Jury voting is a widespread practice in various fields, such as cultural events. While existing literature typically examines decision-making rules, our analysis centers on how the grading behaviors of jury members impact the results. We analyze historical data from the Queen Elisabeth International Competition, which includes cello, piano, violin, and voice categories. The competition consists of three rounds in which candidates perform recitals. Each round culminates in the selection of a subset of candidates. Our findings indicate that judges who demonstrate greater variability in their scoring behaviors exert a more significant influence on the final rankings.

We study the effect of intratumor heterogeneity in the likelihood of cancer cells moving from a primary tumor to other sites in the human body, generating a metastatic process. We model different scenarios of competition between tumor cells using a static evolutionary game in which cells compete for nutrients and oxygen and might choose to stay and proliferate in the primary tumor or opt to a motility strategy in order to find resources in a metastatic site. The theoretical results found in the evolutionarily equilibrium in the mathematical model are in line with the empirical results observed in oncology, namely, the coexistence of both primary and metastatic tumors and the conditions that favor a metastatic process. Particularly, the model finds mathematical support for what is empirically observed in punctuated and branching cancers for the specific case of clear cell renal cell carcinomas: motility of cells is larger in punctuated cancers if the proportion of BAP1 mutations remain below a given cell proportion threshold.

In this paper, we study descriptive norms under the veil of ignorance in symmetric coordination and anti-coordination games. We consider a finite population formed by different types of individuals. Players observe the type of their opponent but play under the veil of ignorance, i.e., act as if they did not know their own type. The question that we address is whether in such a symmetric environment a discriminating norm may arise. We show that there exist symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Whenever individuals display a discriminating behavior, it is equally adopted by all agents, including by the individuals of the discriminated group. However, discrimination has a limit: the maximum number of groups where the treatment differs is three.

The Queen Elisabeth International Music Competition of Belgium founded in 1937, is among the world's most prestigious and demanding music competitions. It alternates between cello, piano, violin, and voice and consists of three rounds in which each candidate gives a recital. Each round selects a subset of candidates. This paper presents and analyses the rule for the selection of candidates and its specificities. It shows that the rule does not satisfy many of the classical properties of the literature on the social choice.

Mathematics, conventional histology, and genomics converge to confirm that highly aggressive clear cell renal cell carcinomas (CCRCCs) display low levels of intratumor heterogeneity (ITH). We hypothesize that therapeutic strategies aimed at maintaining high ITH levels would be advisable to slow down cancer evolution and to improve survival.

Clear cell renal cell carcinoma (CCRCC) is an aggressive form of cancer and a paradigmatic example of intratumor heterogeneity (ITH). The hawk-dove game is a mathematical tool designed to analyze competition in biological systems. Using this game, the study reported here analyzes the early phase of CCRCC development, comparing clonal fitness in homogeneous (linear evolutionary) and highly heterogeneous (branching evolutionary) models. Fitness in the analysis is a measure of tumor aggressiveness. The results show that the fittest clone in a heterogeneous environment is fitter than the clone in a homogeneous context in the early phases of tumor evolution. Early and late periods of tumor evolution in CCRCC are also compared. The study shows the convergence of mathematical, histological, and genomics studies with respect to clonal aggressiveness in different periods of the natural history of CCRCC. Such convergence highlights the importance of multidisciplinary approaches for obtaining a better understanding of the intricacies of cancer.

In this study, we explore interactions between cancer cells by using the hawk-dove game. We analyze the heterogeneity of tumors by considering games with populations composed of 2 or 3 types of cells. We determine what strategies are evolutionarily stable in the 2-type and 3-type population games and the corresponding expected payoffs. Our results show that the payoff of the best-off cell in the 2-type population game is higher than that of the best-off cell in the 3-type population game. Translating these mathematical findings to the field of oncology suggests that a branching-type tumor pursues a less aggressive course than a punctuated-type one. Some histological and genomic data of clear cell renal cell carcinomas are consistent with these results.

Intratumor heterogeneity (ITH) is an inherent characteristic of most tumors and its detection remains a key task for pathologists. However, the clinical significance of the degree of development of this feature is still poorly understood. A series of 28 clear cell renal cell carcinomas (CCRCC) have been exhaustively analyzed with two different sampling protocols [multisite tumor sampling (MSTS) and total sampling] to evaluate to what point the level (low vs. high) of histological ITH detected in routine practice influences tumor behavior and patients’ survival. All CCRCC (n = 14) pursuing an aggressive clinical course presented low levels of ITH. A significant worse survival was detected in CCRCC with low ITH (p < 0.001). The simple quantification of the level of ITH using extensive sampling protocol may be of help in predicting tumor evolution, since all CCRCC with aggressive behavior demonstrated low levels of histological ITH.

