Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of (...) their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

In this paper we analyze two recent conditional interpretations of defaults, one based on probabilities, and the other, on models. We study what makes them equivalent, explore their limitations and develop suitable extensions. The resulting framework ties together a number of important notions in default reasoning, like high-probabilities and model-preference, default priorities and argument systems, and independence assumptions and minimality considerations.

The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.

In binary choice between discrete outcome lotteries, an individual may prefer lottery L1 to lottery L2 when the probability that L1 delivers a better outcome than L2 is higher than the probability that L2 delivers a better outcome than L1. Such a preference can be rationalized by three standard axioms (solvability, convexity and symmetry) and one less standard axiom (a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. (...) Such a utility function has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed. (shrink)

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of (...) their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. (shrink)

Research on preference reversals has demonstrated a disproportionate influence of outcome probability on choices between monetary gambles. The aim was to investigate the hypothesis that this is a prominence effect originally demonstrated for riskless choice. Another aim was to test the structure compatibility hypothesis as an explanation of the effect. The hypothesis implies that probability should be the prominent attribute when compared with value attributes both in a choice and a preference rating procedure. In Experiment 1, (...) two groups of undergraduates were presented with medical treatments described by two value attributes (effectiveness and pain-relief). All participants performed both a matching task and made preference ratings. In the latter task, outcome probabilities were added to the descriptions of the medical treatments for one of the groups. In line with the hypothesis, this reduced the prominence effect on the preference ratings observed for effectiveness. In Experiment 2, a matching task was used to demonstrate that probability was considered more important by a group of participating undergraduates than the value attributes. Furthermore, in both choices and preference ratings the expected prominence effect was found for probability. (shrink)

Under approval voting, each voter just distinguishes the candidates he approves of from those appearing as unacceptable. The preference approval voting is a hybrid version of the approval voting first introduced by Brams and Sanver The mathematics of preference, choice and order. Springer, Berlin, pp 215–237, 2009). Under PAV, each voter ranks all the candidates and then indicates the ones he approves. In this paper, we provide an analytical representation of the limiting probability that PAV elects the (...) Condorcet winner when she exists in three-candidate elections. We perform our analysis by assuming the assumption of the Extended Impartial Culture. The aim is to measure at which extend PAV performs better than AV both on the propensity of electing the Condorcet winner and on that of the non-election of the Condorcet loser. For this purpose, we also provide an analytical representation of the limiting probability that AV elects the Condorcet winner when she exists in three-candidate elections. Our representation of the limiting probability that AV elects the Condorcet winner is more general than that provided by Diss et al. Handbook on approval voting. Springer, Berlin, pp 255–283, 2010) and it leads to the same figures as the representation provided by Gehrlein and Lepelley. (shrink)

Probability has become one of the most characteristic con cepts of modern culture, and a 'probabilistic way of thinking' may be said to have penetrated almost every sector of our in tellectual life. However it would be difficult to determine an explicit list of 'positive' features, to be proposed as identifica tion marks of this way of thinking. One would rather say that it is characterized by certain 'negative' features, i. e. by certain at titudes which appear to be (...) the negation of well established tra ditional assumptions, conceptual frameworks, world outlooks and the like. It is because of this opposition to tradition that the probabilistic approach is perceived as expressing a 'modern' in tellectual style. As an example one could mention the widespread diffidence in philosophy with respect to self -contained systems claiming to express apodictic truths, instead of which much weaker pretensions are preferred, that express 'probable' interpretations of reality, of history, of man (the hermeneutic trend). An ana logous example is represented by the interest devoted to the study of different patterns of 'argumentation', dealing wiht reasonings which rely not so much on the truth of the premisses and stringent formal logic links, but on a display of contextual conditions (depending on the audience, and on accepted stan dards, judgements, and values), which render the premisses and the conclusions more 'probable' (the new rhetoric). (shrink)

