Strategic voting and the logic of knowledge

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.

[1]  Rohit Parikh,et al.  Knowledge-Theoretic Properties of Strategic Voting , 2004, JELIA.

[2]  Andreas Witzel,et al.  The Power of Knowledge in Games , 2013, IGTR.

[3]  J. Benthem.  Games in dynamic epistemic logic , 2001 .

[4]  Jan van Eijck,et al.  Logics of communication and change , 2006, Inf. Comput..

[5]  Lirong Xia,et al.  Sequential composition of voting rules in multi-issue domains , 2009, Math. Soc. Sci..

[6]  Arkadii M. Slinko,et al.  Is it ever safe to vote strategically? , 2014, Soc. Choice Welf..

[8]  A. Gibbard.  Manipulation of Voting Schemes: A General Result , 1973 .

[9]  Salvador Barberà,et al.  Strategy-Proof Probabilistic Rules for Expected Utility Maximizers , 1998 .

[10]  Edith Elkind,et al.  Equilibria of plurality voting with abstentions , 2010, EC '10.

[11]  John Duggan,et al.  Strategic manipulability without resoluteness or shared beliefs: Gibbard-Satterthwaite generalized , 2000, Soc. Choice Welf..

[12]  Alexandru Baltag,et al.  A qualitative theory of dynamic interactive belief revision , 2008 .

[13]  John C. Harsanyi,et al.  Games with Incomplete Information Played by "Bayesian" Players, I-III: Part I. The Basic Model& , 2004, Manag. Sci..

[14]  Vincent Conitzer,et al.  Dominating Manipulations in Voting with Partial Information , 2011, AAAI.

[15]  Ariel Rubinstein,et al.  A Course in Game Theory , 1995 .

[16]  Wiebe van der Hoek,et al.  Dynamic epistemic logic with assignment , 2005, AAMAS '05.

[17]  R. Aumann,et al.  Epistemic Conditions for Nash Equilibrium , 1995 .

[18]  M. Satterthwaite.  Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions , 1975 .

[19]  D. Bergemann,et al.  Robust Mechanism Design , 2003 .

[20]  Vincent Conitzer,et al.  Stackelberg Voting Games: Computational Aspects and Paradoxes , 2010, AAAI.

[21]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[22]  Fenrong Liu,et al.  Reasoning about Preference Dynamics , 2011 .

[23]  Jan A. Plaza,et al.  Logics of public communications , 2007, Synthese.

[24]  M. Trick,et al.  The computational difficulty of manipulating an election , 1989 .

[25]  J. Harsanyi.  Games with Incomplete Information Played by 'Bayesian' Players, Part III. The Basic Probability Distribution of the Game , 1968 .

[26]  Jérôme Lang,et al.  Voting procedures with incomplete preferences , 2005 .

[27]  Barteld Kooi,et al.  Dynamic Epistemic Logic , 2013 .

[28]  Wojciech Jamroga,et al.  Agents that Know How to Play , 2004, Fundam. Informaticae.

[29]  Michael A. Trick,et al.  How hard is it to control an election? Math , 1992 .

[30]  Sarit Kraus,et al.  On the evaluation of election outcomes under uncertainty , 2008, Artif. Intell..

[31]  Hans van Ditmarsch,et al.  What will they say?—Public Announcement Games , 2011, Synthese.