Abstract. We show that, other than for standard complexity theory with known NP-completeness results, the computational complexity of the Dodgson and Young election systems is completely different from a parameterized complexity point of view. That is, on the one hand, we present an efficient fixed-parameter algorithm for determining a Condorcet winner in Dodgson elections by a minimum number of switches in the votes. On the other hand, we prove that the corresponding problem for Young elections, where one has to delete votes instead of performing switches, is W[2]-complete. In addition, we study Dodgson elections that allow ties between the candidates and give fixed-parameter tractability as well as W[2]-hardness results depending on the cost model for switching ties. 1

In group decision making, often the agents need to decide on multiple attributes at the same time, so that there are exponentially many alternatives. In this case, it is unrealistic to ask agents to communicate a full ranking of all the alternatives. To address this, earlier work has proposed decomposing such voting processes by using local voting rules on the individual attributes. Unfortunately, the existing methods work only with rather severe domain restrictions, as they require the voters’ preferences to extend acyclic CP-nets compatible with a common order on the attributes. We first show that this requirement is very restrictive, by proving that the number of linear orders extending an acyclic CP-net is exponentially smaller than the number of all linear orders. Then, we introduce a very general methodology that allows us to aggregate preferences when voters express CP-nets that can be cyclic. There does not need to be any common structure among the submitted CP-nets. Our methodology generalizes the earlier, more restrictive methodology. We study whether properties of the local rules transfer to the global rule, and vice versa. We also address how to compute the winning alternatives.

Key words Preference representation, computational complexity, computational social choice. We analyze the expressivity, succinctness, and complexity of a family of languages based on weighted propositional formulas for the representation of utility functions. The central idea underlying this form of preference modeling is to associate numerical weights with goals specified in terms of propositional formulas, and to compute the utility value of an alternative as the sum of the weights of the goals it satisfies. We define a large number of representation languages based on this idea, each characterized by a set of restrictions on the syntax of formulas and the range of weights. Our aims are threefold. First, for each language we try to identify the class of utility functions it can express. Second, when different languages can express the same class of utility functions, one may allow for a more succinct representation than another. Therefore, we analyze the relative succinctness of languages. Third, for each language we study the computational complexity of the problem of finding the most preferred alternative given a utility function expressed in that language. c ○ 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1

Aggregating the judgments of a group of agents regarding a set of interdependent propositions can lead to inconsistent outcomes. One of the parameters involved is the agenda, the set of propositions on which agents are asked to express an opinion. We introduce the problem of checking the safety of the agenda: for a given agenda, can we guarantee that judgment aggregation will never produce an inconsistent outcome for any aggregation procedure satisfying a given set of axioms? We prove several characterisation results, establishing necessary and sufficient conditions for the safety of the agenda for different combinations of the most important axioms proposed in the literature, and we analyse the computational complexity of checking whether a given agenda satisfies these conditions.

To make a joint decision, agents (or voters) are often required to provide their preferences as linear orders. To determine a winner, the given linear orders can be aggregated according to a voting protocol. However, in realistic settings, the voters may often only provide partial orders. This directly leads to the POSSIBLE WINNER problem that asks, given a set of partial votes, whether a distinguished candidate can still become a winner. In this work, we consider the computational complexity of POSSIBLE WINNER for the broad class of voting protocols defined by scoring rules. A scoring rule provides a score value for every position which a candidate can have in a linear order. Prominent examples include plurality, k-approval, and Borda. Generalizing previous NP-hardness results for some special cases, we settle the computational complexity for all but one scoring rule. More precisely, for an unbounded number of candidates and unweighted voters, we show that POSSIBLE WINNER is NP-complete for all pure scoring rules except plurality, veto, and the scoring rule defined by the scoring vector (2, 1,...,1, 0), while it is solvable in polynomial time for plurality and veto.

Abstract. There are different ways for an external agent to influence the outcome of an election. We concentrate on “control ” by adding or deleting candidates of an election. Our main focus is to investigate the parameterized complexity of various control problems for different voting systems. To this end, we introduce natural digraph problems that may be of independent interest. They help in determining the parameterized complexity of control for different voting systems including Llull, Copeland, and plurality votings. Devising several parameterized reductions, we provide a parameterized complexity overview of the digraph and control problems with respect to natural parameters. 1

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We develop a general framework for social choice problems in which a limited number of alternatives can be recommended to an agent population. In our budgeted social choice model, this limit is determined by a budget, capturing problems that arise naturally in a variety of contexts, and spanning the continuum from pure consensus decision making (i.e., standard social choice) to fully personalized recommendation. Our approach applies a form of segmentation to social choice problems— requiring the selection of diverse options tailored to different agent types—and generalizes certain multi-winner election schemes. We show that standard rank aggregation methods perform poorly, and that optimization in our model is NP-complete; but we develop fast greedy algorithms with some theoretical guarantees. Experiments on real-world datasets demonstrate the effectiveness of our algorithms.

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multi-agent systems is becoming more and more important [1, 2]. Multi-agent systems are generally accepted as valuable tools for designing and building distributed dynamical systems, by using several interacting agents, possibly including humans. In practice, multi-agent systems are often performing tasks in co-operation with, or instead of humans. Examples include software agents participating in online auctions or bargaining [3, 4], electronic institutions [5], developing schedules for air traffic [6] and decentralized resource distribution in large storage facilities [7, 8]. Although multi-agent systems have many potential advantages, designing them raises many difficulties. One of the key problems lies in controlling the behavior of individual agents in such a way that the system as a whole reaches a certain goal. This problem becomes even more prominent in multi-agent systems that interact with humans. Usually, multi-agent systems are designed assuming