The article shows, using elementary examples, that risk assessment depends both on the probability of future events and on their results. Various approaches to the integration of probabilities and numerical estimates of possible outcomes are shown and analyzed. The subjective nature of risk is substantiated. An interdisciplinary definition of risk is proposed, not associated with any science or group of sciences. The definition is based on the idea that risk is a consequence of decisions made by the subject, who (...) evaluates their consequences. The question is raised about responsibility for decisions under risk conditions. (shrink)

Risk preferences of Australian academics are elicited by analyzing the aggregate distribution of their retirement funds across available investment options. Not more than 10 % of retirement funds are invested as if their owners maximize expected utility under the assumption of constant relative risk aversion with an empirically plausible level of risk aversion. An implausibly high level of risk aversion is required to rationalize any investment into bonds when stocks are available. Not more than 36.54 % of all investments can (...) be rationalized by a model of loss averse preferences. Moreover, the levels of loss aversion typically reported in the experimental studies imply overinvestment in bonds, which is not observed in the data. Up to 67.18 % of all investments can be rationalized by rank-dependent utility or Yaari’s dual model with empirically plausible parameters. A median Australian academic behaves as if maximizing rank-dependent utility with parameter γ∈[0.76,0.79]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma \in [0.76, 0.79]$$\end{document} in a Tversky and Kahneman probability weighting function. (shrink)

Even though the Bohmian trajectories given by integral curves of the conserved Klein-Gordon current may involve motions backwards in time, the natural relativistic probability density of particle positions is well-defined. The Bohmian theory predicts subtle deviations from the statistical predictions of more conventional formulations of quantum theory, but it seems that no present experiment rules this theory out. The generalization to the case of many particles or strings is straightforward, provided that a preferred foliation of spacetime is given.

It is commonly assumed that preferences are determinate; that is, that an agent who has a preference knows that she has the preference in question and is disposed to act upon it. This paper argues the dubiousness of that assumption. An account of indeterminate preferences in terms of self-predicting subjective probabilities is given, and a decision rule for choices involving indeterminate preferences is proposed. Wolfgang Spohn’s and Isaac Levi ’s arguments against self-predicting probabilities are also considered, in light (...) of Wlodek Rabinowicz’s recent criticism. (shrink)

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli’s discussion of “convex Bayesianism” (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of “strong independence” (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli’s results and (...) recent developments on the axiomatization of non-binary preferences, and its impact on “complete” independence, are described. (shrink)

This paper offers a metaphysics of physical probability in (or if you prefer, truth conditions for probabilistic claims about) deterministic systems based on an approach to the explanation of probabilistic patterns in deterministic systems called the method of arbitrary functions. Much of the appeal of the method is its promise to provide an account of physical probability on which probability assignments have the ability to support counterfactuals about frequencies. It is argued that the eponymous arbitrary functions are (...) of little philosophical use, but that they can be substituted for facts about frequencies without losing the ability to provide counterfactual support. The result is an account of probability in deterministic systems that has a “propensity-like” look and feel, yet which requires no supplement to the standard modern empiricist tool kit of particular matters of fact and principles of physical dynamics. (shrink)

Adaptive preferences are preferences formed in response to circumstances and opportunities – paradigmatically, they occur when we scale back our desires so they accord with what is probable or at least possible. While few commentators are willing to wholly reject the normative significance of such preferences, adaptive preferences have nevertheless attracted substantial criticism in recent political theory. The groundbreaking analysis of Jon Elster charged that such preferences are not autonomous, and several other commentators have since followed Elster’s lead. On a (...) second front, Capacity Theorists Martha Nussbaum and Amartya Sen have objected that adaptive preferences lead people away from objective goods and constitute an impediment to progressive change in developing countries. In this paper I argue that the criticisms of Elster, Sen and Nussbaum fail on the one hand to take into account what may be positively said in favour of this type of preference formation, and fail on the other hand to distinguish between different types of psychological changes – with the result that many of the critiques offered have a narrower purview than is currently allowed. My analysis of adaptive preferences, even in their most ideal form, is however not entirely positive; I adduce reasons why we can be cautious about allowing adaptive preferences to play certain types of roles in political processes, even as we accept those very preferences as normative and autonomous for the agent holding them. [International scholars without access to the AJPAE are invited to email [email protected] for a pdf copy of this article.]. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference (...) and the status quo, then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

