Strategic voting and the logic of knowledge (Extended Abstract)
Hans van Ditmarsch, Jérôme Lang, Abdallah Saffidine · 2012
A well-known fact in social choice theory is that strategic voting, also known as manipulation, becomes harder when voters know less about the preferences or votes of other voters. Standard approaches to manipulation in social choice theory [6] as well as in computational social choice [3] assume that the manipulating voter or the manipulating coalition knows perfectly how the other voters will vote. Some approaches [2] assume that voters have a probabilistic prior belief on the outcome of the vote, which encompasses the case where each voter has a probability distribution over the set of profiles. A recent paper [5] extends coalitional manipulation to incomplete knowledge, by distinguishing manipulating from non-manipulating voters and by considering that the manipulating coalition has, for each voter outside the coalition, a set of possible votes encoded in the form of a partial order over candidates. Uncertainty of voters about the uncertainties of other voters, i.e., higher-order beliefs of voters, has not been treated in full generality. We model how uncertainty about the preferences of other voters may determine a strategic vote, and how a reduction in this uncertainty may change a strategic vote. A link between epistemic logic and voting has been given in [4]—they use knowledge graphs to indicate that a voter is uncertain about the preference of another voter. A more recent approach, within the area known as social software, is [8]. The recent [5] walks a middle way namely where equivalence classes are called information sets, as in treatments of knowledge and uncertainty in economics, but where the uncertain voter, or coalition, does not take the uncertainty of other voters into account.