The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.     

Selective influence through conditional independence

Let each of several (generally interdependent) random vectors, taken separately, be influenced by a particular set of external factors. Under what kind of the joint dependence of these vectors on the union of these factor sets can one say that each vector is selectively influenced by “its own” factor set? The answer proposed and elaborated in this paper is: One can say this if and only if one can find a factor-independent random vector given whose value the vectors in question are conditionally independent, with their conditional distributions selectively influenced by the corresponding factor sets. Equivalently, the random vectors should be representable as deterministic functions of “their” factor sets and of some mutually independent and factor-independent random variables, some of which may be shared by several of the functions.     

Transfer of a conditional ordering response through conditional equivalence classes

Eight adult humans were taught conditional discriminations in a matching-to-sample format that led to the formation of two four-member equivalence classes. When subjects were taught to select one comparison stimulus from each class in a set order, they then ordered all other members of the equivalence classes without explicit training. When the ordering response itself was brought under conditional control, conditional sequencing also transferred to all other members of the two equivalence classes. When the conditional discriminations in the matching-to-sample task were brought under higher order conditional control, the eight stimulus members were arranged into four conditional equivalence classes. Both ordering and conditional ordering transferred to all members of the four conditional equivalence classes; for some subjects this occurred without a typical test for equivalence. One hundred twenty untrained sequences emerged from eight trained sequences for all subjects. Transfer of functions through equivalence classes may contribute to a behavior-analytic approach to semantics and generative grammar.     

Choice probabilities and choice functions

Choice probabilities are basic to much of the theory of individual choice behavior in mathematical psychology. On the other hand, consumer economics has relied primarily on preference relations and choice functions for its theories of individual choice. Although there are sizable literatures on the connections between choice probabilities and preference relations, and between preference relations and choice functions, little has been done—apart from their common ties to preference relations—to connect choice probabilities and choice functions. The latter connection is studied in this paper. A family of choice functions that depends on a threshold parameter is defined from a choice probability function. It is then shown what must be true of the choice probability function so that the choice functions satisfy three traditional rationality conditions. Conversely, it is shown what must be true of the choice functions so that the choice probability function satisfies a version of Luce's axiom for individual choice probabilities.     

Coherent choice functions under uncertainty

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility.     

Noninstrumental Rationalizing

A central notion in Donald Davidson's philosophy of mind and action is rationalization, a species of causal explanation designed in part to reveal the point or purpose of the explananda. An analogue of this notion - noninstrumental rationalization - merits serious attention. I develop an account of this species of rationalization and display its utility in explaining the production of certain desires and of motivationally biased beliefs.     

A fast procedure for studying conditional accuracy functions

This paper describes a procedure for obtaining conditional accuracy functions(CAFs) from naive observers and a restricted number of trials. The method permits the experimenter to counter the subjects’ tendency to favor accuracy in tasks in which stimulus discrimination is easy. Each time a block of 12 trials contains less than three errors, observers are instructed, by means of a speed-up signal, to respond faster. The subject is continuously informed about her/his effective reaction time. The data show that the desired speed-accuracy tradeoff was obtained within each of the 7 observers. The mean percent error was around 25%.     

Preference-based choice functions: a generalized approach

Although choice and preference are distinct categories, it may in some contexts be a useful idealization to treat choices as fully determined by preferences. In order to construct a general model of such preference-based choice, a method to derive choices from preferences is needed that yields reasonable outcomes for all preference relations, even those that are incomplete and contain cycles. A generalized choice function is introduced for this purpose. It is axiomatically characterized and is shown to compare favourably with alternative constructions.     

Rationalizing our Way into Moral Progress

Research suggests that the explicit reasoning we offer to ourselves and to others is often rationalization, that we act instead on instincts, inclinations, stereotypes, emotions, neurobiology, habits, reactions, evolutionary pressures, unexamined principles, or justifications other than the ones we think we’re acting on, then we tell a post hoc story to justify our actions. This is troubling for views of moral progress according to which moral progress proceeds from our engagement with our own and others’ reasons. I consider an account of rationalization, based on Robert Audi’s, to make clear that rationalization, unlike simple lying, can be sincere. Because it can be sincere, and because we also have a desire to be consistent with ourselves, I argue that rationalization sets us up for becoming better people over time, and that a similar case can be made to explain how moral progress among groups of people can proceed via rationalization.     

Choice between fixed-interval schedules: Graded versus step-like choice functions

Pigeons chose between two fixed-interval schedules of food reinforcement. A single peck on one of two lighted keys started the fixed-interval schedule correlated with that key. The schedule had to be completed before the next choice opportunity. The durations of the fixed intervals were varied over conditions from 15 s to 40 s. To maximize the rate of reinforcement, the pigeons had to choose exclusively the shorter of the two schedules. Nevertheless, choice was not all-or-none. Instead, relative choice, and the rates of producing the fixed intervals, varied in a graded fashion with the disparity between the two schedules. Choice ratios under this procedure (single response to choose) were highly sensitive to the ratios of the fixed-interval schedules.     

Thinking through uncertainty: nonconsequential reasoning and choice.

