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TOWARD A UNIFIED THEORY OF DECISION CRITERION LEARNING IN PERCEPTUAL CATEGORIZATION
 JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR
, 2002
"... Optimal decision criterion placement maximizes expected reward and requires sensitivity to the category base rates (prior probabilities) and payoffs (costs and benefits of incorrect and correct responding). When base rates are unequal, human decision criterion is nearly optimal, but when payoffs are ..."
Abstract

Cited by 26 (12 self)
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Optimal decision criterion placement maximizes expected reward and requires sensitivity to the category base rates (prior probabilities) and payoffs (costs and benefits of incorrect and correct responding). When base rates are unequal, human decision criterion is nearly optimal, but when payoffs are unequal, suboptimal decision criterion placement is observed, even when the optimal decision criterion is identical in both cases. A series of studies are reviewed that examine the generality of this finding, and a unified theory of decision criterion learning is described (Maddox & Dodd, 2001). The theory assumes that two critical mechanisms operate in decision criterion learning. One mechanism involves competition between reward and accuracy maximization: The observer attempts to maximize reward, as instructed, but also places some importance on accuracy maximization. The second mechanism involves a flatmaxima hypothesis that assumes that the observer’s estimate of the rewardmaximizing decision criterion is determined from the steepness of the objective reward function that relates expected reward to decision criterion placement. Experiments used to develop and test the theory require each observer to complete a large number of trials and to participate in all conditions of the experiment. This provides maximal control over the reinforcement history of the observer and allows a focus on individual behavioral profiles. The theory is applied to decision criterion learning problems that examine category discriminability, payoff matrix multiplication and addition effects, the optimal classifier’s independence assumption, and different types of trialbytrial feedback. In every case the theory provides a good account of the data, and, most important, provides useful insights into the psychological processes involved in decision criterion learning.
On the Relation Between Baserate and CostBenefit Learning in Simulated Medical Diagnosis
, 2001
"... Observers completed a series of simulated medical diagnosis tasks that differed in category discriminability and baserate/costbenefit ratio. Point, accuracy, and decision criterion estimates were closer to optimal (a) for category d' = 2.2 than for category d' = 1.0 or 3.2, (b) when baserates, as ..."
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Cited by 17 (13 self)
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Observers completed a series of simulated medical diagnosis tasks that differed in category discriminability and baserate/costbenefit ratio. Point, accuracy, and decision criterion estimates were closer to optimal (a) for category d' = 2.2 than for category d' = 1.0 or 3.2, (b) when baserates, as opposed to costbenefits were manipulated, and (c) when the cost of an incorrect response resulted in no point loss (nonnegative cost) as opposed to a point loss (negative cost). These results support the "flatmaxima" (von Winterfeldt & Edwards, 1982) and COmpetition Between Reward and Accuracy (COBRA; Maddox & Bohil, 1998a) hypotheses. A hybrid model that instantiated simultaneously both hypotheses was applied to the data. The model parameters indicated that (a) the rewardmaximizing decision criterion quickly approached the optimal criterion, (b) the importance placed on accuracy maximization early in learning was larger when the cost of an incorrect response was negative as opposed to nonnegative, and (c) by the end of training the importance placed on accuracy was equal for negative and nonnegative costs.
Category discriminability, baserate, and payoff effects in perceptual organization
 Perception & Psychophysics
, 2001
"... (i.e., d ¢ level), base rates, and payoffs was examined. Baserate and payoff manipulations across two category discriminabilities allowed a test of the hypothesis that the steepness of the objective reward function affects performance (i.e., the flatmaxima hypothesis), as well as the hypothesis th ..."
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Cited by 10 (7 self)
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(i.e., d ¢ level), base rates, and payoffs was examined. Baserate and payoff manipulations across two category discriminabilities allowed a test of the hypothesis that the steepness of the objective reward function affects performance (i.e., the flatmaxima hypothesis), as well as the hypothesis that observers combine baserate and payoff information independently. Performance was (1) closer to optimal for the steeper objective reward function, in line with the flatmaxima hypothesis, (2) closer to optimal in baserate conditions than in payoff conditions, and (3) in partial support of the hypothesis that baserate and payoff knowledge is combined independently. Implications for current theories of baserate and payoff learning are discussed.
Feedback effects on cost–benefit learning in perceptual categorization
 Memory & Cognition
, 2001
"... Two experiments were conducted in which the effects of different feedback displays on decision criterion learning were examined in a perceptual categorization task with unequal cost–benefits. In Experiment 1, immediate versus delayed feedback was combined factorially with objective versus optimal cl ..."
