Use of aggregation functions in decision making

A key component of many decision making processes is the aggregation step, whereby a set of numbers is summarised with a single representative value. This research showed that aggregation functions can provide a mathematical formalism to deal with issues like vagueness and uncertainty, which arise naturally in various decision contexts.

The differential effects of *American and British trial proceedings on juror decision-making

Seven basic elements differentiate British from American trial procedures: confining attorneys to their tables; dealing with objections outside the presence of the jury; resolving disagreements between attorneys prior to objections being made; presenting the defense opening statement at the close of the prosecution case; the judge directly questions witnesses and has a wider latitude in controlling the evidence; and the judge gives a summation of all the evidence presented to the jury (Fulero & Turner, 1997). The present experiment examined the influence of these different courtroom procedures, judges' non-verbal behavior, and evidence strength on juror decision-making. Using models of persuasion to understand how the varying elements may effect juror decision-making, it was predicted that trials following American courtroom procedures would be more distracting for jurors and as such, they would be more likely to rely on the peripheral cue of the judge's expectations for trial outcome as expressed in his nonverbal behavior. In trials following British procedures jurors should be less distracted and better able to scrutinize the strength of the evidence that in turn should minimize the influence of the judge's nonverbal behavior. Two hundred forty-five participants viewed a mock civil trial in which courtroom procedure, judge's nonverbal behavior, and evidence strength were varied. Analyses suggest that courtroom procedure and evidence strength influenced the direction of participants' verdicts, but that judge's nonverbal behavior did not have a direct impact on verdict preference. Judge's nonverbal behavior appeared to influence other measures related to verdict. Participants were more confident in their verdicts when they agreed with judge's nonverbal behavior and when they viewed British courtroom procedures. Participants were more likely to return estimates of the defendant's liability that reflected judge's nonverbal behavior and a congruency with evidence strength. Participants also recalled more facts in the British conditions than in the American conditions. These findings are interpreted as indicating the importance of the impact of trial procedures and of nonverbal influence. ^

The Learning of the Mathematical Models to Aid Decision Making in the High Level Engineering Schools?

At present, in the University curricula in most countries, the decision theory and the mathematical models to aid decision making is not included, as in the graduate program like in Doctored and Master´s programs. In the Technical School of High Level Agronomic Engineers of the Technical University of Madrid (ETSIA-UPM), the need to offer to the future engineers training in a subject that could help them to take decisions in their profession was felt. Along the life, they will have to take a lot of decisions. Ones, will be important and others no. In the personal level, they will have to take several very important decisions, like the election of a career, professional work, or a couple, but in the professional field, the decision making is the main role of the Managers, Politicians and Leaders. They should be decision makers and will be paid for it. Therefore, nobody can understand that such a professional that is called to practice management responsibilities in the companies, does not take training in such an important matter. For it, in the year 2000, it was requested to the University Board to introduce in the curricula an optional qualified subject of the second cycle with 4,5 credits titled " Mathematical Methods for Making Decisions ". A program was elaborated, the didactic material prepared and programs as Maple, Lingo, Math Cad, etc. installed in several IT classrooms, where the course will be taught. In the course 2000-2001 this subject was offered with a great acceptance that exceeded the forecasts of capacity and had to be prepared more classrooms. This course in graduate program took place in the Department of Applied Mathematics to the Agronomic Engineering, as an extension of the credits dedicated to Mathematics in the career of Engineering.

Global analysis of dynamical decision-making models through local computation around the hidden saddle

Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity. © 2012 Trotta et al.

Knowledge gain or system benefit in environmental decision making?

The quality of environmental decisions are gauged according to the management objectives of a conservation project. Management objectives are generally about maximising some quantifiable measure of system benefit, for instance population growth rate. They can also be defined in terms of learning about the system in question, in such a case actions would be chosen that maximise knowledge gain, for instance in experimental management sites. Learning about a system can also take place when managing practically. The adaptive management framework (Walters 1986) formally acknowledges this fact by evaluating learning in terms of how it will improve management of the system and therefore future system benefit. This is taken into account when ranking actions using stochastic dynamic programming (SDP). However, the benefits of any management action lie on a spectrum from pure system benefit, when there is nothing to be learned about the system, to pure knowledge gain. The current adaptive management framework does not permit management objectives to evaluate actions over the full range of this spectrum. By evaluating knowledge gain in units distinct to future system benefit this whole spectrum of management objectives can be unlocked. This paper outlines six decision making policies that differ across the spectrum of pure system benefit through to pure learning. The extensions to adaptive management presented allow specification of the relative importance of learning compared to system benefit in management objectives. Such an extension means practitioners can be more specific in the construction of conservation project objectives and be able to create policies for experimental management sites in the same framework as practical management sites.

Assessing testamentary and decision-making capacity: Approaches and models

The need for better and more accurate assessments of testamentary and decision-making capacity grows as Australian society ages and incidences of mentally disabling conditions increase. Capacity is a legal determination, but one on which medical opinion is increasingly being sought. The difficulties inherent within capacity assessments are exacerbated by the ad hoc approaches adopted by legal and medical professionals based on individual knowledge and skill, as well as the numerous assessment paradigms that exist. This can negatively affect the quality of assessments, and results in confusion as to the best way to assess capacity. This article begins by assessing the nature of capacity. The most common general assessment models used in Australia are then discussed, as are the practical challenges associated with capacity assessment. The article concludes by suggesting a way forward to satisfactorily assess legal capacity given the significant ramifications of getting it wrong.

Leibniz on Rational Decision-Making

In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality.

