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Preventing Manipulation by Restricting Information

It was shown in the last chapter that computational complexity does not seem to be a very strong barrier against manipulation. Consequently, we need to look for new barriers. In this chapter we examine some preliminary ideas to prevent manipulation for the cases where there is one manipulator, by restricting the manipulator’s information about the other voters’ votes. We recall that in all previously studied manipulation problems, it is normally assumed that the manipulator has full information about the votes of the non-manipulators. The argument often given is that if it is NP-hard with full information, then it only can be at least as computationally difficult with partial information. However, when there is only one manipulator, computing a manipulation is in P for most common voting rules, including all positional scoring rules, Copeland, maximin, and voting trees (see Table 3.1). The only known exceptions are STV (Bartholdi and Orlin, 1991), ranked pairs (Xia et al., 2009), and Nanson’s and Baldwin’s rules (Narodytska et al., 2011). It is not clear whether it is computationally easy for a single manipulator to find a manipulation when she only has partial information for other rules.