A New Quota Approach to Electoral Disproportionality

The authors acknowledge and appreciate the comments of two anonymous referees.In this paper electoral disproportionality is split into two types: (1) Forced or unavoidable, due to the very nature of the apportionment problem; and (2) non-forced. While disproportionality indexes proposed in the literature do not distinguish between such components, we design an index, called “quota index”, just measuring avoidable disproportionality. Unlike the previous indexes, the new one can be zero in real situations. Furthermore, this index presents an interesting interpretation concerning transfers of seats. Properties of the quota index and relationships with some usual disproportionality indexes are analyzed. Finally, an empirical approach is undertaken for different countries and elections.We are grateful for the financial support of the Spanish Ministerio de Economía y Competitividad (project ECO2016-77900-P)

Positional voting rules generated by aggregation functions and the role of duplication

Producción CientíficaIn this paper, we consider a typical voting situation where a group of agents show their preferences over a set of alternatives. Under our approach, such preferences are codied into individual positional values which can be aggregated in several ways through particular functions, yielding positional voting rules and providing a social result in each case. We show that scoring rules belong to such class of positional voting rules. But if we focus our interest on OWA operators as aggregation functions, other well-known voting systems naturally appear. In particular, we determine those ones verifying duplication (i.e., clone irrelevance) and present a proposal of an overall social result provided by them.Ministerio de Economía, Industria y Competitividad (ECO2012-32178)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA066U13

Two characterizations of the dense rank

Producción CientíficaIn this paper, we have considered the dense rank for assigning positions to alternatives in weak orders. If we arrange the alternatives in tiers (i.e., indifference classes), the dense rank assigns position 1 to all the alternatives in the top tier, 2 to all the alternatives in the second tier, and so on. We have proposed a formal framework to analyze the dense rank when compared to other well-known position operators, such as the standard, modified and fractional ranks. As the main results, we have provided two different axiomatic characterizations which determine the dense rank by considering position invariance conditions along horizontal extensions (duplication), as well as through vertical reductions and movements (truncation, and upward or downward independency).PROYECTO PID2021-122506NB-I00. Toma de decisiones basadas en valoraciones cualitativas y ordinales. FONDOS FEDER, MICINN. MINISTERIO DE CIENCIA E INNOVACIÓN, AGENCIA ESTATAL DE INVESTIGACIÓN, UNION EUROPE

Desarrollo de una app para la generación preventiva de alertas sanitarias

Desde hace unos años, parece que la informática ha ido invadiendo numerosos campos de la ciencia, se ha ido consolidando como parte fundamental en el desarrollo y la tecnología y ya se puede ver como motor de la economía, las comunicaciones, el comercio e incluso, la medicina. Este trabajo se centra en la aplicación de la informática en el área de las enfermedades infecciosas, intentando contribuir con una nueva idea que revolucione el mundo de las mismas dentro de la medicina, en una situación en la que el término “Smart City” cada vez es más importante. Se trata de un sistema formado por una app para Android y una web controlada y gestionada por un médico, la cual permite identificar posibles usuarios contagiados, localizar focos de contagios y gestionar de una manera óptima, el estado y los avisos de cada usuario. En esta memoria se describe el trabajo realizado, la arquitectura del sistema, las tecnologías utilizadas, el diseño de la aplicación móvil y de la página web, su implementación, las pruebas realizadas, las conclusiones a las que se ha llegado y las posibles mejoras que se podrían incluir en el proyecto en un futuro

Generalizaciones y extensiones de la Regla de Votación de Borda

Se estudia la regla de votación de Borda clásica y variantes más sofisticadas que consideran preferencias graduales o lingüísticas en las opiniones de los agentes. Además se traza la evolución del método, prestando especial atención al análisis del precursor ilustrado José Isidoro Morales. El tratamiento histórico penetra el estudio teórico y hace patente la bondad de la regla de Borda frente a sistemas de votación al uso incuestionablemente peores, por ser más rígidos e incompletos. Como el método la Borda se implementa en dos fases (correspondientes a contadores individuales y colectivos en su formulación) se analiza su idoneidad atendiendo primeramente a la representatividad respecto de las preferencias individuales y a su relación con la transitividad de los agentes. Por otra parte, ya desde un punto de vista agregado, se realiza un análisis de tipo Condorcet. Finalmente se contrastan empíricamente los resultados anteriores, corroborándose y matizándose los aspectos teóricos tratadosDepartamento de Economía Aplicad

