Preference Learning

This report documents the program and the outcomes of Dagstuhl Seminar 14101 “Preference Learning”. Preferences have recently received considerable attention in disciplines such as machine learning, knowledge discovery, information retrieval, statistics, social choice theory, multiple criteria decision making, decision under risk and uncertainty, operations research, and others. The motivation for this seminar was to showcase recent progress in these different areas with the goal of working towards a common basis of understanding, which should help to facilitate future synergies

The 2007 Summer Workshop on Money, Banking and Payments: an overview

The 2007 Summer Workshop on Money, Banking, Payments and Finance met at the Federal Reserve Bank of Cleveland this summer, as we have over the past several years. The following document summarizes and ties together the contributions presented at the workshop this year.Monetary policy ; Monetary theory ; Money ; Banks and banking

Minorities and Storable Votes

The paper studies a simple voting system that has the potential to increase the power of minorities without sacrificing aggregate efficiency. Storable votes grant each voter a stock of votes to spend as desired over a series of binary decisions. By accumulating votes on issues that it deems most important, the minority can win occasionally. But because the majority typically can outvote it, the minority wins only if its strength of preference is high and the majority’s strength of preference is low. The result is that with storable votes, aggregate efficiency either falls little or in fact rises. The theoretical predictions of our model are confirmed by a series of experiments: the frequency of minority victories, the relative payoff of the minority versus the majority, and the aggregate payoffs all match the theory.

Efficient computation of rank probabilities in posets

As the title of this work indicates, the central theme in this work is the computation of rank probabilities of posets. Since the probability space consists of the set of all linear extensions of a given poset equipped with the uniform probability measure, in first instance we develop algorithms to explore this probability space efficiently. We consider in particular the problem of counting the number of linear extensions and the ability to generate extensions uniformly at random. Algorithms based on the lattice of ideals representation of a poset are developed. Since a weak order extension of a poset can be regarded as an order on the equivalence classes of a partition of the given poset not contradicting the underlying order, and thus as a generalization of the concept of a linear extension, algorithms are developed to count and generate weak order extensions uniformly at random as well. However, in order to reduce the inherent complexity of the problem, the cardinalities of the equivalence classes is fixed a priori. Due to the exponential nature of these algorithms this approach is still not always feasible, forcing one to resort to approximative algorithms if this is the case. It is well known that Markov chain Monte Carlo methods can be used to generate linear extensions uniformly at random, but no such approaches have been used to generate weak order extensions. Therefore, an algorithm that can be used to sample weak order extensions uniformly at random is introduced. A monotone assignment of labels to objects from a poset corresponds to the choice of a weak order extension of the poset. Since the random monotone assignment of such labels is a step in the generation process of random monotone data sets, the ability to generate random weak order extensions clearly is of great importance. The contributions from this part therefore prove useful in e.g. the field of supervised classification, where a need for synthetic random monotone data sets is present. The second part focuses on the ranking of the elements of a partially ordered set. Algorithms for the computation of the (mutual) rank probabilities that avoid having to enumerate all linear extensions are suggested and applied to a real-world data set containing pollution data of several regions in Baden-Württemberg (Germany). With the emergence of several initiatives aimed at protecting the environment like the REACH (Registration, Evaluation, Authorisation and Restriction of Chemicals) project of the European Union, the need for objective methods to rank chemicals, regions, etc. on the basis of several criteria still increases. Additionally, an interesting relation between the mutual rank probabilities and the average rank probabilities is proven. The third and last part studies the transitivity properties of the mutual rank probabilities and the closely related linear extension majority cycles or LEM cycles for short. The type of transitivity is translated into the cycle-transitivity framework, which has been tailor-made for characterizing transitivity of reciprocal relations, and is proven to be situated between strong stochastic transitivity and a new type of transitivity called delta*-transitivity. It is shown that the latter type is situated between strong stochastic transitivity and a kind of product transitivity. Furthermore, theoretical upper bounds for the minimum cutting level to avoid LEM cycles are found. Cutting levels for posets on up to 13 elements are obtained experimentally and a theoretic lower bound for the cutting level to avoid LEM cycles of length 4 is computed. The research presented in this work has been published in international peer-reviewed journals and has been presented on international conferences. A Java implementation of several of the algorithms presented in this work, as well as binary files containing all posets on up to 13 elements with LEM cycles, can be downloaded from the website http://www.kermit.ugent.be

Signalling, Incumbency Advantage, and Optimal Reelection Rules

Much literature on political behavior treats politicians as motivated by reelection, choosing actions to signal their types to voters. We identify two novel implications of models in which signalling incentives are important. First, because incumbents only care about clearing a reelection hurdle, signals will tend to cluster just above the threshold needed for reelection. This generates a skew distribution of signals leading to an incumbency advantage in the probability of election. Second, voters can exploit the signalling behavior of politicians by precommitting to a higher threshold for signals received. Raising the threshold discourages signalling effort by low quality politicians but encourages effort by high quality politicians, thus increasing the separation of signals and improving the selection function of an election. This precommitment has a simple institutional interpretation as a supermajority rule, requiring that incumbents exceed some fraction of votes greater than 50% to be reelected.Supermajority, incumbency advantage, signalling

Payment Rules through Discriminant-Based Classifiers

In mechanism design it is typical to impose incentive compatibility and then derive an optimal mechanism subject to this constraint. By replacing the incentive compatibility requirement with the goal of minimizing expected ex post regret, we are able to adapt statistical machine learning techniques to the design of payment rules. This computational approach to mechanism design is applicable to domains with multi-dimensional types and situations where computational efficiency is a concern. Specifically, given an outcome rule and access to a type distribution, we train a support vector machine with a special discriminant function structure such that it implicitly establishes a payment rule with desirable incentive properties. We discuss applications to a multi-minded combinatorial auction with a greedy winner-determination algorithm and to an assignment problem with egalitarian outcome rule. Experimental results demonstrate both that the construction produces payment rules with low ex post regret, and that penalizing classification errors is effective in preventing failures of ex post individual rationality

Essays in applied economic theory

This thesis consists of three essays, all of which use the tools of economic theory to analyze specific situations in which multiple strategic agents interact with each other. The first chapter studies the strategic transmission of information between an informed expert and a decision maker when the latter has access to imperfect private information relevant to the decision. The main insight of the paper is that the access to private information of the decision maker hampers the incentives of the expert to communicate. Surprisingly, in a wide range of environments, the decision maker's information cannot make up for the loss of communication and the welfare of both agents diminishes. The second chapter presents a model of electoral competition between an in- cumbent and a challenger in which the voters receive more information about the quality of the incumbent. If the incumbent can manipulate the information received by the voters through costly effort, the model predicts an incumbency advantage, even though the two candidates are drawn from identical symmetric distributions, and the voters have rational expectations. It is also shown that a supermajority re-election rule improves welfare, mainly through discouraging low-quality politicians from manipulating the information. Finally the third chapter uses a mechanism design approach to characterize the class of social choice functions which cannot be profitably manipulated, when the individuals have symmetric single-peaked preferences. Our result allows for the design of social choice functions to deal with feasibility constraints