Sequential voting and agenda manipulation

We study the possibilities for agenda manipulation under strategic voting for two prominent sequential voting procedures, the amendment and the successive procedure. We show that a well-known result for tournaments, namely that the successive procedure is (weakly) more manipulable than the amendment procedure at any given preference profile, extends to arbitrary majority quotas. Moreover, our characterizations of the attainable outcomes for arbitrary quotas allow us to compare the possibilities for manipulation across different quotas. It turns out that the simple majority quota maximizes the domain of preference profiles for which neither procedure is manipulable, but at the same time neither the simple majority quota nor any other quota uniformly minimize the scope of manipulation, once this becomes possible. Hence, quite surprisingly, simple majority voting is not necessarily the optimal choice of a society that is concerned about agenda manipulation.

[1]  Adrian Vermeule,et al.  Submajority Rules: Forcing Accountability Upon Majorities , 2005 .

[2]  Nicholas R. Miller.  A New Solution Set for Tournaments and Majority Voting: Further Graph- Theoretical Approaches to the Theory of Voting , 1980 .

[3]  Nicholas R. Miller.  Committees, Agendas and Voting , 1995 .

[4]  B. Rasch,et al.  Parliamentary Floor Voting Procedures and Agenda Setting in Europe , 2000 .

[5]  J. Banks.  Sophisticated voting outcomes and agenda control , 1984 .

[6]  Matthew O. Jackson,et al.  Equilibrium agenda formation , 2004, Soc. Choice Welf..

[7]  John Duggan,et al.  Endogenous Voting Agendas , 2006, Soc. Choice Welf..

[8]  R. McKelvey,et al.  A multistage game representation of sophisticated voting for binary procedures , 1978 .

[9]  Jean-François Laslier,et al.  Tournament Solutions And Majority Voting , 1997 .

[10]  H. Moulin.  Choosing from a tournament , 1986 .

[11]  Gretlein Rodney J,et al.  DOMINANCE SOLVABLE VOTING SCHEMES: A COMMENT , 1982 .

[12]  Yusufcan Masatlioglu,et al.  A foundation for strategic agenda voting , 2014, Games Econ. Behav..

[13]  Nicholas R. Miller,et al.  Graph- Theoretical Approaches to the Theory of Voting* , 1977 .

[14]  Barry R. Weingast,et al.  Uncovered Sets and Sophisticated Voting Outcomes with Implications for Agenda Institutions , 1984 .

[15]  H. Moulin.  Dominance Solvable Voting Schemes , 1979 .

[16]  S. Barberà,et al.  Sequential Voting and Agenda Manipulation: The Case of Forward Looking Tie-Breaking , 2015 .

[17]  David Austen-Smith,et al.  Positive Political Theory II: Strategy and Structure , 2005 .

[18]  Arnold B. Urken,et al.  Classics of social choice , 1995 .

[19]  Robin Farquharson,et al.  Theory of voting , 1969 .

[20]  Jeffrey S. Banks,et al.  Voting games, indifference, and consistent sequential choice rules , 1988 .