Sequential decision making in general state space models

Many problems in control and signal processing can be formulated as sequential decision problems for general state space models. However, except for some simple models one cannot obtain analytical solutions and has to resort to approximation. In this thesis, we have investigated problems where Sequential Monte Carlo (SMC) methods can be combined with a gradient based search to provide solutions to online optimisation problems. We summarise the main contributions of the thesis as follows. Chapter 4 focuses on solving the sensor scheduling problem when cast as a controlled Hidden Markov Model. We consider the case in which the state, observation and action spaces are continuous. This general case is important as it is the natural framework for many applications. In sensor scheduling, our aim is to minimise the variance of the estimation error of the hidden state with respect to the action sequence. We present a novel SMC method that uses a stochastic gradient algorithm to find optimal actions. This is in contrast to existing works in the literature that only solve approximations to the original problem. In Chapter 5 we presented how an SMC can be used to solve a risk sensitive control problem. We adopt the use of the Feynman-Kac representation of a controlled Markov chain flow and exploit the properties of the logarithmic Lyapunov exponent, which lead to a policy gradient solution for the parameterised problem. The resulting SMC algorithm follows a similar structure with the Recursive Maximum Likelihood(RML) algorithm for online parameter estimation. In Chapters 6, 7 and 8, dynamic Graphical models were combined with with state space models for the purpose of online decentralised inference. We have concentrated more on the distributed parameter estimation problem using two Maximum Likelihood techniques, namely Recursive Maximum Likelihood (RML) and Expectation Maximization (EM). The resulting algorithms can be interpreted as an extension of the Belief Propagation (BP) algorithm to compute likelihood gradients. In order to design an SMC algorithm, in Chapter 8 uses a nonparametric approximations for Belief Propagation. The algorithms were successfully applied to solve the sensor localisation problem for sensor networks of small and medium size.

Delayed decision-making in bistable models

Switching between two modes of operation is a common property of biological systems. In continuous-time differential equation models, this is often realised by bistability, i.e. the existence of two asymptotically stable steadystates. Several biological models are shown to exhibit delayed switching, with a pronounced transient phase, in particular for near-threshold perturbations. This study shows that this delay in switching from one mode to the other in response to a transient input is reflected in local properties of an unstable saddle point, which has a one dimensional unstable manifold with a significantly slower eigenvalue than the stable ones. Thus, the trajectories first approximatively converge to the saddle point, then linger along the saddle's unstable manifold before quickly approaching one of the stable equilibria. ©2010 IEEE.

Neural Models of Motion Integration, Segmentation, and Probablistic Decision-Making

When brain mechanism carry out motion integration and segmentation processes that compute unambiguous global motion percepts from ambiguous local motion signals? Consider, for example, a deer running at variable speeds behind forest cover. The forest cover is an occluder that creates apertures through which fragments of the deer's motion signals are intermittently experienced. The brain coherently groups these fragments into a trackable percept of the deer in its trajectory. Form and motion processes are needed to accomplish this using feedforward and feedback interactions both within and across cortical processing streams. All the cortical areas V1, V2, MT, and MST are involved in these interactions. Figure-ground processes in the form stream through V2, such as the seperation of occluding boundaries of the forest cover from the boundaries of the deer, select the motion signals which determine global object motion percepts in the motion stream through MT. Sparse, but unambiguous, feauture tracking signals are amplified before they propogate across position and are intergrated with far more numerous ambiguous motion signals. Figure-ground and integration processes together determine the global percept. A neural model predicts the processing stages that embody these form and motion interactions. Model concepts and data are summarized about motion grouping across apertures in response to a wide variety of displays, and probabilistic decision making in parietal cortex in response to random dot displays.

The use of a mathematical multicriteria decision-making model for selecting the fire origin room

Over the last three decades, the fire safety codes have been changing from a prescriptive approach to a performance-based one. Some countries, such as the USA, Sweden, New Zealand, Australia and the UK, are in an advanced stage of development and implementation of the performance-based codes. However, there are some difficulties in this process. Most of them are due to the uncertainties associated with fire design. For instance, one of the questions that need to be answered is how to select the most probable fire origin room (FOR)? On the other hand, to know where the FOR is located is also an important aspect in terms of forensic issues. Given that, to address this question is an important step for the establishment of fire designs (i.e., pre-fire phases) and also for fire investigations (i.e., post-fire phases). This paper proposes a methodology for selecting the FOR through the use of a mathematical multicriteria decision-making model: the analytical hierarchy process (AHP). The proposed method is then applied to a hypothetical study case. The results are presented and discussed in this paper.

The psychophysics of decision making in a two-direction random dot motion target selection task

La tâche de kinématogramme de points aléatoires est utilisée avec le paradigme de choix forcé entre deux alternatives pour étudier les prises de décisions perceptuelles. Les modèles décisionnels supposent que les indices de mouvement pour les deux alternatives sont encodés dans le cerveau. Ainsi, la différence entre ces deux signaux est accumulée jusqu’à un seuil décisionnel. Cependant, aucune étude à ce jour n’a testé cette hypothèse avec des stimuli contenant des mouvements opposés. Ce mémoire présente les résultats de deux expériences utilisant deux nouveaux stimuli avec des indices de mouvement concurrentiels. Parmi une variété de combinaisons d’indices concurrentiels, la performance des sujets dépend de la différence nette entre les deux signaux opposés. De plus, les sujets obtiennent une performance similaire avec les deux types de stimuli. Ces résultats supportent un modèle décisionnel basé sur l’accumulation des indices de mouvement net et suggèrent que le processus décisionnel peut intégrer les signaux de mouvement à partir d’une grande gamme de directions pour obtenir un percept global de mouvement.