Speculative Trade and the Value of Public Information

In environments with expected utility, it has long been established that speculative trade cannot occur (Milgrom and Stokey [1982]), and that the value of public information is negative in economies with risk-sharing and no aggregate uncertainty (Hirshleifer [1971], Schlee [2001]). We show that these results are still true even if we relax expected utility, so that either Dynamic Consistency (DC) or Consequentialism is violated. We characterise no speculative trade in terms of a weakening of DC and find that Consequentialism is not required. Moreover, we show that a weakening of both DC and Consequentialism is sufficient for the value of public information to be negative. We therefore generalise these important results for convex preferences which contain several classes of ambiguity averse preferences

Theorems and unawareness

This paper provides a set-theoretic model of knowledge and unawareness, in which reasoning through theorems is employed. A new property called Awareness Leads to Knowledge shows that unawareness of theorems not only constrains an agent's knowledge, but also, can impair his reasoning about what other agents know. For example, in contrast to Li (2006), Heifetz, Meier, and Schipper (2006) and the standard model of knowledge, it is possible that two agents disagree on whether another agent knows a particular event

Information Aggregation Under Ambiguity: Theory and Experimental Evidence

We study information aggregation in a dynamic trading model with partially informed and ambiguity averse traders. We show theoretically that separable securities, introduced by Ostrovsky (2012) in the context of Subjective Expected Utility, no longer aggregate information if some traders have imprecise beliefs and are ambiguity averse. Moreover, these securities are prone to manipulation, as the degree of information aggregation can be influenced by the initial price, set by the uninformed market maker. These observations are also confirmed in our experiment, using prediction markets. We define a new class of strongly separable securities which are robust to the above considerations, and show that they characterize information aggregation in both strategic and non-strategic environments. We derive several theoretical predictions, which we are able to confirm in the lab

Towards a Theory of Analytical Behaviour: A Model of Decision-Making in Visual Analytics

This paper introduces a descriptive model of the human-computer processes that lead to decision-making in visual analytics. A survey of nine models from the visual analytics and HCI literature are presented to account for different perspectives such as sense-making, reasoning, and low-level human-computer interactions. The survey examines the people and computers (entities) presented in the models, the divisions of labour between entities (both physical and role-based), the behaviour of both people and machines as constrained by their roles and agency, and finally the elements and processes which define the flow of data both within and between entities. The survey informs the identification of four observations that characterise analytical behaviour - defined as decision-making facilitated by visual analytics: bilateral discourse, divisions of labour, mixed-synchronicity information flows, and bounded behaviour. Based on these principles, a descriptive model is presented as a contribution towards a theory of analytical behaviour. The future intention is to apply prospect theory, a economic model of decision-making under uncertainty, to the study of analytical behaviour. It is our assertion that to apply prospect theory first requires a descriptive model of the processes that facilitate decision-making in visual analytics. We conclude it necessary to measure the perception of risk in future work in order to apply prospect theory to the study of analytical behaviour using our proposed model

Representation Effects and Loss Aversion in Analytical Behaviour: An Experimental Study into Decision Making Facilitated by Visual Analytics

This paper presents the results of an experiment into the relationship between the representation of data and decision-making. Three hundred participants online, were asked to choose between a series of financial investment opportunities using data presented in line charts. A single dependent variable of investment choice was examined over four levels of varying display conditions and randomised data. Three variations to line chart visualisations provided a controlled factor between subjects divided into three groups; -˜standard’ line charts, -˜tall’ line charts, and one dual-series line chart. The final results revealed a consistent main effect and two other interactions between certain display conditions and decision-making. The findings of this paper are significant to the study visualisation and to the field of visual analytics. This experiment was devised as part of a study into Analytical Behaviour, defined as decision-making facilitated by visual analytics - a new topic that encompasses existing research and real-world applications

Dynamic Consistency, Valuable Information and Subjective Beliefs

Ambiguity sensitive preferences must fail either Consequentialism or Dynamic Consistency (DC), two properties that are compatible with subjective expected utility and Bayesian updating, while forming the basis of backward induction and dynamic programming. We examine the connection between these properties in a general environment of convex preferences over monetary acts and find that, far from being incompatible, they are connected in an economically meaningful way. In single-agent decision problems, positive value of information characterises one direction of DC. We propose a weakening of DC and show that one direction is equivalent to weakly valuable information, whereas the other characterises the Bayesian updating of the subjective beliefs which are revealed by trading behavior. In financial markets, we characterize no speculative trade, without requiring any form of Consequentialism, and show that there is weakly negative value of public information in risk-sharing environments with no aggregate uncertainty

Design Spaces in Visual Analytics Based on Goals: Analytical Behaviour, Exploratory Investigation, Information Design & Perceptual Tasks

This paper considers a number of perspectives on design spaces in visual analytics and proposes a new set of four design spaces, based on user goals. Three of the user goals are derived from the literature and are categorised under the terms exploratory investigation, perceptual tasks, and information design. The fourth goal is categorised as analytical behaviour; a recently defined term referring to the study of decision-making facilitated by visual analytics. This paper contributes to the literature on decision-making in visual analytics with a survey of real-world applications within the analytical behaviour design space and by providing a new perspective on design spaces. Central to our analysis is the introduction of decision concepts and theories from economics into a visual analytics context. Given the recent interest in decision-making we wanted to understand the emerging topic of analytical behaviour as a design space and found it necessary to look at more than just decision-making to make a valuable contribution. The result is an initial framework suitable for use in the analysis or design of analytical behaviour applications

The relationship between the Jacobi and the successive overrelaxation (SOR) matrices of a k-cyclic matrix

AbstractLet A be a (k−l, l)-generalized consistently ordered matrix with T and Lω its associated Jacobi and SOR matrices whose eigenvalues μ and λ satisfy the well-known relationship (λ+ω−1)k=ωkμkλk−1. For a subclass of the above matrices A we prove that the matrix analogue of the previous relationship holds. Exploiting the matrix relationship we show that the SOR method is equivalent to a certain monoparametric k-step iterative one when used for the solution of the fixed-point problem x=Tx+c