Composition-consistent tournament solutions and social choice functions

This paper introduces a new axiom for choice in preference profiles and tournaments, called composition-consistency. A social choice function is composition-consistent if it is non-sensitive to the cloning of one or several outcomes. The key feature of the composition consistency property is an operation concept called multiple composition product of profiles. The paper provides a brief overview of some social choice functions studied in the literature. Concerning the tournament solutions, it is proved that the Top Cycle, the Slater and the Copeland solutions are not composition-consistent, whereas the Banks, Uncovered Set, TEQ, Minimal Covering Set are composition-consistent. Moreover, we define the composition-consistent hull of a solution as the smallest composition-consistent solution containing . The composition-consistent hulls of the Top cycle and Copeland solutions are specified, and we give some hints about the location of the hull of the Slater set. Concerning social choice functions, it is shown that Kemeny, Borda and Minimax social choice functions are not composition-consistent, whereas the Paretian one is composition-consistent. Moreover, we prove that the latter is the composition-consistent hull of the Borda and Minimax functions.     

Health Risk Assessment of a Modern Municipal Waste Incinerator

During the modernization of the municipal waste incinerator (MWI, maximum capacity of 180,000 tons per year) of Metropolitan Grenoble (405,000 inhabitants), in France, a risk assessment was conducted, based on four tracer pollutants: two volatile organic compounds (benzene and 1, 1, 1 trichloroethane) and two heavy metals (nickel and cadmium, measured in particles). A Gaussian plume dispersion model, applied to maximum emissions measured at the MWI stacks, was used to estimate the distribution of these pollutants in the atmosphere throughout the metropolitan area. A random sample telephone survey (570 subjects) gathered data on time-activity patterns, according to demographic characteristics of the population. Life-long exposure was assessed as a time-weighted average of ambient air concentrations. Inhalation alone was considered because, in the Grenoble urban setting, other routes of exposure are not likely. A Monte Carlo simulation was used to describe probability distributions of exposures and risks. The median of the life-long personal exposures distribution to MWI benzene was 3.2·10^–5 g/m³ (20th and 80th percentiles = 1.5·10^–5 and 6.5·10^–5 g/m³), yielding a 2.6·10^–10 carcinogenic risk (1.2·10^–10–5.4·10^–10). For nickel, the corresponding life-time exposure and cancer risk were 1.8·10^–4 g/m³ (0.9.10^–4 – 3.6·10^–4 g/m³) and 8.6·10^–8 (4.3·10^–8–17.3·10^–8); for cadmium they were respectively 8.3·10^–6 g/m³ (4.0·10^–6–17.6·10^–6) and 1.5·10^–8 (7.2·10^–9–3.1·10^–8). Inhalation exposure to cadmium emitted by the MWI represented less than 1% of the WHO Air Quality Guideline (5 ng/m³), while there was a margin of exposure of more than 10⁹ between the NOAEL (150 ppm) and exposure estimates to trichloroethane. Neither dioxins nor mercury, a volatile metal, were measured. This could lessen the attributable life-long risks estimated. The minute (VOCs and cadmium) to moderate (nickel) exposure and risk estimates are in accord with other studies on modern MWIs meeting recent emission regulations, however.     

Condorcet choice and the Ostrogorski paradox

The Ostrogorski paradox refers to the fact that, facing finitely many dichotomous issues, choosing issue-wise according to the majority rule may lead to a majority defeated overall outcome. This paper investigates the possibility for a similar paradox to occur under alternative specifications of the collective preference relation. The generalized Ostrogorski paradox occurs when the issue-wise majority rule leads to an outcome which is not maximal according to some binary relation φ defined over pairs of alternatives. We focus on three possible definitions of φ, whose sets of maximal elements are respectively the Uncovered Set, the Top-Cycle, and the Pareto Set. We prove that a generalized paradox may prevail for the Uncovered Set. Moreover, it may be avoided for the same issue-wise majority margins as for the Ostrogorski paradox. However, the issue-wise majority rule always selects a Pareto-optimal alternative in the Top-Cycle. Gilbert Laffond and Jean Lainé are grateful to two anonymous referees for their helpful comments and suggestions.     

Slaters's winners of a tournament may not be in the Banks set

An exemple is given of a tournament in which none of the Kemeny-Slater's winners of the tournament belong to the Banks set.The authors thanks Michel LeBreton, who provided the initial stimulus for this investigation, and an anonymous referee for helpfull comments.     

Weak covering relations

This paper proposes and justifies a natural way to weaken the concept of covering relation defined on a finite tournament. Various weak covering relations, calledk-covering relations, are introduced. To eachk-covering relation corresponds a strong uncovered set containing all nonk-covered outcomes. It is proved that those strong uncovered sets may be empty. Moreover, the set of all tournaments having an empty strong uncovered set is characterized within two rather large classes of tournaments. Finally, we offer a complete study of the cases where the directed graph defined by ak-covering relation coincides with the initial tournament.     

The Budget-Voting Paradox

The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives. Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension rule.      

K–Player Additive Extension of Two-Player games with an Application to the Borda Electoral Competition Game

In this note we introduce the notion of K–player additive extension of a symmetric two-player game and prove a result relating the equilibria in mixed strategies in the two games. Then we apply the result to the Borda electoral competition game.     

Majority voting on orders

We characterize two lexicographic-type preference extension rules from a set X to the set of all orders on this set. Elements of X are interpreted as basic economic policy decisions, whereas elements of are conceived as political programs among which a collectivity has to choose through majority voting. The main axiom is called tournament-consistency, and states that whenever majority pairwise comparisons based on initial preferences on X define an order on X, then this order is also chosen by a majority among all other orders in . Tournament-consistency thus allows to predict the outcome of majority voting upon orders from the knowledge of majority preferences on their components.