Social choice theory, belief merging and elections

Intelligent agents have to be able to merge inputs received from different sources in a coherent and rational way. Several proposals have been made for the merging of structures in which it is possible to encode the preferences of sources [5, 4, 12, 16, 17, 1]. Information merging has much in common with the goals of social choice theory: to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection it seems reasonable to require that any framework for the merging of information provide satisfactory ways of dealing with the problems raised in social choice theory. We investigate the link between the merging of epistemic states and two important results in social choice theory. We show that Arrow’s well-known impossibility theorem [2] can be circumvented when the preferences of sources are represented in terms of epistemic states. This is achieved by providing a consistent set of properties for merging from which Arrow-like properties can be derived. We extend this to a consistent framework which includes properties corresponding to the notion of being strategy-proof. The existence of such an extended framework can be seen as a circumvention of the impossibility result of Gibbard and Satterthwaite [8, 21, 22] and related results [6, 3].