Foundations of risk measurement. II. Effects of gains on risk

This paper presents the second part of a two-part study on axiomatizations of perceived risk. The first part (P. C. Fishburn, Foundations of risk measurement, I. Risk as probable loss. Mimeo., Bell Laboratories, 1981) focussed on risk as probable loss. The second part considers measures of risk that include effects of gains on perceived risk. It adopts the position that increased gains can reduce the risk of fixed probable losses without completely negating this risk. Moreover, every prospect that has no chance of yielding a loss is presumed to have no risk. Several numerical measures of risk are axiomatized. The more specialized are separable in gains and losses. Further specializations isolate the effects of loss and gain probabilities.     

A test of the Sophisticated Guessing Theory of word perception

Under difficult viewing conditions, a letter in a familiar word can be perceived more accurately than the same letter alone or in a string of unrelated letters. Sophisticated Guessing Theory asserts that perception is more accurate when a letter appears in a word because its identity is constrained by the identity of neighboring context letters. Experiment 1 tested the following prediction: A letter in a word should be perceived more accurately in strongly constraining word contexts than in weakly constraining word contexts. No such trend was found using a number of different measures of contextual constraint and perceptual accuracy. Experiment 2 verified that, with the same conditions used in Experiment 1 to test Sophisticated Guessing Theory, a strong perceptual advantage could be obtained for letters in words vs. letters alone or in unrelated-letter strings. Several alternative theories of word perception are discussed. The most attractive asserts that for words an additional higher-level perceptual code is formed that is more resistant to degradation than the code formed for letters.     

Memory without organization: Properties of a model with random storage and undirected retrieval

A very simple spatial model of memory storage and retrieval is described, analyzed, and discussed. The postulated memory is without organization in the sense that neither the place of storage nor the order of search during retrieval is influenced by the nature of the information being stored or retrieved. The memory consists of a three-dimensional space containing a large number of homogeneously distributed loci at which data may be stored. Data received near each other in time are stored at nearby locations. Access is by an undirected expanding-sphere search. The model exhibits a wide variety of quantitatively and qualitatively humanlike behavior with respect to both standard learning and forgetting paradigms and with respect to frequency effects and other phenomena in word processing.     

Nontransitive measurable utility

A new theory of preferences under risk is presented that does not use the transitivity and independence axioms of the von Neumann-Morgenstern linear utility theory. Utilities in the new theory are unique up to a similarity transformation (ratio scale measurement). They key to this generalization of the traditional linear theory lies in its representation of binary preferences by a bivariate rather than univariate real valued function. Linear theory obtains a linear function u on a set P of probability measures for which u(p) > u(q) if and only if p is preferred to q. The new theory obtains a skew-symmetric bilinear function φ on P × P for which φ(p, q) > 0 if and only if p is preferred to q. Continuity, dominance, and symmetry axioms are shown to be necessary and sufficient for the new representation.     

Restricted thresholds for interval orders: A case of nonaxiomatizability by a universal sentence

Let $\text{P}$_n be the class of all finite interval orders that can be interval-represented using no more than n interval lengths or threshold levels. Thus $\text{P}$₁ is the class of finite semiorders, and $\text{P}$, the union of the $\text{P}$_n, is the class of finite interval orders. While each of $\text{P}$₁ and $\text{P}$ is axiomatizable by a universal sentence in first-order logic, no $\text{P}$_n for $\text{n ≧ 2}$ is axiomatizable in the same sense.     

Selective attention by children and adults to pictures specified by color

Four conditions were used to investigate developmental trends in the ability to establish and use a color set to direct the selective processing of pictures. In three conditions, 6-year-old, 9-year-old, and adult subjects viewed a series of pairs of pictures, with one red and one black line drawing in each pair. Subjects were asked to look either at the red pictures only, the black pictures only, or both pictures. In a fourth condition, subjects viewed a series of singly presented red and black pictures. Pictures of both colors were included in a subsequent recognition memory test. At all ages recognition memory was comparable for pictures of each color in the both and single conditions but was higher for pictures of the specified color in the selective red and selective black conditions. There was no evidence at any age that memory for pictures of the specified color was decreased by the presence of the second picture. These results, showing roughly comparable selectivity at all ages, were discussed in relation to findings of developmental trends in selective attention on more “traditional” central-incidental learning tasks.     

Cognitive processes in person perception: Retrieval of personality trait and behavioral information

The processes people use to retrieve information about another person's behavior and personality were investigated. Subjects viewed different lengths of segments from videotaped sequences of actors' behaviors. The subjects' reaction times to questions about the actors' behaviors and about personality traits were both an increasing function of the duration of the segment about which the questions were asked. These data were taken as an indication that people do, in general, carefully examine the contents of their memories in order to respond to questions about another person. In particular, an exhaustive serial search model was supported. Additional data and analyses demonstrated that relatively abstract trait terms usually were answered on the basis of the exhaustive search, while relatively specific trait terms were not. A two-stage process model was proposed to explain the differences in the results for the two types of trait terms.     

