Multi-valued decision rules and coalitional non-manipulability: Two possibility theorems

In this paper we show that under the restriction that the individual's sincere preference orderings are linear (strict), there exists a fairly wide class of coalitionally non-manipulable democratic decision rules. These positive results are established without any restriction on the pairwise choice. It is also shown that the possibility of manipulation even by a single individual arises once he adopts a pessimistic approach in comparing two different sets of outcomes which reflect his attitude to risk.