Selectional preferences have a long history in both generative and computational linguistics. However, since the publication of Resnik's dissertation in 1993, a new approach has surfaced in the computational linguistics community. This new line of research combines knowledge represented in a pre‐defined semantic class hierarchy with statistical tools including information theory, statistical modeling, and Bayesian inference. These tools are used to learn selectional preferences from examples in a corpus. Instead of simple sets of semantic classes, selectional preferences are viewed as (...) probability distributions over various entities. We survey research that extends Resnik's initial work, discuss the strengths and weaknesses of each approach, and show how they together form a cohesive line of research. (shrink)

Epistemic probability theories of luck come in two versions. They are easiest to distinguish by the epistemic property they claim eliminates luck. One view says that the property is knowledge. The other view says that the property is being guaranteed by a subject’s evidence. Asbjørn Steglich-Petersen defends the Knowledge Account (KA). He has recently argued that his view is preferable to my Epistemic Analysis of Luck (EAL), which defines luck in terms of evidential probability. In this paper, I (...) defend EAL against Steglich-Petersen’s arguments, clarify the view, and argue for the explanatory significance of EAL with respect to some core epistemological issues. My overall goal is to show that an epistemic probability account of luck rooted in the concepts of evidence and evidential support remains a viable and fruitful overall account of luck. (shrink)

We propose two different characterizations for preference relations representable by lower (upper) expectations with the aim of removing either fair price or completeness requirements. Moreover, we give an explicit characterization for comparative degrees of belief on a finite algebra of events representable by lower probabilities.

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single (...) case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of the (...) Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

We generalize the Kolmogorov axioms for probability calculus to obtain conditions defining, for any given logic, a class of probability functions relative to that logic, coinciding with the standard probability functions in the special case of classical logic but allowing consideration of other classes of "essentially Kolmogorovian" probability functions relative to other logics. We take a broad view of the Bayesian approach as dictating inter alia that from the perspective of a given logic, rational degrees of (...) belief are those representable by probability functions from the class appropriate to that logic. Classical Bayesianism, which fixes the logic as classical logic, is only one version of this general approach. Another, which we call Intuitionistic Bayesianism, selects intuitionistic logic as the preferred logic and the associated class of probability functions as the right class of candidate representions of epistemic states (rational allocations of degrees of belief). Various objections to classical Bayesianism are, we argue, best met by passing to intuitionistic Bayesianism—in which the probability functions are taken relative to intuitionistic logic—rather than by adopting a radically non-Kolmogorovian, for example, nonadditive, conception of (or substitute for) probability functions, in spite of the popularity of the latter response among those who have raised these objections. The interest of intuitionistic Bayesianism is further enhanced by the availability of a Dutch Book argument justifying the selection of intuitionistic probability functions as guides to rational betting behavior when due consideration is paid to the fact that bets are settled only when/if the outcome bet on becomes known. (shrink)

Words are processed more easily when they have canonical phonotactic shapes, i.e., shapes that are frequent both in the lexicon and in usage. We explore whether this cognitively grounded constraint or preference implies testable predictions about the implementation of sound change. Specifically, we hypothesise that words with canonical shapes favour, or ‘select for’, sound changes that produce words with the same shapes. To test this, we investigate a Middle English sound change known as Open Syllable Lengthening. OSL lengthened vowels (...) in disyllables such as ME /ma.kə/ make, but more or less only when they became monosyllabic and when their vowels were non-high. We predict that word shapes produced by this implementation pattern should correspond to the shapes that were most common among morphologically simple monosyllables and disyllables at the time when OSL occurred. We test this prediction against Early Middle English corpus data. Our results largely confirm our prediction: monosyllables produced by OSL indeed conformed to the shapes that were most frequent among already existing monosyllables. At the same time, the failure of OSL to affect disyllables prevented them from assuming shapes that were far more typical of morphologically complex word forms than of simple ones. This suggests that the actuation and implementation of sound changes may be even more sensitive to lexical probabilities than hitherto suspected. Also, it demonstrates how diachronic data can be used to test hypotheses about constraints on word recognition and processing. (shrink)