When thinking under uncertainty, people often do not consider appropriately each of the relevant branches of a decision tree, as required by consequentialism. As a result they sometimes violate Savage's sure-thing principle. In the Prisoner's Dilemma game, for example, many subjects compete when they know that the opponent has competed and when they know that the opponent has cooperated, but cooperate when they do not know the opponent's response. Newcomb's Problem and Wason's selection task are also interpreted as manifestations of nonconsequential decision making and reasoning. The causes and implications of such behavior, and the notion of quasi-magical thinking, are discussed.     

Sequential effects of foreperiod duration and conditional probability of the signal in a choice reaction time task

The aim of the present study was to determine whether the negative relationship usually found between reaction time and foreperiod duration in the variable foreperiod paradigm is entirely due to sequential foreperiod effects. It has been shown that when a particular foreperiod has been preceded by a longer one on the previous trial, reaction time is longer than when the preceding foreperiod was equal or shorter. This may be sufficient to explain the increase in reaction time observed for short foreperiods in variable foreperiod conditions.The present results show that, when sequential effects were controlled by the elimination of all trials where the foreperiod was shorter than the preceding one, the negative slope of the reaction time-foreperiod function diminished but did not disappear. The results suggest an interpretation of the role of conditional probability of stimulus arrival in terms of variation in the tendency to reprepare when the moment initially chosen for preparation appears to fall short of the moment at which the stimulus is actually presented.     

Rationalizing flow: agency in skilled unreflective action

In recent work, Peter Railton, Julia Annas, and David Velleman aim to reconcile the phenomenon of “flow”—broadly understood as describing the “unreflective” aspect of skilled action—with one or another familiar conception of agency. While there are important differences between their arguments, Railton, Annas, and Velleman all make, or are committed to, at least one similar pivotal claim. Each argues, directly or indirectly, that agents who perform skilled unreflective actions can, in principle, accurately answer “Anscombean” questions—”what” and “why” questions— about what they do. I argue against this claim and explore the ramifications for theories of skilled action and agency.     

Rationalizing beliefs: evidential vs. pragmatic reasons

Beliefs can be evaluated from a number of perspectives. Epistemic evaluation involves epistemic standards and appropriate epistemic goals. On a truth-conducive account of epistemic justification, a justified belief is one that serves the goal of believing truths and avoiding falsehoods. Beliefs are also prompted by non-epistemic reasons. This raises the question of whether, say, the pragmatic benefits of a belief are able to rationalize it. In this paper, after criticizing certain responses to this question, I shall argue that, as far as beliefs are concerned, justification has an essentially epistemic character. This conclusion is then qualified by considering the conditions under which pragmatic consequences of a belief can be epistemically relevant.     

Speed-accuracy tradeoff functions in choice reaction time: Experimental designs and computational procedures

The existence of tradeoffs between speed and accuracy is an important interpretative problem in choice reaction time (RT) experiments. A recently suggested solution to this problem is the use of complete speed-accuracy tradeoff functions as the primary dependent variable in choice RT ,experiments instead of a single mean RT and error rate. This paper reviews and compares existing procedures for generating empirical speed-accuracy tradeoff, functions for use as dependent variables in choice RT experiments. Two major types of tradeoff function are identified, and their experimental designs and computational procedures are discussed and evaluated. Systematic disparities are demonstrated between the two tradeoff functions in both empirical and computer-simulated data. Although all existing procedures for generating speed-accuracy tradeoff functions involve empirically untested assumptions, one procedure requires less stringent assumptions and is less sensitive to sources of experimental and statistical error. This procedure involves plotting accuracy against RT over a set of experimental conditions in which subjects’ criteria for speed vs. accuracy are systematically varied.     

A transfer of self-discrimination response functions through equivalence relations

The present study tested the idea that human self-discrimination response functions may transfer through equivalence relations. Four subjects were trained in six symbolic matching-to-sample tasks (if see A1, choose B1; A1-C1, A2-B2, A2-C2, A3-B3, A3-C3) and were then tested for the formation of three equivalence relations (B1-C1, B2-C2, B3-C3). Two of the B stimuli (B1 and B2) were then used to train two different self-discrimination responses using either detailed instructions (Subjects 1 to 3) or minimal instructions (Subject 4) on two complex schedules of reinforcement (i.e., subjects were trained to pick the B1 stimulus if they had not emitted a response, and to pick the B2 stimulus if they had emitted one or more responses on the previous schedule). All 4 subjects showed the predicted transfer of self-discrimination response functions through equivalence relations (i.e., no response on the schedule, pick C1; one or more responses on the schedule, pick C2). Subjects also demonstrated this transfer when they were required to discriminate their schedule performance before exposure to the schedule (i.e., “what I intend to do”). Four control subjects were also used in the study. Two of these (Subjects 5 and 6) were not exposed to any form of matching-to-sample training and testing (nonequivalence controls). The 2 remaining subjects (7 and 8) were exposed to matching-to-sample training and testing that incorporated stimuli not used during the transfer test; C1 and C2 were replaced by N1 and N2 during the matching-to-sample training and testing, but C1 and C2 were used for the transfer tests (equivalence controls). All 4 subjects failed to produce the self-discrimination transfer performances observed with the experimental subjects.