Harsanyi’s Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions

This paper provides new versions of Harsanyi’s social aggregation theorem that are formulated in terms of prospects rather than lotteries. Strengthening an earlier result, fixed-population ex-ante utilitarianism is characterized in a multi-profile setting with fixed probabilities. In addition, we extend the social aggregation theorem to social-evaluation problems under uncertainty with a variable population and generalize our approach to uncertain alternatives, which consist of compound vectors of probability distributions and prospects.

Non-Deteriorating Choice without Full Transitivity

Although the theory of greatest-element rationalizability and maximal-element rationalizability under general domains and without full transitivity of rationalizing relations is well-developed in the literature, these standard notions of rational choice are often considered to be too demanding. An alternative definition of rationality of choice is that of non-deteriorating choice, which requires that the chosen alternatives must be judged at least as good as a reference alternative. In game theory, this definition is well-known under the name of individual rationality when the reference alternative is construed to be the status quo. This alternative form of rationality of individual and social choice is characterized in this paper on general domains and without full transitivity of rationalizing relations.

Allocation rules on networks

When allocating a resource, geographical and infrastructural constraints have to be taken into account. We study the problem of distributing a resource through a network from sources endowed with the resource to citizens with claims. A link between a source and an agent depicts the possibility of a transfer from the source to the agent. Given the supplies at each source, the claims of citizens, and the network, the question is how to allocate the available resources among the citizens. We consider a simple allocation problem that is free of network constraints, where the total amount can be freely distributed. The simple allocation problem is a claims problem where the total amount of claims is greater than what is available. We focus on consistent and resource monotonic rules in claims problems that satisfy equal treatment of equals. We call these rules fairness principles and we extend fairness principles to allocation rules on networks. We require that for each pair of citizens in the network, the extension is robust with respect to the fairness principle. We call this condition pairwise robustness with respect to the fairness principle. We provide an algorithm and show that each fairness principle has a unique extension which is pairwise robust with respect to the fairness principle. We give applications of the algorithm for three fairness principles: egalitarianism, proportionality and equal sacrifice.

Escolha social e valores irredutíveis: uma aproximação da economia política e a ideologia

No presente paper, nós provamos que qualquer função da escolha social satisfaz o princípio da independência das alternativas irrelevantes (IIA) de Arrow se o comportamento individual é menu-dependente. Portanto, o 'Teorema da Possibilidade Geral' de Arrow não é válido quando as preferências individuais são determinadas por valores irredutíveis. Nesse contexto, qualquer instrumento de agregação que satisfaça os princípios não-ditatoriais e paretianos de unanimidade (maioria simples, por exemplo) também faz IIA. Esse poderia ser um resultado importante para a teoria da escolha social, enquanto um comportamento individual determinado por valores irredutíveis (interesse próprio, ideologia, Ética e normas sociais, por exemplo) podendo validar democracia representativa. A importância relativa de tais valores e da possibilidade de reversão da preferência determina a dinâmica da escolha social, de acordo com os princípios democráticos.

Strategy-proof choice of acts : a preliminary study

We model social choices as acts mapping states of the world to (social) outcomes. A (social choice) rule assigns an act to every profile of subjective expected utility preferences over acts. A rule is strategy-proof if no agent ever has an incentive to misrepresent her beliefs about the world or her valuation of the outcomes; it is ex-post efficient if the act selected at any given preference profile picks a Pareto-efficient outcome in every state of the world. We show that every two-agent ex-post efficient and strategy-proof rule is a top selection: the chosen act picks the most preferred outcome of some (possibly different) agent in every state of the world. The states in which an agent’s top outcome is selected cannot vary with the reported valuations of the outcomes but may change with the reported beliefs. We give a complete characterization of the ex-post efficient and strategy-proof rules in the two-agent, two-state case, and we identify a rich class of such rules in the two-agent case.