This essay gives necessary and sufficient conditions for recovering expected utility from choice behavior in several popular models of uncertainty. In particular, these techniques handle a finite state model; a model for which the choice space consists of probability densities and the expected utility representation requires bounded, measurable utility; and a model for which the choice space consists of Borel probability measures and the expected utility representation requires bounded, continuous utility. The key result is the identification of the (...) continuity condition necessary for the revelation of linear utility. (shrink)

Experimental evidence suggests that individual consumption has not only personal value but also enters the social part of the utility. Existing models of social preferences make ad hoc parametric assumptions about the nature of this duality. This creates a problem of experimental identification of preferences since without such assumptions it is impossible to distinguish whether consumption or social concerns are driving the behavior. Given observed choice, the Axiomatic model of preferences in this article makes it possible to unambiguously determine personal (...) and social utility without any assumptions about their relationship. The unique separation can be achieved only if the individual choices in different subgroups of other people are available. Preferences over consumption and status are used as an example to demonstrate how the utility is constructed. The model shows what kind of information about choice is needed to empirically determine the nature of social preferences without making restrictive assumptions. This can help to estimate whether personal consumption or social value is more important in economic decisions. (shrink)

The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.

Subjective probability considered as a logic of partial belief succumbs to three fundamental fallacies. These concern the representation of preference via expectation, the measurability of partial belief, and the normalization of belief.

How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to (...) define or measure subjective probability for partly irrational agents. (shrink)

We consider a setting where a decision maker’s uncertainty is represented by a set of probability measures, rather than a single measure. Measure-by-measure updating of such a set of measures upon acquiring new information is well known to suffer from problems. To deal with these problems, we propose using weighted sets of probabilities: a representation where each measure is associated with a weight, which denotes its significance. We describe a natural approach to updating in such a situation and a (...) natural approach to determining the weights. We then show how this representation can be used in decision making, by modifying a standard approach to decision making—minimizing expected regret—to obtain minimax weighted expected regret. We provide an axiomatization that characterizes preferences induced by MWER both in the static and dynamic case. (shrink)

In attempting to form rational personal probabilities by direct inference, it is usually assumed that one should prefer frequency information concerning more specific reference classes. While the preceding assumption is intuitively plausible, little energy has been expended in explaining why it should be accepted. In the present article, I address this omission by showing that, among the principled policies that may be used in setting one’s personal probabilities, the policy of making direct inferences with a preference for frequency information (...) for more specific reference classes yields personal probabilities whose accuracy is optimal, according to all proper scoring rules, in situations where all of the relevant frequency information is point-valued. Assuming that frequency information for narrower reference classes is preferred, when the relevant frequency statements are point-valued, a dilemma arises when choosing whether to make a direct inference based upon relatively precise-valued frequency information for a broad reference class, R, or upon relatively imprecise-valued frequency information for a more specific reference class, R*. I address such cases, by showing that it is often possible to make a precise-valued frequency judgment regarding R* based on precise-valued frequency information for R, using standard principles of direct inference. Having made such a frequency judgment, the dilemma of choosing between and is removed, and one may proceed by using the precise-valued frequency estimate for the more specific reference class as a premise for direct inference. (shrink)

Probably many people have cyclic preferences: they prefer A to B, B to C and C to A for some objects of choice A, B and C. Recent work has resurrected the objection to cyclic preference that agents possessing them are open to exploitation by means of ‘money pumps’. The paper briefly reviews this work and proposes a general approach to problems of sequential choice that makes cyclic preference immune to exploitation by means of these new mechanisms.

