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.     

The Multidimensionality of Child Poverty: Evidence from Afghanistan

This paper examines multidimensional poverty among children in Afghanistan using the Alkire-Foster method. Several previous studies have underlined the need to separate children from their adult nexus when studying poverty and treat them according to their own specificities. From the capability approach, child poverty is understood to be the lack of freedom to do and to be what children themselves value and have reason to value. The case of Afghanistan is particularly relevant as years of conflict aggravated by several severe droughts, political insecurity, bad governance and ongoing violence have significantly increased poverty in the country. The paper discusses the relevant dimensions when analysing child poverty and uses data from a survey carried out by Handicap International which contains information on dimensions of children’s wellbeing that is typically missing in standard surveys. Ten dimension are considered in this paper: health, care and love, material deprivation, food security, social inclusion, education, freedom from economic and non-economic exploitation, shelter and environment, autonomy, and mobility. Our results show that younger children, those living in rural areas, girls and disabled children are the most deprived.     

Preference intensity representation: strategic overstating in large elections

If voters vote strategically, is it useful to offer them the possibility of expressing nuanced opinions, or would they always overstate the intensity of their preferences? For additive voting rules, say that a ballot is extremal if it is neither abstention-like nor can be expressed as a mixture of the available ballots. We give a sufficient condition for strategic equivalence: if two rules share the same set of extremal ballots (up to an homothetic transformation), they are strategically equivalent in large elections. This condition is also necessary for the strategic equivalence of positional rules. These results do not hold for small electorates.     

The stein effect and bayesian analysis: a reexamination

The Stein, that one could improve frequentist risk by combining “independent” problems, has long been an intriguing paradox to statistics. We briefly review the Bayesian view of the paradox, and indicate that previous justifications of the Stein effect, through concerns of “Bayesian robustness,” were misleading. In the course of doing so, several existing robust Bayesian and Stein-effect estimators are compared for a variety of situations.     

Comparison functions and choice correspondences

In this paper, we introduce the concept of a comparison function, which is a mapping g that assigns numbers to ordered pairs of alternatives (x,y) with the property that g(x,y)=−g(y,x). The paper discusses how some well-known choice correspondences on tournaments such as the uncovered set, the minimal covering set and the bipartisan set can be extended to this general framework. Axiomatic characterizations and properties are studied for these correspondences. Received: 4 November 1996/Accepted: 13 April 1998     

Interpersonal comparisons of utility in bargaining: evidence from a transcontinental ultimatum game

This article presents the experimental results of a “Transcontinental Ultimatum Game” implemented between India and France. We use a standard ultimatum game, but in one treatment, Indian subjects made offers to French subjects (ItoF treatment) and, in another treatment, French subjects made offers to Indian subjects (FtoI treatment). We observed that FtoI treatment bargaining mostly ended up with unequal splits of money in favor of French, while nearly equal splits were the most frequent outcome in ItoF treatment interactions. The experimental results are organized through a standard social reference model, modified for taking into account the different marginal value of money for bargainers. In our model, bargaining is driven by relative standing comparisons between players, occurring in terms of real earnings (that is monetary earnings corrected for a purchasing power factor) obtained in the game. The norm of equity behind the equalization of real earnings is called local equity norm, and contrasted to a global equity norm which would encompass the wealth of players beyond the game. According to what we observed, no beyond-game concern seems to be relevantly endorsed by subjects.     

Aggregation of preferences with a variable set of alternatives

A social choice correspondence called the Essential set is studied with the help of an axiom called Cloning Consistency. Cloning consistency is the requirement that the formal choice rule be insensitive to the replication of alternatives. The Essential set is the support of the optimal mixed strategies in a symmetric two-party electoral competition game. Received: 24 March 1998/Accepted: 3 March 1999     

Consistency between tastes and values: A universalization approach

The object of this paper is to propose a consistency test for an individual involved in collective choice process. Collective choice processes considered in the paper are those that transform individuals ‘tastes’– which reflect the self-interested view point of the individuals – into (social) ranking of alternatives. In addition to her tastes, an individual has values about the way by which collective decision should be made. We distinguish two categories of such values. First, there are end-values that restrict the class of social rankings that the individual considers ethically acceptable. Second there are aggregation-values that specify the way by which the social ranking should depend upon the individuals tastes. The consistency test stands on an hypothetical operation of universalization of the individual tastes to everyone. Five illustrations of the potential usefulness of our approach for interpreting social choice theory and welfare economics are proposed. These illustrations deal with utilitarian aggregation in the presence of income inequality aversion, the so-called ‘ethics of responsibility’ and the aggregation of individual ranking of opportunity sets based on their freedom of choice. A discussion of the relevance of the consistency test for addressing the problem of ‘laundering’ individual preferences is also provided. Received: 25 June 1998/Accepted: 16 March 1999