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72
Budgeted Social Choice: From Consensus to Personalized Decision Making
- PROCEEDINGS OF THE TWENTY-SECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... 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 ..."
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Cited by 31 (6 self)
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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.
Parameterized computational complexity of Dodgson and Young elections
, 2007
"... 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- ..."
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Cited by 30 (9 self)
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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
Voting on Multiattribute Domains with Cyclic Preferential Dependencies
"... 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 decomp ..."
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Cited by 25 (11 self)
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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.
Parameterized Complexity of Candidate Control in Elections and Related Digraph Problems
"... 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 t ..."
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Cited by 18 (3 self)
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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
Representing utility functions via weighted goals.
- Mathematical Logic Quarterly,
, 2009
"... Representing utility functions via weighted goals Uckelman, J.D.; Chevaleyre, Y.; Endriss, U.; Lang, J. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, ..."
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Cited by 17 (11 self)
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Representing utility functions via weighted goals Uckelman, J.D.; Chevaleyre, Y.; Endriss, U.; Lang, J. General rights It is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. 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.
Automated search for impossibility theorems in social choice theory: ranking sets of objects’.
- In: Artificial Intelligence Research
, 2011
"... Abstract We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision ..."
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Cited by 16 (8 self)
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Abstract We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important applications in social choice theory and decision making under uncertainty, is how to extend an agent's preferences over a number of objects to a preference relation over nonempty sets of such objects. Certain combinations of seemingly natural principles for this kind of preference extension can result in logical inconsistencies, which has led to a number of important impossibility theorems. We first prove a general result that shows that for a wide range of such principles, characterised by their syntactic form when expressed in a many-sorted first-order logic, any impossibility exhibited at a fixed (small) domain size will necessarily extend to the general case. We then show how to formulate candidates for impossibility theorems at a fixed domain size in propositional logic, which in turn enables us to automatically search for (general) impossibility theorems using a SAT solver. When applied to a space of 20 principles for preference extension familiar from the literature, this method yields a total of 84 impossibility theorems, including both known and nontrivial new results.
Towards a Dichotomy for the Possible Winner Problem in Elections Based on Scoring Rules
, 2010
"... 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 direc ..."
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Cited by 14 (0 self)
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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.
Complexity of Judgment Aggregation: Safety of the Agenda
, 2010
"... 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 t ..."
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Cited by 13 (11 self)
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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.
Fixing a tournament
- In Proceedings of AAAI’10
, 2010
"... We consider a very natural problem concerned with game manipulation. Let G be a directed graph where the nodes represent players of a game, and an edge from u to v means that u can beat v in the game. (If an edge (u, v) is not present, one cannot match u and v.) Given G and a “favorite ” node A, is ..."
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Cited by 13 (5 self)
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We consider a very natural problem concerned with game manipulation. Let G be a directed graph where the nodes represent players of a game, and an edge from u to v means that u can beat v in the game. (If an edge (u, v) is not present, one cannot match u and v.) Given G and a “favorite ” node A, is it possible to set up the bracket of a balanced single-elimination tournament so that A is guaranteed to win, if matches occur as predicted by G? We show that the problem is NPcomplete for general graphs. For the case when G is a tournament graph we give several interesting conditions on the desired winner A for which there exists a balanced single-elimination tournament which A wins, and it can be found in polynomial time.
