A set of related majority rule-based social choice correspondences are considered: the union of minimal Р-dominating sets MPD (Duggan 2011, Subochev 2016) the union of weakly stable sets MWS (Aleskerov & Kurbanov 1999), the union of minimal P-externally stable sets MPES (Wuffl et al. 1989, Subochev 2008) and the union of minimal R-externally stable sets MRES (Aleskerov & Subochev 2009, 2013). These tournament solutions have not attracted much attention so far. However, the analysis of their properties suggests that MPES and MRES can be useful as instruments of choice, for instance when it is necessary to aggregate rankings. Their implementation is also possible under certain conditions.
The results presented are the following.
1) In a general case of a topological space of alternatives, a sufficient and necessary condition has been provided for an alternative to belong to a minimal P-dominating set. This characteristic condition is related to some version of the covering relation. It has been established that the union of minimal P-dominating sets and the uncovered set are logically nested neither in a general case, nor in finite tournaments. The characterization obtained provides a sufficient condition of nonemptiness of MPES and MRES in a general case of a topological space of alternatives.
2) It has been found that MPES and MRES both satisfy the following axioms:
a) monotonicity with respect to changes in social preferences (P-monotonicity),
b) the generalized Nash independence of irrelevant alternatives,
c) the idempotence,
d) the Aizerman-Aleskerov property,
e) the independence of social preferences for irrelevant alternatives (the independence of losers),
but they do not satisfy the extension axiom (Sen’s property g). It has also been demonstrated that MPD satisfies neither of these axioms, and MWS satisfies P-monotonicity only.
3) It has been found that MPES and MRES both satisfy Sanver monotonicity (a.k.a. cover monotonicity). Thus, despite they are not Maskin monotonic, these social choice correspondences can be implemented in a nonstandard setting, where actors have (extended) preferences for sets of alternatives. It has also been demonstrated that MPD and MWS do not satisfy Sanver monotonicity.
Various Condorcet consistent social choice functions based on majority rule (tournament solutions) are considered in the general case, when ties are allowed: the core, the weak and strong top cycle sets, versions of the uncovered and minimal weakly stable sets, the uncaptured set, the untrapped set, classes of k-stable alternatives and k-stable sets. The main focus of the paper is to construct a unified matrix-vector representation of a tournament solution in order to get a convenient algorithm for its calculation. New versions of some solutions are also proposed.
We use data on economic, management and political science journals to produce quantitative estimates of (in)consistency of evaluations based on seven popular bibliometric indicators (impact factor, 5-year impact factor, immediacy index, article influence score, h-index, SNIP and SJR). We propose a new approach to aggregating journal rankings: since rank aggregation is a multicriteria decision problem, ordinal ranking methods from social choice theory may solve it. We apply either a direct ranking method based on majority rule (the Copeland rule, the Markovian method) or a sorting procedure based on a tournament solution, such as the uncovered set and the minimal externally stable set. We demonstrate that aggregate rankings reduce the number of contradictions and represent the set of single-indicator-based rankings better than any of the seven rankings themselves.
We use data on economic, management and political science journals to produce quan- titative estimates of (in)consistency of the evaluations based on six popular bibliometric indicators (impact factor, 5-year impact factor, immediacy index, article influence score, SNIP and SJR). We advocate a new approach to the aggregation of journal rankings. Since the rank aggregation is a multicriteria decision problem, ranking methods from social choice theory may solve it. We apply either a direct ranking method based on the majority rule (the Copeland rule, the Markovian method) or a sorting procedure based on a tournament solution, such as the uncovered set and the minimal externally stable set. We demonstrate that the aggregate rankings reduce the number of contradictions and represent the set of the single-indicator-based rankings better than any of the six rankings themselves.
We address the external effects on public sector efficiency measures acquired using Data Envelopment Analysis. We use the health care system in Russian regions in 2011 to evaluate modern approaches to accounting for external effects. We propose a promising method of correcting DEA efficiency measures. Despite the multiple advantages DEA offers, the usage of this approach carries with it a number of methodological difficulties. Accounting for multiple factors of efficiency calls for more complex methods, among which the most promising are DMU clustering and calculating local production possibility frontiers. Using regression models for estimate correction requires further study due to possible systematic errors during estimation. A mixture of data correction and DMU clustering together with multi-stage DEA seems most promising at the moment. Analyzing several stages of transforming society’s resources into social welfare will allow for picking out the weak points in a state agency’s work.