Recognising Multidimensional Euclidean Preferences

Euclidean preferences are a widely studied preference model, in which decision makers and alternatives are embedded in d-dimensional Euclidean space. Decision makers prefer those alternatives closer to them. This model, also known as multidimensional unfolding, has applications in economics, psychometrics, marketing, and many other fields. We study the problem of deciding whether a given preference profile is d-Euclidean. For the one-dimensional case, polynomial-time algorithms are known. We show that, in contrast, for every other fixed dimension d > 1, the recognition problem is equivalent to the existential theory of the reals (ETR), and so in particular NP-hard. We further show that some Euclidean preference profiles require exponentially many bits in order to specify any Euclidean embedding, and prove that the domain of d-Euclidean preferences does not admit a finite forbidden minor characterisation for any d > 1. We also study dichotomous preferencesand the behaviour of other metrics, and survey a variety of related work.Comment: 17 page

Quantum-like Representation of Extensive Form Games: Wine Testing Game

We consider an application of the mathematical formalism of quantum mechanics (QM) outside physics, namely, to game theory. We present a simple game between macroscopic players, say Alice and Bob (or in a more complex form - Alice, Bob and Cecilia), which can be represented in the quantum-like (QL) way -- by using a complex probability amplitude (game's ``wave function'') and noncommutative operators. The crucial point is that games under consideration are so called extensive form games. Here the order of actions of players is important, such a game can be represented by the tree of actions. The QL probabilistic behavior of players is a consequence of incomplete information which is available to e.g. Bob about the previous action of Alice. In general one could not construct a classical probability space underlying a QL-game. This can happen even in a QL-game with two players. In a QL-game with three players Bell's inequality can be violated. The most natural probabilistic description is given by so called contextual probability theory completed by the frequency definition of probability

Structure in Dichotomous Preferences

Many hard computational social choice problems are known to become tractable when voters' preferences belong to a restricted domain, such as those of single-peaked or single-crossing preferences. However, to date, all algorithmic results of this type have been obtained for the setting where each voter's preference list is a total order of candidates. The goal of this paper is to extend this line of research to the setting where voters' preferences are dichotomous, i.e., each voter approves a subset of candidates and disapproves the remaining candidates. We propose several analogues of the notions of single-peaked and single-crossing preferences for dichotomous profiles and investigate the relationships among them. We then demonstrate that for some of these notions the respective restricted domains admit efficient algorithms for computationally hard approval-based multi-winner rules.Comment: A preliminary version appeared in the proceedings of IJCAI 2015, the International Joint Conference on Artificial Intelligenc

A fuzzy hierarchical multiple criteria group decision support system - Decider - and its applications

Decider is a Fuzzy Hierarchical Multiple Criteria Group Decision Support System (FHMC-GDSS) designed for dealing with subjective, in particular linguistic, information and objective information simultaneously to support group decision making particularly on evaluation. In this chapter, the fuzzy aggregation decision model, functions and structure of Decider are introduced. The ideas to resolve decision and evaluation problems we have faced in the development and application of Decider are presented. Two real applications of the Decider system are briefly illustrated. Finally, we discuss our further research in this area. © 2011 Springer-Verlag Berlin Heidelberg

Eliciting New Wikipedia Users' Interests via Automatically Mined Questionnaires: For a Warm Welcome, Not a Cold Start

Every day, thousands of users sign up as new Wikipedia contributors. Once joined, these users have to decide which articles to contribute to, which users to seek out and learn from or collaborate with, etc. Any such task is a hard and potentially frustrating one given the sheer size of Wikipedia. Supporting newcomers in their first steps by recommending articles they would enjoy editing or editors they would enjoy collaborating with is thus a promising route toward converting them into long-term contributors. Standard recommender systems, however, rely on users' histories of previous interactions with the platform. As such, these systems cannot make high-quality recommendations to newcomers without any previous interactions -- the so-called cold-start problem. The present paper addresses the cold-start problem on Wikipedia by developing a method for automatically building short questionnaires that, when completed by a newly registered Wikipedia user, can be used for a variety of purposes, including article recommendations that can help new editors get started. Our questionnaires are constructed based on the text of Wikipedia articles as well as the history of contributions by the already onboarded Wikipedia editors. We assess the quality of our questionnaire-based recommendations in an offline evaluation using historical data, as well as an online evaluation with hundreds of real Wikipedia newcomers, concluding that our method provides cohesive, human-readable questions that perform well against several baselines. By addressing the cold-start problem, this work can help with the sustainable growth and maintenance of Wikipedia's diverse editor community.Comment: Accepted at the 13th International AAAI Conference on Web and Social Media (ICWSM-2019

CAN HYPOTHETICAL, QUESTIONS PREDICT ACTUAL, PARTICIPATION IN PUBLIC PROGRAMS? A FIELD VALIDITY TEST USING A PROVISION POINT MECHANISM

Niagara Mohawk Power Corporation utilized a demand revealing public good mechanism to implement a green electricity program for provision of renewable energy and planting trees. This GreenChoiceTM program provided an opportunity to test the reliability of contingent valuation for predicting actual participation levels. In this study, participation levels predicted by hypothetical open-ended and dichotomous choice questions are compared to a reference level obtained from the actual GreenChoiceTM program. This approach represents an important improvement over past public goods contingent valuation validity tests which have relied on voluntary contribution mechanisms to elicit actual willingness to pay, and thus are likely to overestimate hypothetical bias because of free riding. Yet, even with a demand revealing mechanism and controlling for awareness, hypothetical participation levels obtained from dichotomous choice responses are found to significantly exceed actual contributions. In contrast, open-ended responses predict actual contribution levels, in that hypothetical open-ended responses are not significantly different from actual responses. Calibration of hypothetical responses is also explored.Public Economics, Resource /Energy Economics and Policy,

Neural coding strategies and mechanisms of competition

A long running debate has concerned the question of whether neural representations are encoded using a distributed or a local coding scheme. In both schemes individual neurons respond to certain specific patterns of pre-synaptic activity. Hence, rather than being dichotomous, both coding schemes are based on the same representational mechanism. We argue that a population of neurons needs to be capable of learning both local and distributed representations, as appropriate to the task, and should be capable of generating both local and distributed codes in response to different stimuli. Many neural network algorithms, which are often employed as models of cognitive processes, fail to meet all these requirements. In contrast, we present a neural network architecture which enables a single algorithm to efficiently learn, and respond using, both types of coding scheme

Getting beyond the surface : using geometric data analysis in cultural sociology

Geometric Data Analysis (GDA) refers to a group of statistical techniques that disclose underlying patterns in categorized data. GDA represents categories of variables and individuals as points in a multi-dimensional Euclidean space. This contribution presents some of GDA’s analytic properties and their connection to a relational approach of the social world. Moreover, the potential of GDA for cultural sociology will be discussed. What does GDA add to insights based on ‘orthodox’ correlational techniques and exactly how does it get beyond the surface of things? Research on the association between cultural consumption and socio-economic background will serve as an illustration

Using ICT to enhance student understanding of classification

It is common for 13-year-old students in Victoria, Australia to learn how to classify animals and plants using the Linnaean system and dichotomous keys. This is usually done with text based research on the major groups of animals and plants and a few simple exercises with various objects to explain the underlying concept of classification. In this paper we describe our attempt to achieve similar goals using three computer software programs to build dichotomous keys and represent the data: Inspiration, MS PowerPoint, and MicroWorlds. Student work is included to illustrate what can be achieved by students of various abilities with these information and communication technologies