Social choice theory, belief merging, and strategy-proofness

Intelligent agents have to be able to merge informational inputs received from different sources in a coherent and rational way. Several proposals have been made for information merging in which it is possible to encode the preferences of sources [5], [4], [19], [24], [25] and [1]. Information merging has much in common with social choice theory, which aims to define operations reflecting the preferences of a society from the individual preferences of the members of the society. Given this connection, frameworks for information merging should provide satisfactory resolutions of problems raised in social choice theory. We investigate the link between the merging of epistemic states and some results in social choice theory. This is achieved by providing a consistent set of properties—akin to those used in Arrow’s theorem [2]—for merging. It is shown that in this framework there is no Arrow-like impossibility result. By extending this to a consistent framework which includes properties corresponding to the notion of being strategy-proof, we show that results due to Gibbard and Satterthwaite [13], [31] and [32] and others [6] and [3] do not hold in merging frameworks.