Abstract
Transferir preferencias sobre candidatos a preferencias sobre conjuntos de candidatos permite dar una noción muy natural de manipulación para funciones de elección social. En este trabajo damos condiciones sobre esas funciones de transferencia que implican la manipulabilidad de funciones de elección social con un mínimo de propiedades razonables. Nuestro resultado es una versión débil del teorema de Barberà y Kelly, de hecho puede ser obtenido como una consecuencia de éste. Sin embargo, damos una prueba directa y natural de nuestro teorema de manipulabilidad, la cual da una información clara sobre la naturaleza de las funciones de transferencia que permiten la manipulación.
Highlights
Studying preferences is a common issue in different domains: Decision Making under Uncertainty [18, 17], Merging Information in Logical Frameworks [34, 35, 36], Knowledge Representation [13], Belief Dynamics [1], Social Choice [2, 41], etc
Which are the properties of social choice functions that guarantee they are free of manipulation? This is the issue addressed in the current work
Notice that if f : P n × P∗(X) −→ P∗(X) is a social choice function satisfying the Strong Standard Domain Condition (SSD) and Transitive Explanations (TE), f has a weak dictator or f is manipulable with respect to the leximax-precise lifting, the Egli-Milner lifting, the Fishburn lifting, the Gardenfors lifting, and the Kelly lifting
Summary
Studying preferences is a common issue in different domains: (qualitative) Decision Making under Uncertainty [18, 17], Merging Information in Logical Frameworks [34, 35, 36], Knowledge Representation [13], Belief Dynamics [1], Social Choice [2, 41], etc. Via this common issue, preferences, there are some interesting problems which can be translated from one domain to another [35, 25]. The surprising result of Arrow [2, 32, 46], known as Arrow’s Impossibility Theorem, says that there are no such functions (in Section 2 we find the precise formulation)
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