Effects of quantitative shifts in a visual reinforcer on the instrumental response of infants.

Two studies examined the effects of quantitative (“complexity”) differences in a visual reinforcer and subsequent reward shifts, on operant response rates. Footkicks and visual attention of 3-month-old infants were measured across daily sessions with conjugate reinforcement provided by an overhead mobile containing either two, six or ten identical components. In Experiment 1, initial rates to the three mobiles differed. The relation between components and kicking was not linear, but was an inverted U-shaped function of component numerosity. The infant responses as a function of numerosity from Experiment 1 were used to define “complexity” in Experiment 2, and all subjects were switched to an intermediate complexity level (two components) after achieving a criterion of stable responding. Although the number of mobile components did not differentially affect acquisition rates, infants who received a shift from six to two components exhibited a reliable and immediate response increase whereas those experiencing a ten- to two-component shift exhibited negative behaviors. These results imply that infants respond relationally, actively manipulating their visual environments as a function of their previous contextual experiences.     

Choice based on separately established response tendencies: The effect of recency of reinforcement

The responding of pigeons was studied in a chamber with two adjacent keys that could each be lit with either a red or a green dot. Fixed-length trials were used, with pecking on positive trials reinforced by presenting food at the end of the trial. In each session the first 40 trials were one-key trials with one key lit on each trial, either red or green, and the next four trials were choice trials with both keys lit, one red and the other green. When blocks of sessions were presented in which all one-key trials were positive trials of a single color, choice responding gradually shifted to the color presented most recently during one-key trials. When all one-key trials were nonreinforced trials of a single color, responding on choice trials shifted toward the other color. When positive one-key trials of one color were intermingled with negative one-key trials of the other color, choice responding shifted exclusively to the reinforced color. These shifts in choice responding occurred even when responding on choice trials was never reinforced, and were viewed as based on separate response tendencies for pecking red and pecking green built up during one-key trials.     

The development of communication: When a bad model makes a good teacher

Five experiments were conducted on what 6-year-old children learn about communication by switching listener and speaker roles with competent and incompetent adults and peers. Experiment I demonstrated that children become better communicators to adults after listening to competent adults, competent peers, and incompetent peers, but not incompetent adults. The age of the listener was shown to have an effect in Experiment II, with children becoming less effective communicators when speaking to a peer after listening to an incompetent peer but better communicators when speaking to an adult after listening to an incompetent peer. Experiments III, IV, and V were designed to determine why children do not improve or deteriorate after listening to incompetent adults. It is not deficient memory: Children remember well the ambiguous messages of adults (Experiment IV). It is not implicit demands to be polite to an adult (Experiment III). It is that children think the ambiguous messages of an adult are competent (Experiment V). Mixing the authority and prestige of an adult with incompetent messages leads the child to ignore the adult's behavior as a standard for his or her own performance. These results suggest that social learning of communication skills might occur best when the child can learn what not to do by interacting with peers and what to do when interacting with adults.     

Disentangling Type A behavior: The roles of ambition,insensitivity, and anxiety

This study identified stable components of Type A behavior as usually defined, and examined their relationships with more traditional psychological constructs. Overall scores on the most popular Type A measure (a version of the Jenkins Activity Survey) were moderately associated with ambition but largely unrelated to measures of adjustment. An item analysis yielded subcomponents of Drivenness and Involvement. Drivenness was unrelated to ambition, but was positively related to anxiety and negatively related to interpersonal perceptiveness. Involvement was positively related to ambition and to interpersonal competence. It is suggested that the Jenkins Activity Survey measures a heterogeneous mixture of constructive commitment and self-defeating responses that clouds its psychological interpretation.     

Conditioned inhibition of fear: Evidence for a competing response mechanism

In two experiments, inhibitory conditioning was attempted by presenting a discrete CS in a neutral stimulus environment shortly following the termination of either shock (Experiment 1) or a second discrete CS which had been paired in a forward manner with shock (Experiment 2). Evidence of successful inhibitory conditioning was mixed in Experiment 1, where the properties of the CS were assessed within an escape-from-fear procedure. Postresponse presentations of the CS enhanced performance, whereas the presentation of the CS prior to responding did not have the expected degrading effect on performance. In Experiment 2, the inhibitory properties of the CS were assessed by combining this stimulus with an excitatory CS and presenting the compound to rats engaged in a water-reinforced licking response. Less response suppression was found in reaction to this compound relative to three separate comparison conditions, thus witnessing the success of the inhibitory-conditioning procedure used. The common assumption that inhibitory conditioning results from the nonreinforcement of a CS in a situation where reinforcement is expected, i.e., one which contains previously reinforced cues, is not supported by these data, for no previously reinforced cues were simultaneously presented with the CS during inhibitory training. The data are in agreement with a conditioned antagonistic-response interpretation of inhibitory conditioning.     

