Mathematical Programming formulations for the efficient solution of the kk-sum approval voting problem

In this paper we address the problem of electing a committee among a set of $m$ candidates and on the basis of the preferences of a set of $n$ voters. We consider the approval voting method in which each voter can approve as many candidates as she/he likes by expressing a preference profile (boolean $m$-vector). In order to elect a committee, a voting rule must be established to `transform' the $n$ voters' profiles into a winning committee. The problem is widely studied in voting theory; for a variety of voting rules the problem was shown to be computationally difficult and approximation algorithms and heuristic techniques were proposed in the literature. In this paper we follow an Ordered Weighted Averaging approach and study the $k$-sum approval voting (optimization) problem in the general case $1 \leq k <n$. For this problem we provide different mathematical programming formulations that allow us to solve it in an exact solution framework. We provide computational results showing that our approach is efficient for medium-size test problems ($n$ up to 200, $m$ up to 60) since in all tested cases it was able to find the exact optimal solution in very short computational times

Geography, culture, and religion: Explaining the bias in Eurovision song contest voting

This paper analyses votes cast in the Eurovision Song Contest in the period 1975 - 2003. We test whether accusations of 'political' voting among participants can be substantiated by looking at geographical influences. Our approach differs in two ways from earlier studies. First, we take into account a variety of variables to distinguish political voting from preferences based on cultural, linguistic, ethnic, and religious differences and similarities between countries. Secondly, we analyse the determinants of the voting behaviour separately per country, instead of looking at average effects over all participating countries. We find that geographical factors substantially affect the votes. Even after correction for cultural, linguistic and other factors many countries prefer or dislike the songs of surrounding countries. This leads to the suspicion that the geograph¬ical preferences reflect political voting. Also, we show that several countries favour songs of participants with the same religious background, while others prefer the contributions of countries with a different religion. Moreover, using data on the amount of Turkish immigrants across European countries, we document that countries with a substantial Turkish population favour the Turkish songs ('patriotic' voting). Furthermore, we study the repercussions of opening up the voting system to the general public by the introduction of televoting. It turns out that religious and patriotic voting have become considerably stronger since the introduction of the new voting system. Finally, we confront our em¬pirical findings to the publicly debated accusations of political voting made against certain blocks of countries. Although our analysis uncovers significant geographical patterns (suggesting political voting), we do hardly establish any empirical evidence for the claims against these particular countries

Aggregating Dependency Graphs into Voting Agendas in Multi-Issue Elections

Many collective decision making problems have a combinatorial structure: the agents involved must decide on multiple issues and their preferences over one issue may depend on the choices adopted for some of the others. Voting is an attractive method for making collective decisions, but conducting a multi-issue election is challenging. On the one hand, requiring agents to vote by expressing their preferences over all combinations of issues is computationally infeasible; on the other, decomposing the problem into several elections on smaller sets of issues can lead to paradoxical outcomes. Any pragmatic method for running a multi-issue election will have to balance these two concerns. We identify and analyse the problem of generating an agenda for a given election, specifying which issues to vote on together in local elections and in which order to schedule those local elections

Ontology Merging as Social Choice

The problem of merging several ontologies has important applications in the Semantic Web, medical ontology engineering and other domains where information from several distinct sources needs to be integrated in a coherent manner.We propose to view ontology merging as a problem of social choice, i.e. as a problem of aggregating the input of a set of individuals into an adequate collective decision. That is, we propose to view ontology merging as ontology aggregation. As a first step in this direction, we formulate several desirable properties for ontology aggregators, we identify the incompatibility of some of these properties, and we define and analyse several simple aggregation procedures. Our approach is closely related to work in judgment aggregation, but with the crucial difference that we adopt an open world assumption, by distinguishing between facts not included in an agent’s ontology and facts explicitly negated in an agent’s ontology

Consensus theories: an oriented survey

This article surveys seven directions of consensus theories: Arrowian results, federation consensus rules, metric consensus rules, tournament solutions, restricted domains, abstract consensus theories, algorithmic and complexity issues. This survey is oriented in the sense that it is mainly – but not exclusively – concentrated on the most significant results obtained, sometimes with other searchers, by a team of French searchers who are or were full or associate members of the Centre d'Analyse et de Mathématique Sociale (CAMS).Consensus theories ; Arrowian results ; aggregation rules ; metric consensus rules ; median ; tournament solutions ; restricted domains ; lower valuations ; median semilattice ; complexity

How does Europe Make Its Mind Up? Connections, cliques, and compatibility between countries in the Eurovision Song Contest

We investigate the complex relationships between countries in the Eurovision Song Contest, by recasting past voting data in terms of a dynamical network. Despite the British tendency to feel distant from Europe, our analysis shows that the U.K. is remarkably compatible, or 'in tune', with other European countries. Equally surprising is our finding that some other core countries, most notably France, are significantly 'out of tune' with the rest of Europe. In addition, our analysis enables us to confirm a widely-held belief that there are unofficial cliques of countries -- however these cliques are not always the expected ones, nor can their existence be explained solely on the grounds of geographical proximity. The complexity in this system emerges via the group 'self-assessment' process, and in the absence of any central controller. One might therefore speculate that such complexity is representative of many real-world situations in which groups of 'agents' establish their own inter-relationships and hence ultimately decide their own fate. Possible examples include groups of individuals, societies, political groups or even governments