Department of Mathematics

Voting procedures

Voting is an indispensable part of the democratic process and in general, an important tool that is used whenever a group of agents needs to make a joint decision that in some way accommodates preferences of all the participants.


Elections can be single-winner, eg, when we need to select a president and multi-winner, eg, when we need to elect a parliament, and each type has its own problems.

A famous result of Kenneth Arrow (1951) shows that there is no truly perfect single-winner voting system that satisfies a simple set of desired properties. This explains why, throughout history, people have come up with a great number of very diverse election methods, each with its own set of advantages and flaws. In addition to this, another famous result proved by Gibbard (1973) and Satterthwaite (1975) state that every non-dictatorial voting rule is vulnerable to strategic voting. Some of the voting systems, especially for multi-winner elections, are very complex to implement.

One goal of this project is to analyse and classify voting rules according to their properties and complexity of their implementation. Another is the use of complexity for protection against any abuse of democratic procedures by agents. Since voting rules are prototypes for many aggregation procedures, this also illuminates problems faced by economics and decision sciences in general.

Selected recent publications


  • Robin Christian, Mike Fellows, Fran Rosamond and Arkadii Slinko. On Complexity of Lobbying in Multiple Referenda, Review of Economic Design, 2007, 11(3): 217--224.
  • Arkadii Slinko and Shaun White. On the manipulability of proportional representation, Journal of Theoretical Politics, 2010, 22(3): 1–32.
  • Edith Elkind, Piotr Faliszewski, Arkadii M. Slinko. Cloning in Elections. Journal of Artificial Intelligence Research, 2011, 42: 529-573.
  • Edith Elkind, Piotr Faliszewski, Arkadii M. Slinko: Clone structures in voters’ preferences. EC '12 Proceedings of the 13th ACM Conference on Electronic Commerce 2012:496-513, ACM, New York, NY.
  • Nadja Betzler, Johannes Ulhman and Arkadii Slinko. On the computation of fully proportional representation. Journal of Artificial Intelligence Research, 2013 47: 475--519.
  • Arkadii Slinko and Shaun White. Is it ever safe to vote strategically? Social Choice and Welfare, 2013, 10.1007/s00355-013-0785-4,  pp.1-25.

Researchers at The University of Auckland


External collaborators