In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show that there exists symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Moreover, discrimination has a limit: the maximum number of groups where the treatment differs is three. We then discuss the theoretical results in light of the observed behavior of people in some specific psychological contexts.

In participatory budgeting, citizens are invited to vote on different projects. This paper sets out to study the voting stage of participatory budgeting from theoretical and practical perspectives. At theoretical level, the potential objectives of voting procedures are examined. From the practical point of view it should be easy to select projects, even when the number of projects is large. This paper proposes three algorithms which are theoretically justified and can be easily applied. Participatory budgeting in the town of Portugalete (Spain) provides a test for them. The results obtained with 2018 voting data suggest that the algorithm that includes the costs of the projects at the selection stage performs better than the others. (C) 2020 Elsevier B.V. All rights reserved.

This overview focuses on two different perspectives to analyze the metastatic process taking clear cell renal cell carcinoma as a model, molecular and ecological. On the one hand, genomic analyses have demonstrated up to seven different constrained routes of tumor evolution and two different metastatic patterns. On the other hand, game theory applied to cell encounters within a tumor provides a sociological perspective of the possible behaviors of individuals (cells) in a collectivity. This combined approach provides a more comprehensive understanding of the complex rules governing a neoplasm.

Highlights The decision structures aggregate the opinions of voters on several dimensions. Characterization of weighted multi-dimensional rules is provided. Some multi-dimensional rules are represented by a combination of single dimension rules. Links to the referendum paradox and the Ostrogorski paradox are made.AbstractThis paper deals with rules that specify the collective acceptance or rejection of a proposal with several dimensions. We introduce the notions of separability and weightedness in this context. We provide a partial characterization of separable rules and show the independence between separability and weightedness.

In this paper we study collective identity functions that deal with formation of clubs. Usually the choice offered to individuals is to cast a vote in favor of qualification or not, and the final outcome is qualification or non-qualification. In this context we show that independent collective identity functions are naturally characterized by voting rules, and in particular, consent rules can be represented by one single collection of weighted majorities. In addition, we consider the extended model where voters are allowed to abstain and we distinguish between disqualification and a neutral outcome. We show that this environment allows agents to act in different capacities that cannot be distinguished in the original formulation of the problem.

This paper looks at the issue of selecting candidates when the votes cast in ballots enable voters to approve or disapprove each candidate. More precisely, three options are offered: voters can approve, disapprove or remain neutral in regard to each candidate. We define a large family of rules that satisfy desirable properties and prove that solving a dilemma is sufficient to characterize any rule which belongs to this family. In this context a dilemma appears when candidates with only neutral votes face candidates with both supporters and opponents. On the basis of this result, we provide comparable axiomatizations of four rules including some proposed in the literature.

This paper deals with rules that specify the collective acceptance or rejection of a proposal with several dimensions. We introduce the notions of separability and weightedness in this context. We provide a partial characterization of separable rules and show the independence between separability and weightedness.

In this article, we study a simple mathematical model of a bilingual community in which all agents are fluent in the majority language but only a fraction of the population has some degree of proficiency in the minority language. We investigate how different distributions of proficiency, combined with the speakers' attitudes toward or against the minority language, may influence its use in pair conversations.

In April 2017, during the first round of the French presidential election, we performed a set of experiments on the use of voting rules. Participants to these experiments were asked to test several alternative voting methods, like approval voting, and other variants of evaluative voting. The experiments were both carried out in situ in polling stations during the first round of the presidential election (using paper ballots), and on line during the month preceding the first round, and until the second round of the election (using a web application). A total of 6358 participants took part to the in situ experiment and 37739 participants took part to the on line experiment. This paper describes the protocol of the in situ experiments and the format of the collected dataset

In this paper, we define the problem of group identification in an extended environment. We concentrate on the problem where the society is required to self-determine the belongingness of each member to a specific group, characterized by a single attribute. In general terms, this case consists of a collective identity issue that can be regarded as an aggregation problem of individual assessments within a group. Here we introduce the possibility that opinions are incomplete and that a status quo option intervenes in the process.

The support of the Spanish Ministerio de Economia y Competitividad under project ECO2015-67519-P, and of the Departamento de Educacion, Politica Linguistica y Cultura from the Basque Government (Research Group IT568-13) is gratefully acknowledged.