A note on selecting maximals in finite spaces

Given a choice problem, the maximization rule may select many alternatives. In such cases, it is common practice to interpret that the final choice will end up being made by some random procedure, assigning to any maximal alternative the same probability of being chosen. However, there may be reasons based on the same original preferences for which it is suitable to select certain maximal alternatives over others. This paper introduces two choice criteria induced by the original preferences such that maximizing with respect to each of them may give a finer selection of alternatives than maximizing with respect to the original preferences. Those criteria are built by means of several preference relations induced by the original preferences, namely, two (weak) dominance relations, two indirect preference relations and the dominance relations defined with the help of those indirect preferences. It is remarkable that as the original preferences approach being complete and transitive, those criteria become both simpler and closer to such preferences. In particular, they coincide with the original preferences when these are complete and transitive, in which case they provide the same solution as those preference

A non-proposition-wise variant of majority voting for aggregating judgments

Majority voting is commonly used in aggregating judgments. The literature to date on judgment aggregation (JA) has focused primarily on proposition-wise majority voting (PMV). Given a set of issues on which a group is trying to make collective judgments, PMV aggregates individual judgments issue by issue, and satisfies a salient property of JA rules—independence. This paper introduces a variant of majority voting called holistic majority voting (HMV). This new variant also meets the condition of independence. However, instead of aggregating judgments issue by issue, it aggregates individual judgments en bloc. A salient and straightforward feature of HMV is that it guarantees the logical consistency of the propositions expressing collective judgments, provided that the individual points of view are consistent. This feature contrasts with the known inability of PMV to guarantee the consistency of the collective outcome. Analogously, while PMV may present a set of judgments that have been rejected by everyone in the group as collectively accepted, the collective judgments returned by HMV have been accepted by a majority of individuals in the group and, therefore, rejected by a minority of them at most. In addition, HMV satisfies a large set of appealing properties, as PMV also does. However, HMV may not return any complete proposition expressing the judgments of the group on all the issues at stake, even in cases where PMV does. Moreover, demanding completeness from HMV leads to impossibility results similar to the known impossibilities on PMV and on proposition-wise JA rules in genera

Complete intersections in simplicial toric varieties

Given a set $\mathcal A = \{a_1,\ldots,a_n\} \subset \mathbb{N}^m$ of nonzero vectors defining a simplicial toric ideal $I_{\mathcal A} \subset k[x_1,...,x_n]$, where $k$ is an arbitrary field, we provide an algorithm for checking whether $I_{\mathcal A}$ is a complete intersection. This algorithm does not require the explicit computation of a minimal set of generators of $I_{\mathcal A}$. The algorithm is based on the application of some new results concerning toric ideals to the simplicial case. For homogenous simplicial toric ideals, we provide a simpler version of this algorithm. Moreover, when $k$ is an algebraically closed field, we list all ideal-theoretic complete intersection simplicial projective toric varieties that are either smooth or have one singular point.Comment: 28 pages, 2 tables. To appear in Journal of Symbolic Computatio

Building and Using Models as Examples

Sometimes, theoreticians explicitly state that they consider their models as examples. When this is not the case, it is fairly common for theoreticians to attribute to their models the characteristics and objectives of illustrative examples. However, this way of understanding models has not received enough attention in the methodological literature focused on economics. Given that didactic examples and their properties are extremely familiar in practice, considering theoretical models as examples can offer a useful perspective on models and their properties. On the basis of both explanatory and exemplifying role played by the deductive arguments by which results are proved, the paper emphasizes also the importance of understanding in theoretical work, the analogical and tentative character of the application of models, the central role played by the above mentioned arguments in such application, the didactic function of theory, and the transmision of plausibility from those arguments to the results obtained.models; examples; explanatory arguments; theoretical understanding; analogical application

A pooling approach to judgment aggregation

The literature has focused on a particular way of aggregating judgments: Given a set of yes or no questions or issues, the individuals’ judgments are then aggregated separately, issue by issue. Applied in this way, the majority method does not guarantee the logical consistency of the set of judgments obtained. This fact has been the focus of critiques of the majority method and similar procedures. This paper focuses on another way of aggregating judgments. The main difference is that aggregation is made en bloc on all the issues at stake. The main consequence is that the majority method applied in this way does always guarantee the logical consistency of the collective judgments. Since it satisfies a large set of attractive properties, it should provide the basis for more positive assessment if applied using the proposed pooling approach than if used separately. The paper extends the analysis to the pooling supermajority and plurality rules, with similar result

Analysis of vocabulary in CLIL textbooks for 5th year of Primary Education.

En el presente estudio se analiza el vocabulario al que los alumnos están expuestos en dos libros de texto utilizados en AICLE (Aprendizaje Integrado de Contenidos y Lenguas Extranjeras), pertenecientes a las asignaturas de “Natural Science” y “Social Science” para 5º curso de educación primaria. El vocabulario de estos libros de texto se analiza desde una perspectiva de frecuencia, teniendo en cuenta también el tamaño de vocabulario necesario para comprender el texto en ambos libros en conjunto y en cada uno de ellos por separado. Para el estudio del vocabulario presente en ambos libros de texto se elaboró un corpus lingüístico y posteriormente se procedió a su análisis. Los resultados obtenidos en nuestro estudio parecen indicar que el libro de texto perteneciente a la asignatura de “Social Science” es más exigente en lo que respecta a vocabulario que la asignatura de “Natural Science”.In the present study, the vocabulary to which students are exposed in two different textbooks used in CLIL (Content and Language Integrated Learning) subjects will be analysed. The textbooks belong to ‘Natural Science’ and ‘Social Science’ subjects for 5th year of Primary Education. The analysis of the vocabulary is carried out from a frequency perspective, bearing also in mind the vocabulary size necessary to understand properly both textbooks and each one of them separately. In order to analyse the vocabulary, a linguistic corpus containing both textbooks was compiled. The results obtained in our analysis seem to indicate that the ‘Social Science’ textbook is more demanding concerning vocabulary than the ‘Natural Science’ textbook.peerReviewe

Algunas cuestiones jurídicas en torno al islote del Perejil

Análisis de la situación creada por la invasión del islote del Perejil por parte de las tropas marroquíes desde el punto de vista jurídico

¿Es Palestina un estado? Reflexiones a la luz del derecho internacional y de la práctica europea sobre los acontecimientos recientes en torno al reconocimiento de un Estado palestino

The Palestinian Authority is committed not to take unilateral action outside the framework of negotiations with Israel. However, in recent years, Palestinian leaders have launched a major diplomatic and political race in order to obtain international recognition for Palestine as a state. This may jeopardize, in the short and medium term, the two states project.L’Autorité palestinienne s’est engagée à ne pas prendre des mesures unilatérales en dehors du cadre des négociations avec Israël. Cependant, au cours des dernières années, les dirigeants palestiniens sont entrés dans une grande course diplomatique et politique afin d’obtenir une certaine reconnaissance internationale pour la Palestine en tant qu’Etat. Cela pourrait mettre en danger, à court et moyen terme, le projet des deux états