Generality of a strength model for three conditions of repeated recall

A Markovian model of repeated recall is presented that is based on four memory processes: (a) a presentation increment that strengthens the memory trace of a word when the word is shown to a subject, (b) a recall increment that strengthens the trace when the subject successfully recalls the word, (c) a cueing decrement that weakens the trace as contextual cues for retrieving a word change over successive trials of attempted recall, and (d) a sampling rule that translates the strength of a memory trace into a probability of recall. Mathematically, the model predicts the relative frequencies of the recall patterns that are defined by sequences of recalls and forgets for individual words over trials. According to the model, the recallability of a word depends on its state, which is a function of (a) whether the word has been recalled for the first time, and if so, then (b) how many consecutive forgets of the word immediately precede the current trial, (c) how many successful recalls of the word have accumulated, and (d) how many previous trials of attempted recall have elapsed. Paradigms that were well described by the model were (a) no reminding, in which words were presented once and then recalled repeatedly without additional presentations; (b) restricted reminding, in which words were presented before each trial of attempted recall up to their first successful recall but not thereafter; and (c) complete reminding, in which all words were presented befor each attempted recall, whether previously recalled or not. Differences in recall among these conditions were explained in terms of differences in values of the model's parameters.     

Self-control and choice in humans: Effects of video game playing as a positive reinforcer

Participants chose between reinforcement schedules differing in delay of reinforcement (interval between a choice response and onset of a video game) and/or amount of reinforcement (duration of access to the game). Experiment 1 showed that immediate reinforcement was preferred to delayed reinforcement with amount of reinforcement held constant, and a large reinforcer was preferred to a small reinforcer when both were obtainable immediately. Imposing a delay before the large reinforcer produced a preference for the immediate, small reinforcer in 40% of participants. This suggested a limited degree of “impulsivity.” In Experiment 2, unequal delays were extended by equal intervals, the amounts being kept equal. Preference for the shorter delay decreased, an effect that presumably makes possible the “preference reversal” phenomenon in studies of self-control. Overall, the results demonstrate that video game playing can produce useful, systematic data when used as a positive reinforcer for choice behavior in humans.     

The effect of deprivation level during noncontingent pairings and instrumental learning on subsequent instrumental performance

In Experiment 1, rats received either response-noncontingent pairings of a tone stimulus with food or response-contingent instrumental training during which only responses in the presence of the tone were reinforced. During this training rats were maintained at either 70 or 90% of their growth-adjusted predeprivation body weights. In a subsequent test phase, one-half of the subjects in each training condition were tested under either 70 or 90% body weight. Subjects which had received response-contingent instrumental training under 70% body weight responded significantly faster to presentations of the tone than did 90% body weight-trained subjects, regardless of test deprivation condition. There was no effect of the deprivation level in effect during response-noncontingent pairings. In Experiment 2, rats received noncontingent tone-reward pairings or nonpairings under either 70 or 90% body weight. In a later test phase under 90% body weight, instrumental responding to the tone was significantly faster for subjects which had received the tone-reward pairings. Deprivation level during the pairings again produced no effect. These results support two conclusions. First, the expectancy learning process appears to be relatively independent of deprivation conditions in effect when such learning takes place; and secondly, deprivation conditions in effect during instrumental learning affect the strength of S-R associative bonds formed.     

Misconceptions about the Fishbein model: Reflections on a study by Songer-Nocks

Songer-Nocks has questioned the generality and sufficiency of Fishbein's model of intentions. It is shown that her conclusions reflect a basic misunderstanding of the model and its implications. Several misconceptions are identified and an attempt is made to clarify some of the theoretical and methodological issues involved.     

Spontaneous private speech and performance on a delayed match-to-sample task

Spontaneous private speech samples were obtained from 65 kindergarten children (mean age 70.3 months) from one suburban (n = 36) and one city (n = 29) school as they worked alone on a delayed match-to-sample (DMS) task with three levels of difficulty (2, 10, and 30 sec delays). As expected increases in DMS delay intervals produced decreased performance and increases in private speech. The expected increased positive relationship between task relevant private speech and performance for longer delays was found in city children but not suburban children. Since mean IQ scores were significantly different for the two groups this variable was further examined in post hoc analyses and discussed along with socio-economic status as possible explanations for the observed school-sample differences. A within-subject comparison for all children showed the percentage of speaking trials correct at 30-sec delay to be significantly greater than the percentage of nonspeaking trials correct. The effect of one experimenter modeled trial on a subsequent 10 trials at 30-sec delay was to increase speech and performance and to show a stronger relationship between speech and performance than for premodeling trials. These exploratory findings with a relatively simple two color matching task suggest further explorations of spontaneous private speech as a way of studying internalization of self regulatory cognitive strategies.