Electoral Mathematics and Asymmetrical Treatment to Political Parties: The Mexican Case

The Mexican Chamber of Deputies is composed of 500 representatives: 300 of them elected by relative majority and another 200 ones elected through proportional representation in five electoral clusters (constituencies) with 40 representatives each. In this mixed-member electoral system, the seats distribution of proportional representation is not independent of the election by relative majority, as it attempts to correct representation imbalances produced in single-member districts. This two-fold structure has been maintained in the successive electoral reforms carried out along the last three decades (eight from 1986 to 2014). In all of them, the election process of 200 seats becomes complex: Formulas in the Law are difficult to understand and to be interpreted. This paper analyzes the Mexican electoral system after the electoral reform of 2014, which was applied for the first time in 2015. The research focuses on contradictions and issues of applicability, in particular situations where seats allocation is affected by ambiguity in the law and where asymmetrical treatment of political parties arises. Due to these facts, a proposal of electoral reform will be presented. It is intended to be simpler, clearer, and more enduring than the current system. Furthermore, this model is more suitable for producing electoral outcomes free of contradictions and paradoxes. This approach would allow a fair treatment of political parties and as a result an improved opportunity to exercise democracy

Mathematical political districting taking care of minority groups

AbstractPolitical districting (PD) is a wide studied topic in the literature since the 60s. It typically requires a multi-criteria approach, and mathematical programs are frequently suggested to model the many aspects of this difficult problem. This implies that exact models cannot be solved to optimality when the size of the territory is too large. In spite of this, an exact formulation can also be exploited in a heuristic framework to find at least a sub-optimal solution for large size problem instances. We study the design of electoral districts in Mexico, where the population is characterized by the presence of minority groups ("indigenous community") who have a special right to be represented in the Parliament. For this, the Mexican electoral law prescribes that a fixed number of districts must be designed to support the representation of the indigenous community. We formulate mixed integer linear programs (MILP) following these two principles, but also including the basic PD criteria of contiguity and population balance. The district map is obtained in two stages: first we produce the fixed number of indigenous districts established by the Law; then we complete the district map by forming the non-indigenous districts. This two-phase approach has two advantages: a dedicated objective function can be formulated in Phase 1 to form indigenous districts at best; in the second phase the instance size is reduced (both in the number of territorial units and in the number of districts) so that the computational effort to solve the problem is reduced as well. We test our procedure on the territory of Chiapas in Mexico and on some fictitious problem instances in which the territory is represented by a grid graph. We also compare our district map with the Institutional one currently adopted in Chiapas

New indexes for measuring electoral disproportionality

The number of representatives obtained by each political party in an electoral process must be a whole number. So, the percentage of votes for each party usually differs from the corresponding percentage of seats, forcing a certain unavoidable disproportionality. On the other hand, different elements of the electoral system (constituencies, thresholds, etc.) may produce some avoidable disproportionality. Those indexes traditionally used to analyse disproportionality take into account an unreachable exact proportionality as a reference. Instead, our more realistic approach quantifies distortions from a specific allotment, namely the seat distribution obtained when applying a proportional method to the total votes (that is, as if it were a unique constituency, without electoral thresholds or incentives to the winning party). Hence, we measure the avoidable disproportionality associated with such method. Unlike traditional indexes, we propose indexes associated with proportional allotment methods that can be zero in real situations. They are simple to calculate and allow us to decipher the number of seats assigned beyond the inevitable disproportionality which arises from the constraint of whole numbers. We are particularly interested in the indexes associated with Jefferson and Webster methods, which are compared to Gallagher, Loosemore-Hanby and SainteLaguë indexes for the results of 55 elections held in several countries