Strategy-proof choice of acts : a preliminary study

We model social choices as acts mapping states of the world to (social) outcomes. A (social choice) rule assigns an act to every profile of subjective expected utility preferences over acts. A rule is strategy-proof if no agent ever has an incentive to misrepresent her beliefs about the world or her valuation of the outcomes; it is ex-post efficient if the act selected at any given preference profile picks a Pareto-efficient outcome in every state of the world. We show that every two-agent ex-post efficient and strategy-proof rule is a top selection: the chosen act picks the most preferred outcome of some (possibly different) agent in every state of the world. The states in which an agent’s top outcome is selected cannot vary with the reported valuations of the outcomes but may change with the reported beliefs. We give a complete characterization of the ex-post efficient and strategy-proof rules in the two-agent, two-state case, and we identify a rich class of such rules in the two-agent case.

Public choice of species for the 'Ark': Phylogenetic similarity and preferred wildlife species for survival

Humans play a role in deciding the fate of species in the current extinction wave. Because of the previous Similarity Principle, physical attractiveness and likeability, it has been argued that public choice favours the survival of species that satisfy these criteria at the expense of other species. This paper empirically tests this argument by considering a hypothetical ‘Ark’ situation. Surveys of 204 members of the Australian public inquired whether they are in favour of the survival of each of 24 native mammal, bird and reptile species (prior to and after information provision about each species). The species were ranked by percentage of ‘yes’ votes received. Species composition by taxon in various fractions of the ranking was determined. If the previous Similarity Principle holds, mammals should rank highly and dominate the top fractions of animals saved in the hierarchical list. We find that although mammals would be over-represented in the ‘Ark’, birds and reptiles are unlikely to be excluded when social choice is based on numbers ‘voting’ for the survival of each species. Support for the previous Similarity Principle is apparent particularly after information provision. Public policy implications of this are noted and recommendations are given.

Fogalmak, módszerek. Páros összehasonlításokon alapuló rangsorolási módszerek (Ranking methods based on paired comparisons)

A páronként összehasonlított alternatívák rangsorolásának problémája egyaránt felmerül a szavazáselmélet, a statisztika, a tudománymetria, a pszichológia és a sport területén. A nemzetközi szakirodalom alapján részletesen áttekintjük a megoldási lehetőségeket, bemutatjuk a gyakorlati alkalmazások során fellépő kérdések kezelésének, a valós adatoknak megfelelő matematikai környezet felépítésének módjait. Kiemelten tárgyaljuk a páros összehasonlítási mátrix megadását, az egyes pontozási eljárásokat és azok kapcsolatát. A tanulmány elméleti szempontból vizsgálja a Perron-Frobenius tételen alapuló invariáns, fair bets, PageRank, valamint az irányított gráfok csúcsainak rangsorolásra javasolt internal slackening és pozíciós erő módszereket. A közülük történő választáshoz az axiomatikus megközelítést ajánljuk, ennek keretében bemutatjuk az invariáns és a fair bets eljárások karakterizációját, és kitérünk a módszerek vitatható tulajdonságaira. _____ The ranking of the alternatives or selecting the best one are fundamental issues of social choice theory, statistics, psychology and sport. Different solution concepts, and various mathematical models of applications are reviewed based on the international literature. We are focusing on the de¯nition of paired comparison matrix, on main scoring procedures and their relation. The paper gives a theoretical analysis of the invariant, fair bets and PageRank methods, which are founded on Perron-Frobenius theorem, as well as the internal slackening and positional power procedures used for ranking the nodes of a directed graph. An axiomatic approach is proposed for the choice of an appropriate method. Besides some known characterizations for the invariant and fair bets methods, we also discuss the violation of some properties, meaning their main weakness.

Kernelization complexity of possible winner and coalitional manipulation problems in voting

