Free Triples, Large Indifference Classes and the Majority Rule

We consider situations in which agents are not able to completely distinguish between all alternatives. Preferences respect individual objective indifferences if any two alternatives are indifferent whenever an agent cannot distinguish between them. We present necessary and sufficient conditions of such a domain of preferences under which majority rule is quasi-transitive and thus Condorcet winners exist for any set of alternatives. Finally, we compare our proposed restrictions with others in the literature, to conclude that they are independent of any previously discussed domain restriction.Quasi-Transitivity

Social choice and game theory: recent results with a topological approach

This chapter presents a summary of recent results obtained in game and social choice theories, and highlights the application and the development of tools in algebraic topology. The purpose is expository: no attempt is made to provide complete proofs, for which references are given, nor to review the previous work in this area, which covers a significant subset of the economic literature. The aim is to provide an oriented guide to recent results, through economic examples with geometric interpretations, and to indicate possible fruitful avenues of research.social choice; game theory; algebraic topology; topological; pareto condition; preferences; Nash equilibrium; transversality

Voces Populi and the Art of Listening

The strategy most damaging to many preferential election methods is to give insincerely low rank to the main opponent of one’s favorite candidate. Theorem 1 determines the 3-candidate Condorcet method that minimizes the number of noncyclic profiles allowing this strategy. Theorems 2, 3, and 4 establish conditions for an anonymous and neutral 3-candidate single-seat election to be monotonic and still avoid this strategy completely. Plurality elections combine these properties; among the others "conditional IRV" gives the strongest challenge to the plurality winner. Conditional IRV is extended to any number of candidates. Theorem 5 is an impossibility of Gibbard-Satterthwaite type, describing 3 specific strategies that cannot all be avoided in meaningful anonymous and neutral elections.Preferential Election methods; Plurality Election methods

Testing Transitivity of Preferences on Two-Alternative Forced Choice Data

As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary problems and are subject to nontrivial order constrained statistical inference. The present paper discusses Luce's challenge for a particularly prominent axiom: Transitivity. The axiom of transitivity is a central component in many algebraic theories of preference and choice. We offer the currently most complete solution to the challenge in the case of transitivity of binary preference on the theory side and two-alternative forced choice on the empirical side, explicitly for up to five, and implicitly for up to seven, choice alternatives. We also discuss the relationship between our proposed solution and weak stochastic transitivity. We recommend to abandon the latter as a model of transitive individual preferences

Reasoning & Querying – State of the Art

Various query languages for Web and Semantic Web data, both for practical use and as an area of research in the scientific community, have emerged in recent years. At the same time, the broad adoption of the internet where keyword search is used in many applications, e.g. search engines, has familiarized casual users with using keyword queries to retrieve information on the internet. Unlike this easy-to-use querying, traditional query languages require knowledge of the language itself as well as of the data to be queried. Keyword-based query languages for XML and RDF bridge the gap between the two, aiming at enabling simple querying of semi-structured data, which is relevant e.g. in the context of the emerging Semantic Web. This article presents an overview of the field of keyword querying for XML and RDF

Social choice and game theory: recent results with a topological approach

This chapter presents a summary of recent results obtained in game and social choice theories, and highlights the application and the development of tools in algebraic topology. The purpose is expository: no attempt is made to provide complete proofs, for which references are given, nor to review the previous work in this area, which covers a significant subset of the economic literature. The aim is to provide an oriented guide to recent results, through economic examples with geometric interpretations, and to indicate possible fruitful avenues of research