Beginning with an analysis of the "reluctant gambler problem"—in which the notion of guiding one's life by probability seems to conflict with the preferences of rational people—we draw a distinction between rule and act probabilism. Arguing that humans are rule probabilists by default, we show that reluctant gamblers can be viewed as rule probabilists. If so viewed, their reluctance to gamble is consistent with their rational use of probability judgments to guide their lives.The distinction between rule and act (...) probabilism suggests a way to analyze the risks stemming from the September 11 terrorist attacks. Assessing the risks posed by the new reality of terrorism in the U.S. in light of the rule versus act probabilist distinction shows the risks Americans face from a terrorist attack are essentially the same as they were before September 11, 2002. Yet empirical investigation indicates Americans exaggerate their personal risks from terrorism.The perception that the risks of terrorism mushroomed on September 11 is partially explained by the 24-hour news stations' TV coverage and the current administration's "interest" in diverting attention from their own questionable practices. While the risks of terrorism are not appreciably higher than they were prior to September 11, they might be further reduced. Unfortunately, our government's strategy to reduce the risks of terrorist strikes involves weakening the Constitution. Americans face the question how much it is appropriate to pay—in diminished rights and liberties—to reduce a risk that is essentially the same as it was prior to the attacks. (shrink)

We describe two anomalies in Bohm’s quantum theory that shed light on the notion of probability zero in quantum mechanics. In one anomaly the preferred reference frame may be discovered.

When do probability distribution functions (PDFs) about future climate misrepresent uncertainty? How can we recognise when such misrepresentation occurs and thus avoid it in reasoning about or communicating our uncertainty? And when we should not use a PDF, what should we do instead? In this paper we address these three questions. We start by providing a classification of types of uncertainty and using this classification to illustrate when PDFs misrepresent our uncertainty in a way that may adversely affect decisions. (...) We then discuss when it is reasonable and appropriate to use a PDF to reason about or communicate uncertainty about climate. We consider two perspectives on this issue. On one, which we argue is preferable, available theory and evidence in climate science basically excludes using PDFs to represent our uncertainty. On the other, PDFs can legitimately be provided when resting on appropriate expert judgement and recognition of associated risks. Once we have specified the border between appropriate and inappropriate uses of PDFs, we explore alternatives to their use. We briefly describe two formal alternatives, namely imprecise probabilities and possibilistic distribution functions, as well as informal possibilistic alternatives. We suggest that the possibilistic alternatives are preferable. -/- . (shrink)

Randomized controlled clinical trials play an important role in the development of new medical therapies. There is, however, an ethical issue surrounding the use of randomized treatment allocation when the patient is suffering from a life threatening condition and requires immediate treatment. Such patients can only benefit from the treatment they actually receive and not from the alternative therapy, even if it ultimately proves to be superior. We discuss a novel new way to analyse data from such clinical trials based (...) on the use of the recently developed theory of imprecise probabilities. This work draws an explicit distinction between the related but nevertheless distinct questions of inference and decision in clinical trials. The traditional question of scientific interest asks 'Which treatment offers the greater chance of success?' and is the primary reason for conducting the clinical trial. The question of decision concerns the welfare of the patients in the clinical trial, asking whether the accumulated evidence favours one treatment over the other to such an extent that the next patient should decline randomization and instead express a preference for one treatment. Consideration of the decision question within the framework of imprecise probabilities leads to a mathematical definition of equipoise and a method for governing the randomization protocol of a clinical trial. This paper describes in detail the protocol for the conduct of clinical trials based on this new method of analysis, which is illustrated in a retrospective analysis of data from a clinical trial comparing the anti-emetic drugs ondansetron and droperidol in the treatment of postoperative nausea and vomiting. The proposed methodology is compared quantitatively using computer simulation studies with conventional clinical trial designs and is shown to maintain high statistical power with reduced sample sizes, at the expense of a high type I error rate that we argue is irrelevant in some specific circumstances. Particular emphasis is placed on describing the type of medical conditions and treatment comparisons where the new methodology is expected to provide the greatest benefit. (shrink)