Generating functions: a useful tool for computing power indices

In the theory of simple games, the study of power indices plays an important role. One of the main di culties with these indices is that computation generally requires the sum of a very large number of terms. The generating functions are e cient tools to make more easy this computation. In this paper, we provide a revision of the main elements of this method when we use it to compute the Shapley-Shubik and the BanzhafColeman power indices. Further, we provide a new method to compute the Banzhaf-Coleman indexS

The general elections of 2008 and the game of parliament

En este artículo analizamos el resultado de las elecciones generales desde un punto de vista Teórico de Juegos. Para cuantificar el poder que cada partido tiene en el nuevo Parlamento introducimos tres conceptos, los índices de poder de Shapley-Shubik, de Banzhaf-Penrose y de Deegan-Packel. De esta forma, podemos saber cuál es el partido más decisivo y comparando los resultados obtenidos con los de las elecciones de 2004, qué partidos han aumentado o disminuido más poder. Para terminar se proponen extensiones al modelo propuestoIn this paper we analyze the result of the elections for the Spanish Parliament in a Game Theoretical approach. In order to measure the power each party has in the new Parliament we introduce three concepts, the Shapley-Shubik, Banzhaf-Penrose and DeeganPackel power indices. In this way, we are able to know which the most decisive party is and comparing the result with the elections of 2004, we conclude which party has gain and which has lost more power. At last, we present different extensions of the proposed modelS

Mergeable weighted majority games and characterizations of some power indices

In this paper, we introduce a notion of mergeable weighted majority games with the aim of providing the first characterization of the Colomer–Martínez power index (Colomer and Martínez in J Theor Polit 7(1):41–63, 1995). Furthermore, we define and characterize a new power index for the family of weighted majority games that combines ideas of the Public Good (Holler in Polit Stud 30(2):262–271, 1982) and Colomer–Martínez power indices. Finally, we analyze the National Assembly of Ecuador using these and some other well-known power indicesWe would like to thank Balbina V. Casas-Méndez and two anonymous referees for their valuable comments. This work is part of the R+D+I project grants MTM2017-87197-C3-2-P, MTM2017-87197-C3-3-P, PID2021-124030NB-C32, and PID2021-124030NB-C33, that were funded by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”/EU. This research was also funded by Grupos de Referencia Competitiva ED431C-2020/03 and ED431C-2021/24 from the Consellería de Cultura, Educación e Universidades, Xunta de Galicia. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer NatureS

The proportional partitional Shapley value

A new coalitional value is proposed under the hypothesis of isolated unions. The main difference between this value and the Aumann–Drèze value is that the allocations within each union are not given by the Shapley value of the restricted game but proportionally to the Shapley value of the original game. Axiomatic characterizations of the new value, examples illustrating its application and a comparative discussion are provided.Peer ReviewedPostprint (author’s final draft

Risk Factors for COVID-19 in Inflammatory Bowel Disease: A National, ENEIDA-Based Case–Control Study (COVID-19-EII)

(1) Scant information is available concerning the characteristics that may favour the acquisition of COVID-19 in patients with inflammatory bowel disease (IBD). Therefore, the aim of this study was to assess these differences between infected and noninfected patients with IBD. (2) This nationwide case-control study evaluated patients with inflammatory bowel disease with COVID-19 (cases) and without COVID-19 (controls) during the period March-July 2020 included in the ENEIDA of GETECCU. (3) A total of 496 cases and 964 controls from 73 Spanish centres were included. No differences were found in the basal characteristics between cases and controls. Cases had higher comorbidity Charlson scores (24% vs. 19%; p = 0.02) and occupational risk (28% vs. 10.5%; p < 0.0001) more frequently than did controls. Lockdown was the only protective measure against COVID-19 (50% vs. 70%; p < 0.0001). No differences were found in the use of systemic steroids, immunosuppressants or biologics between cases and controls. Cases were more often treated with 5-aminosalicylates (42% vs. 34%; p = 0.003). Having a moderate Charlson score (OR: 2.7; 95%CI: 1.3-5.9), occupational risk (OR: 2.9; 95%CI: 1.8-4.4) and the use of 5-aminosalicylates (OR: 1.7; 95%CI: 1.2-2.5) were factors for COVID-19. The strict lockdown was the only protective factor (OR: 0.1; 95%CI: 0.09-0.2). (4) Comorbidities and occupational exposure are the most relevant factors for COVID-19 in patients with IBD. The risk of COVID-19 seems not to be increased by immunosuppressants or biologics, with a potential effect of 5-aminosalicylates, which should be investigated further and interpreted with caution

A proportional extension of the Shapley value for monotone games with a coalition structure

The Owen value is a modification of the Shapley value for games with a coalition structure. In this paper, we propose another modification of the Shapley value for monotone games with a coalition structure. This new value is a double- extension of the Shapley value in the next sense: the amount obtained by an union coincides with the Shapley value of the union in the quotient game, and the players of each union share this amount proportionally to their Shapley values in the game without unions. We give two characterizations of this new value. The axiomatic systems used here can be compared with parallel axiomatizations of the Owen value

A new power index based on minimal winning coalitions

Nou índex de poder basat en coalicions shift-minimal

A proportional extension of the Shapley value for monotone games with a coalition structure

The Owen value is a modification of the Shapley value for games with a coalition structure. In this paper, we propose another modification of the Shapley value for monotone games with a coalition structure. This new value is a double- extension of the Shapley value in the next sense: the amount obtained by an union coincides with the Shapley value of the union in the quotient game, and the players of each union share this amount proportionally to their Shapley values in the game without unions. We give two characterizations of this new value. The axiomatic systems used here can be compared with parallel axiomatizations of the Owen value.Postprint (author’s final draft

A new power index based on minimal winning coalitions

Nou índex de poder basat en coalicions shift-minimalsPreprin