In the POSSIBLE WINNER problem in computational social choice theory, we are given a set of partial preferences and the question is whether a distinguished candidate could be made winner by extending the partial preferences to linear preferences. Previous work has provided, for many common voting rules, fixed parameter tractable algorithms for the POSSIBLE WINNER problem, with number of candidates as the parameter. However, the corresponding kernelization question is still open and in fact, has been mentioned as a key research challenge 10]. In this paper, we settle this open question for many common voting rules. We show that the POSSIBLE WINNER problem for maximin, Copeland, Bucklin, ranked pairs, and a class of scoring rules that includes the Borda voting rule does not admit a polynomial kernel with the number of candidates as the parameter. We show however that the COALITIONAL MANIPULATION problem which is an important special case of the POSSIBLE WINNER problem does admit a polynomial kernel for maximin, Copeland, ranked pairs, and a class of scoring rules that includes the Borda voting rule, when the number of manipulators is polynomial in the number of candidates. A significant conclusion of our work is that the POSSIBLE WINNER problem is harder than the COALITIONAL MANIPULATION problem since the COALITIONAL MANIPULATION problem admits a polynomial kernel whereas the POSSIBLE WINNER problem does not admit a polynomial kernel. (C) 2015 Elsevier B.V. All rights reserved.

Democratic Values Transmission

This study addresses the issue of intergenerational transmission of democratic values embedded in social choice rules. We focus on a few rules which have been the focus of social choice theory: plurality, plurality with a runoff, majoritarian compromise, social compromise and Borda rule. We confront subjects with preferences profiles of a hypothetical electorate over a set of four alternatives. Different rules produce different outcomes and subjects decide which alternative should be chosen for the society whose preference profile is shown. We elicit each subject's preferences over rules and his/her parents' and check whether there is any relationship; 186 students and their parents attended the sessions at Istanbul Bilgi University. Overall, we find support for the hypothesis of parental transmission of democratic values and gender differences in the transmitted rule.

Learning design contingent valuation (LDCV): NOAA guidelines, preference learning and coherent arbitrariness

We extend the contingent valuation (CV) method to test three differing conceptions of individuals' preferences as either (i) a-priori well-formed or readily divined and revealed through a single dichotomous choice question (as per the NOAA CV guidelines [K. Arrow, R. Solow, P.R. Portney, E.E. Learner, R. Radner, H. Schuman, Report of the NOAA panel on contingent valuation, Fed. Reg. 58 (1993) 4601-4614]); (ii) learned or 'discovered' through a process of repetition and experience [J.A. List, Does market experience eliminate market anomalies? Q. J. Econ. (2003) 41-72; C.R. Plott, Rational individual behaviour in markets and social choice processes: the discovered preference hypothesis, in: K. Arrow, E. Colombatto, M. Perleman, C. Schmidt (Eds.), Rational Foundations of Economic Behaviour, Macmillan, London, St. Martin's, New York, 1996, pp. 225-250]; (iii) internally coherent but strongly influenced by some initial arbitrary anchor [D. Ariely, G. Loewenstein, D. Prelec, 'Coherent arbitrariness': stable demand curves without stable preferences, Q. J. Econ. 118(l) (2003) 73-105]. Findings reject both the first and last of these conceptions in favour of a model in which preferences converge towards standard expectations through a process of repetition and learning. In doing so, we show that such a 'learning design CV method overturns the 'stylised facts' of bias and anchoring within the double bound dichotomous choice elicitation format. (C) 2007 Elsevier Inc. All rights reserved.

Secure Implementation in Production Economies

This paper shows that, in production economies, the generalized serial social choice functions defined by Shenker (1992) are securely implementable (in the sense of Saijo et al., 2007) and that they include the well-known fixed path social choice functions.

Sharing a River

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. We are interested in efficiency, stability (in the sense of the core), and fairness (in a sense to be defined). We first show that the cooperative game associated with our problem is convex : its core is therefore large and easily described. Next, we propose the following fairness requirement : no group of agents should enjoy a welfare higher than what it could achieve in the absence of the remaining agents. We prove that only one welfare vector in the core satisfies this condition : it is the marginal contribution vector corresponding to the ordering of the agents along the river. We discuss how it could be decentralized or implemented.

Core Retionalizability in Two-Agent Exchange Economies.

We provide a characterization of selection correspondences in two-person exchange economies that can be core rationalized in the sense that there exists a preference profile with some standard properties that generates the observed choices as the set of core elements of the economy for any given initial endowment vector. The approach followed in this paper deviates from the standard rational choice model in that a rationalization in terms of a profile of individual orderings rather than in terms of a single individual or social preference relation is analyzed.