Additive representations on rank-ordered sets. I. The algebraic approach

This paper considers additive conjoint measurement on subsets of Cartesian products containing “rank-ordered‘ n-tuples. Contrary to what has often been thought, additive conjoint measurement on subsets of Cartesian products has characteristics different from additive conjoint measurement on full Cartesian products

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Personality in Computational Advertising: A Benchmark

In the last decade, new ways of shopping online have increased the possibility of buying products and services more easily and faster than ever. In this new context, personality is a key determinant in the decision making of the consumer when shopping. A person’s buying choices are influenced by psychological factors like impulsiveness; indeed some consumers may be more susceptible to making impulse purchases than others. Since affective metadata are more closely related to the user’s experience than generic parameters, accurate predictions reveal important aspects of user’s attitudes, social life, including attitude of others and social identity. This work proposes a highly innovative research that uses a personality perspective to determine the unique associations among the consumer’s buying tendency and advert recommendations. In fact, the lack of a publicly available benchmark for computational advertising do not allow both the exploration of this intriguing research direction and the evaluation of recent algorithms. We present the ADS Dataset, a publicly available benchmark consisting of 300 real advertisements (i.e., Rich Media Ads, Image Ads, Text Ads) rated by 120 unacquainted individuals, enriched with Big-Five users’ personality factors and 1,200 personal users’ pictures

Normative foundations of scarcity

The elevation of scarcity to the fundamental economic problem rests on some unstated normative assumptions. These include a political commitment to private property, a methodological commitment to not inquire about taste formation, and the idea that human welfare is roughly equivalent to preference satisfaction.Scarcity; Normative Positive Distinction; Fact Value Distinction; private property; welfare; revealed preference

A network centrality method for the rating problem

We propose a new method for aggregating the information of multiple reviewers rating multiple products. Our approach is based on the network relations induced between products by the rating activity of the reviewers. We show that our method is algorithmically implementable even for large numbers of both products and consumers, as is the case for many online sites. Moreover, comparing it with the simple average, which is mostly used in practice, and with other methods previously proposed in the literature, it performs very well under various dimension, proving itself to be an optimal trade--off between computational efficiency, accordance with the reviewers original orderings, and robustness with respect to the inclusion of systematically biased reports.Comment: 25 pages, 8 figure

Quantum decision making by social agents

The influence of additional information on the decision making of agents, who are interacting members of a society, is analyzed within the mathematical framework based on the use of quantum probabilities. The introduction of social interactions, which influence the decisions of individual agents, leads to a generalization of the quantum decision theory developed earlier by the authors for separate individuals. The generalized approach is free of the standard paradoxes of classical decision theory. This approach also explains the error-attenuation effects observed for the paradoxes occurring when decision makers, who are members of a society, consult with each other, increasing in this way the available mutual information. A precise correspondence between quantum decision theory and classical utility theory is formulated via the introduction of an intermediate probabilistic version of utility theory of a novel form, which obeys the requirement that zero-utility prospects should have zero probability weights.Comment: This paper has been withdrawn by the authors because a much extended and improved version has been submitted as arXiv:1510.02686 under the new title "Role of information in decision making of social agents

Rationality and dynamic consistency under risk and uncertainty

For choice with deterministic consequences, the standard rationality hypothesis is ordinality - i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann{Morgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage's sure thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behaviour in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behavior violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments