, early neoclassical economists created their &dquo;revolution&dquo; by simply substituting &dquo;utility&dquo; for &dquo;energy&dquo; in the physics of their day. In a limited respect, this project was successful-the mathematical formalism of energy physics did (and does) contribute to the scientific respectability of the neoclassical research program-but this status was achieved at substantial cost. Mirowski argues that there were (and are) deep problems associated with the economic appropriation of the energy metaphor; physical systems have properties that make the mathematics appropriate, but these properties are not shared by economic systems. For example, the physical requirement that potential energy and kinetic energy sum to a constant translates into the economic requirement that utility and income sum to a constant. This is a problem because utility and income are measured in entirely different units. Mirowski argues that such difficulties were exacerbated by the scientific naivete of the early neoclassical economists who were trained in science and engineering-they had been exposed to the basic ideas of energy physics-but their knowledge was relatively rudimentary (p. 250). The result was energy physics appropriated in a &dquo;shoddy and slipshod manner&dquo; (p. 108). Mirowski provides a detailed discussion of how this misappropriation of the energy metaphor has surreptitiously influenced the development of modern economic thought. He reconstructs and explains certain generally accepted facts of theoretical life in economics (such as the problems of neoclassical production theory) and exposes some of the fundamental weaknesses of neoclassical theory (such as its inability to explain preference changes). Mirowski also argues that the dominance of the energy metaphor from nineteenth-century physics has prevented economists from taking advantage of more recent developments in physical theory, such as quantum mechanics and the theory of relativity. The result, according to Mirowski, is a tale reminiscent of Dorian Gray .... Neoclassicals, by imbibing some mystical elixir of modern mathematical techniques, have maintained the figure of vibrant youth, while hidden away somewhere in the attic is the real portrait, the original metaphor of a conserved preference field in an independently constituted commodity space, growing progressively desiccated and decrepit. (p. 374) My overall evaluation of Mirowski’s thesis is quite positive. I believe that he is entirely correct about the role of the energy metaphor in early neoclassical economics (probably reaching an apogee in Irving Fisher), and he is also correct that the metaphor has been lurking ever since in the background of neoclassical economics. The energy metaphor and its mathematics have been actively influential in the development of modem neoclassical theory, although I would probably weaken its impact from Mirowski’s story by saying &dquo;influenced&dquo; whereas Mirowski would say &dquo;dominated.&dquo; Where I mainly differ from Mirowski is on the implications of his thesis. For Mirowski, uncovering this hidden influence amounts to a scathing critique of modern neoclassical economics (and given the neoclassical dominance of the profession, this means most of modem economics). For him, the metaphor and its mathematics have been both dominant and pernicious. I disagree. While I am convinced that Mirowski has uncovered something important that can be used to further our understanding of the development of modem economic theory, I am not convinced that his thesis entails the kind of critical bite that he would like it to have. Given this overall evaluation of More Heat than Light, I will divide my comments into two sections. The first-more light-lends additional support to Mirowski’s general historical thesis by using it to illuminate two areas of modem neoclassical economics that Mirowski does not emphasize. The second-less heat-offers some arguments against Mirowski’s critical interpretation of his general thesis