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Cited by 8 (5 self)
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Two experiments were conducted in which the effects of different feedback displays on decision criterion learning were examined in a perceptual categorization task with unequal cost–benefits. In Experiment 1, immediate versus delayed feedback was combined factorially with objective versus optimal classifier feedback. Immediate versus delayed feedback had no effect. Performance improved significantly over blocks with optimal classifier feedback and remained relatively stable with objective feedback. Experiment 2 used a withinsubjects design that allowed a test of modelbased instantiations of the flatmaxima (von Winterfeldt & Edwards, 1982) and competition between reward and accuracy (Maddox & Bohil, 1998a) hypotheses in isolation and of a hybrid model that incorporated assumptions from both hypotheses. The modelbased analyses indicated that the flatmaxima model provided a good description of early learning but that the assumptions of the hybrid model were necessary to account for later learning. An examination of the hybrid model parameters indicated that the emphasis placed on accuracy maximization generally declined with experience for optimal classifier feedback but remained high, and fairly constant for objective classifier feedback. Implications for cost–benefit training are discussed.
A Theoretical Framework for Understanding the Effects of Simultaneous BaseRate and Payoff . . .
, 2003
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Linear Transformations of the Payoff Matrix and Decision Criterion Learning in Perceptual Categorization
 J EXP PSYCHOL LEARN MEM COGN
, 2003
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A test of the optimal classifier's independence . . .
 PERCEPTION & PSYCHOPHYSICS
, 2003
"... this article are based on the decision boundmodel in Equation 5. Specifically, each model includes one "noise" parameter that represents the sum of perceptual and criterial noise (Ashby, 1992a; Maddox& Ashby, 1993). Each model assumes that the observer has accurate knowledge of the category structur ..."
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this article are based on the decision boundmodel in Equation 5. Specifically, each model includes one "noise" parameter that represents the sum of perceptual and criterial noise (Ashby, 1992a; Maddox& Ashby, 1993). Each model assumes that the observer has accurate knowledge of the category structures [i.e., l o (x pi )]. To ensure that this was a reasonable assumption, each observer completed a number of baseline trials and was required to meet a stringent performance criterion (see Method section). Finally,each model allows for suboptimal decision criterion placement where the decision criterion is determined from the flatmaxima hypothesis, the COBRA hypothesis, or both, following Equation 6. To determine whether the flatmaxima and COBRA hypothesesare important in accountingfor each observer's data, we developed four models. Each model makes different assumptions about the k r and w values used. The nested structure of the models is represented in Figure 5, with each arrow pointing to a more general model and Figure 4. Decision criterion [ln( b )] predicted from the flatmaxima hypothesisplotted against the decision criterion [ln( b )] predicted from the independence assumption of the optimal classifier for the six simultaneous baserate/payoff conditions. (A) 2:1B/2:1P condition. (B) 3:1B/3:1P condition
Matching, Maximizing and the Independence Assumption 1 Probability Matching, Accuracy Maximization, and a Test of the Optimal Classifier’s Independence Assumption in Perceptual Categorization
, 2003
"... Accepted for publication in Perception & Psychophysics Observers completed perceptual categorization tasks that included 25 baserate/payoff conditions constructed from the factorial combination of 5 baserate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with 5 payoff ratios (1:3, 1:2, 1:1, 2:1, and 3:1). T ..."
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Accepted for publication in Perception & Psychophysics Observers completed perceptual categorization tasks that included 25 baserate/payoff conditions constructed from the factorial combination of 5 baserate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with 5 payoff ratios (1:3, 1:2, 1:1, 2:1, and 3:1). This large database allowed an initial comparison of the competition between reward and accuracy maximization (COBRA) hypothesis with a competition between reward maximization and probability matching (COBRM) hypothesis, and an extensive and critical comparison of the flatmaxima hypothesis with the independence assumption of the optimal classifier. Modelbased instantiations of the COBRA and COBRM hypotheses provided good accounts of the data, but there was a consistent advantage for the COBRM instantiation early in learning, and the COBRA instantiation later in learning. This pattern held in the current study, and in a reanalysis of Bohil and Maddox (in press). Strong support was obtained for the flatmaxima hypothesis over the independence assumption, especially as the observers gained experience with the task. Model parameters indicated that observers ’ rewardmaximizing decision criterion rapidly approaches the optimal value, and that more weight is placed on accuracy maximization in separate baserate/payoff conditions than in simultaneous baserate/payoff conditions. The superiority of the flatmaxima hypothesis suggests that violations of the independence assumption are to be expected, and are well captured by the flatmaxima hypothesis without requiring any additional assumptions.