Probabilistic Conditional Preference Networks (UAI 2013)

International audienceThis paper proposes a \probabilistic" extension of conditional preference networks as a way to compactly represent a probability distributions over preference orderings. It studies the probabilistic counterparts of the main reasoning tasks, namely dominance testing and optimisation from the algorithmical and complexity viewpoints. Efficient algorithms for tree-structured probabilistic CP-nets are given. As a by-product we obtain a lineartime algorithm for dominance testing in standard, tree-structured CP-nets

The Complexity of Online Manipulation of Sequential Elections

Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a framework, in which manipulators can see the past votes but not the future ones, to model online coalitional manipulation of sequential elections, and we show that in this setting manipulation can be extremely complex even for election systems with simple winner problems. Yet we also show that for some of the most important election systems such manipulation is simple in certain settings. This suggests that when using sequential voting, one should pay great attention to the details of the setting in choosing one's voting rule. Among the highlights of our classifications are: We show that, depending on the size of the manipulative coalition, the online manipulation problem can be complete for each level of the polynomial hierarchy or even for PSPACE. We obtain the most dramatic contrast to date between the nonunique-winner and unique-winner models: Online weighted manipulation for plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive case) and NP-hard (destructive case) in the unique-winner model. And we obtain what to the best of our knowledge are the first P^NP[1]-completeness and P^NP-completeness results in the field of computational social choice, in particular proving such completeness for, respectively, the complexity of 3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition manipulation of veto elections.Comment: 24 page

On the Hardness of Bribery Variants in Voting with CP-Nets

We continue previous work by Mattei et al. (Mattei, N., Pini, M., Rossi, F., Venable, K.: Bribery in voting with CP-nets. Ann. of Math. and Artif. Intell. pp. 1--26 (2013)) in which they study the computational complexity of bribery schemes when voters have conditional preferences that are modeled by CP-nets. For most of the cases they considered, they could show that the bribery problem is solvable in polynomial time. Some cases remained open---we solve two of them and extend the previous results to the case that voters are weighted. Moreover, we consider negative (weighted) bribery in CP-nets, when the briber is not allowed to pay voters to vote for his preferred candidate.Comment: improved readability; identified Cheapest Subsets to be the enumeration variant of K.th Largest Subset, so we renamed it to K-Smallest Subsets and point to the literatur; some more typos fixe

Efficient minimal preference change

In this article, we study a minimal change approach to preference dynamics. We treat a set of preferences as a special kind of theory, and define minimal change preference contraction and revision operations in the spirit of the Alchourrón, Gärdenfors, and Makinson theory of belief revision. We characterise minimal contraction of preference sets by a set of postulates and prove a representation theorem. We also give a linear time algorithm which implements minimal contraction by a single preference. We then define minimal contraction by a set of preferences, and show that the problem of a minimal contraction by a set of preferences is NP-hard

REPRESENTING AND LEARNING PREFERENCES OVER COMBINATORIAL DOMAINS

Agents make decisions based on their preferences. Thus, to predict their decisions one has to learn the agent\u27s preferences. A key step in the learning process is selecting a model to represent those preferences. We studied this problem by borrowing techniques from the algorithm selection problem to analyze preference example sets and select the most appropriate preference representation for learning. We approached this problem in multiple steps. First, we determined which representations to consider. For this problem we developed the notion of preference representation language subsumption, which compares representations based on their expressive power. Subsumption creates a hierarchy of preference representations based solely on which preference orders they can express. By applying this analysis to preference representation languages over combinatorial domains we found that some languages are better for learning preference orders than others. Subsumption, however, does not tell the whole story. In the case of languages which approximate each other (another piece of useful information for learning) the subsumption relation cannot tell us which languages might serve as good approximations of others. How well one language approximates another often requires customized techniques. We developed such techniques for two important preference representation languages, conditional lexicographic preference models (CLPMs) and conditional preference networks (CP-nets). Second, we developed learning algorithms for highly expressive preference representations. To this end, we investigated using simulated annealing techniques to learn both ranking preference formulas (RPFs) and preference theories (PTs) preference programs. We demonstrated that simulated annealing is an effective approach to learn preferences under many different conditions. This suggested that more general learning strategies might lead to equally good or even better results. We studied this possibility by considering artificial neural networks (ANNs). Our research showed that ANNs can outperform classical models at deciding dominance, but have several significant drawbacks as preference reasoning models. Third, we developed a method for determining which representations match which example sets. For this classification task we considered two methods. In the first method we selected a series of features and used those features as input to a linear feed-forward ANN. The second method converts the example set into a graph and uses a graph convolutional neural network (GCNN). Between these two methods we found that the feature set approach works better. By completing these steps we have built the foundations of a portfolio based approach for learning preferences. We assembled a simple version of such a system as a proof of concept and tested its usefulness

CP-nets: From Theory to Practice

Conditional preference networks (CP-nets) exploit the power of ceteris paribus rules to represent preferences over combinatorial decision domains compactly. CP-nets have much appeal. However, their study has not yet advanced sufficiently for their widespread use in real-world applications. Known algorithms for deciding dominance---whether one outcome is better than another with respect to a CP-net---require exponential time. Data for CP-nets are difficult to obtain: human subjects data over combinatorial domains are not readily available, and earlier work on random generation is also problematic. Also, much of the research on CP-nets makes strong, often unrealistic assumptions, such as that decision variables must be binary or that only strict preferences are permitted. In this thesis, I address such limitations to make CP-nets more useful. I show how: to generate CP-nets uniformly randomly; to limit search depth in dominance testing given expectations about sets of CP-nets; and to use local search for learning restricted classes of CP-nets from choice data