Abstract
Collective decision making is the process of mapping the individual views of several individual agents into a joint decision. The need for collective decision making mechanisms is abundant, not just in the realm of politics, but also for a wide range of scientific and technological applications. These include, for instance, logistics, grid computing, and recommender systems. The alternatives to be decided upon often have a combinatorial structure: an alternative is characterised by a tuple of variables, each ranging over a finite domain. Classical approaches to collective decision making, developed in social choice theory, do not take the computational limitations induced by the combinatorial nature of the problem into account. For instance, if we are asked to elect a committee consisting of k representatives, choosing from a pool of n candidates, then we are in fact faced with a social choice problem with \((^n_k)\) alternatives. Asking each voter for their full preferences over these \((^n_k)\) alternatives may not be feasible in practice. Similarly, if we have to choose between accepting or rejecting each of n different propositions, then we are dealing with a social choice problem with 2n possible outcomes.
In this talk I will report on a number of recent developments in the area of collective decision making in combinatorial domains. This includes the study of languages for the compact representation of preferences [2,4], the design of voting rules for multi-issue elections [1], and the analysis of the computational complexity of decision problems arising in judgment aggregation [3].
Chapter PDF
Similar content being viewed by others
References
Airiau, S., Endriss, U., Grandi, U., Porello, D., Uckelman, J.: Aggregating dependency graphs into voting agendas in multi-issue elections. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence, IJCAI 2011 (2011)
Bouveret, S., Endriss, U., Lang, J.: Conditional importance networks: A graphical language for representing ordinal, monotonic preferences over sets of goods. In: Proceedings of the 21st International Joint Conference on Artificial Intelligence, IJCAI 2009 (2009)
Endriss, U., Grandi, U., Porello, D.: Complexity of judgment aggregation. Journal of Artificial Intelligence Research 45, 481–514 (2012)
Uckelman, J., Chevaleyre, Y., Endriss, U., Lang, J.: Representing utility functions via weighted goals. Mathematical Logic Quarterly 55(4), 341–361 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Endriss, U. (2013). Recent Developments in Collective Decision Making in Combinatorial Domains. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-39053-1_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39052-4
Online ISBN: 978-3-642-39053-1
eBook Packages: Computer ScienceComputer Science (R0)