Embracing data uncertainty in water decision-making: an application to evaluate water supply and sewerage in Spain

Analyses of complex water management decision-making problems, involving tradeoffs amongst multiple criteria, are often undertaken using multi-criteria decision analysis (MCDA) techniques. Various forms of uncertainty may arise in the application of MCDA methods, including imprecision, inaccuracy or ill determination of data. The ELECTRE family methods deal with imperfect knowledge of data by incorporating ‘pseudo-criteria’, with discrimination thresholds, to interpret the outranking relation as a fuzzy relation. However, the task of selecting thresholds for each criterion can be difficult and ambiguous for decision-makers. In this paper, we propose a confidence-interval-based approach which aims to reduce the subjective input required by decision-makers. The proposed approach involves defining the uncertainty in the input values using confidence intervals and expressing thresholds as a function of the interval estimates. The usefulness of the approach is illustrated by applying it to evaluate the water supply and sewerage services in Spain. Results show that the confidence interval approach may be interesting in some cases (e.g. when dealing with statistical data from surveys or measuring equipment), but should never replace the preferences or judgments of the actors involved in the decision process.Peer ReviewedPostprint (author's final draft

Perfect Prediction in Minkowski Spacetime: Perfectly Transparent Equilibrium for Dynamic Games with Imperfect Information

The assumptions of necessary rationality and necessary knowledge of strategies, also known as perfect prediction, lead to at most one surviving outcome, immune to the knowledge that the players have of them. Solutions concepts implementing this approach have been defined on both dynamic games with perfect information and no ties, the Perfect Prediction Equilibrium, and strategic games with no ties, the Perfectly Transparent Equilibrium. In this paper, we generalize the Perfectly Transparent Equilibrium to games in extensive form with imperfect information and no ties. Both the Perfect Prediction Equilibrium and the Perfectly Transparent Equilibrium for strategic games become special cases of this generalized equilibrium concept. The generalized equilibrium, if there are no ties in the payoffs, is at most unique, and is Pareto-optimal. We also contribute a special-relativistic interpretation of a subclass of the games in extensive form with imperfect information as a directed acyclic graph of decisions made by any number of agents, each decision being located at a specific position in Minkowski spacetime, and the information sets and game structure being derived from the causal structure. Strategic games correspond to a setup with only spacelike-separated decisions, and dynamic games to one with only timelike-separated decisions. The generalized Perfectly Transparent Equilibrium thus characterizes the outcome and payoffs reached in a general setup where decisions can be located in any generic positions in Minkowski spacetime, under necessary rationality and necessary knowledge of strategies. We also argue that this provides a directly usable mathematical framework for the design of extension theories of quantum physics with a weakened free choice assumption.Comment: 25 pages, updated technical repor

Decision blocks: A tool for automating decision making in CLIPS

The human capability of making complex decision is one of the most fascinating facets of human intelligence, especially if vague, judgemental, default or uncertain knowledge is involved. Unfortunately, most existing rule based forward chaining languages are not very suitable to simulate this aspect of human intelligence, because of their lack of support for approximate reasoning techniques needed for this task, and due to the lack of specific constructs to facilitate the coding of frequently reoccurring decision block to provide better support for the design and implementation of rule based decision support systems. A language called BIRBAL, which is defined on the top of CLIPS, for the specification of decision blocks, is introduced. Empirical experiments involving the comparison of the length of CLIPS program with the corresponding BIRBAL program for three different applications are surveyed. The results of these experiments suggest that for decision making intensive applications, a CLIPS program tends to be about three times longer than the corresponding BIRBAL program

The theory of international business: the role of economic models

This paper reviews the scope for economic modelling in international business studies. It argues for multi-level theory based on classic internalisation theory. It present a systems approach that encompasses both firm-level and industry-level analysis

Dynamic Bayesian Combination of Multiple Imperfect Classifiers

Classifier combination methods need to make best use of the outputs of multiple, imperfect classifiers to enable higher accuracy classifications. In many situations, such as when human decisions need to be combined, the base decisions can vary enormously in reliability. A Bayesian approach to such uncertain combination allows us to infer the differences in performance between individuals and to incorporate any available prior knowledge about their abilities when training data is sparse. In this paper we explore Bayesian classifier combination, using the computationally efficient framework of variational Bayesian inference. We apply the approach to real data from a large citizen science project, Galaxy Zoo Supernovae, and show that our method far outperforms other established approaches to imperfect decision combination. We go on to analyse the putative community structure of the decision makers, based on their inferred decision making strategies, and show that natural groupings are formed. Finally we present a dynamic Bayesian classifier combination approach and investigate the changes in base classifier performance over time.Comment: 35 pages, 12 figure

No-Regret Learning in Extensive-Form Games with Imperfect Recall

Counterfactual Regret Minimization (CFR) is an efficient no-regret learning algorithm for decision problems modeled as extensive games. CFR's regret bounds depend on the requirement of perfect recall: players always remember information that was revealed to them and the order in which it was revealed. In games without perfect recall, however, CFR's guarantees do not apply. In this paper, we present the first regret bound for CFR when applied to a general class of games with imperfect recall. In addition, we show that CFR applied to any abstraction belonging to our general class results in a regret bound not just for the abstract game, but for the full game as well. We verify our theory and show how imperfect recall can be used to trade a small increase in regret for a significant reduction in memory in three domains: die-roll poker, phantom tic-tac-toe, and Bluff.Comment: 21 pages, 4 figures, expanded version of article to appear in Proceedings of the Twenty-Ninth International Conference on Machine Learnin

Molinism, Creature-types, and the Nature of Counterfactual Implication

Granting that there could be true subjunctive conditionals of libertarian freedom (SCLs), I argue (roughly) that there could be such conditionals only in connection with individual "possible creatures" (in contrast to types). This implies that Molinism depends on the view that, prior to creation, God grasps possible creatures in their individuality. In making my case, I explore the notions of counterfactual implication (that relationship between antecedent and consequent of an SCL which consists in its truth) and counterfactual relevance (that feature of an antecedent in virtue of which it counterfactually implies something or other)