Probability matching in risky choice: The interplay of feedback and strategy availability

Probability matching in sequential decision making is a striking violation of rational choice that has been observed in hundreds of experiments. Recent studies have demonstrated that matching persists even in described tasks in which all the information required for identifying a superior alternative strategy—maximizing—is present before the first choice is made. These studies have also indicated that maximizing increases when (1)?the asymmetry in the availability of matching and maximizing strategies is reduced and (2)?normatively irrelevant outcome feedback is provided. In the two experiments reported here, we examined the joint influences of these factors, revealing that strategy availability and outcome feedback operate on different time courses. Both behavioral and modeling results showed that while availability of the maximizing strategy increases the choice of maximizing early during the task, feedback appears to act more slowly to erode misconceptions about the task and to reinforce optimal responding. The results illuminate the interplay between “top-down” identification of choice strategies and “bottom-up” discovery of those strategies via feedback.     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

Probability matching: encouraging optimal responding in humans.

Two hundred undergraduate students participated in a repeated-trials binary choice procedure in which choice of one outcome was correct on 75% of trials. Subjects received 192 trials and were divided into five conditions: (1) control; (2) subjects were given the actual probabilities; (3) subjects were told if they did well they could leave early; (4) competition condition; (5) midway through the task subjects were asked to recommend a strategy for another subject. Half of the subjects in each group were told that the best they could do was to be correct on 75% of the trials. This manipulation permitted assessment of the hypothesis that subjects in probability-matching tasks are seeking a strategy that will be correct on 100% of the trials. The results partially confirmed this hypothesis. In addition, two of the variables improved performance significantly (giving probabilities and asking subjects to recommend a strategy). However, while subjects in all groups improved significantly over trials, optimal choice did not occur in this task.     

When confidence in a choice is independent of which choice is made

For forced-choice two-alternative general-information questions, confidence in the correctness of the answer differed reliably for different questions, regardless of which answer was chosen. Results suggested that this choice-independent confidence is mediated by the domain familiarity of the question and by its tendency to bring to mind either few or many thoughts and considerations. Ratings of the questions on familiarity and accessibility yielded strong correlations with participants’ confidence in whichever of two answers they had chosen, and with estimates of the percentage of participants who were likely to have chosen either of the answers in a previous experiment. The results were interpreted in terms of confirmation bias: Because items differ in the extent to which they bring to mind few or many pertinent thoughts, selective focusing on supportive evidence should yield a positive correlation between mean confidence in one answer and mean confidence in the alternative answer, as if there is no competition between them.     

Probability and delay of reinforcement as factors in discrete-trial choice.

Pigeons chose between two alternatives that differed in the probability of reinforcement and the delay to reinforcement. A peck on the red key always produced a delay of 5 s and then a possible reinforcer. The probability of reinforcement for responding on this key varied from .05 to 1.0 in different conditions. A response on the green key produced a delay of adjustable duration and then a possible reinforcer, with the probability of reinforcement ranging from .25 to 1.0 in different conditions. The green-key delay was increased or decreased many times per session, depending on a subject's previous choices. The purpose of these adjustments was to estimate an indifference point, or a delay that resulted in a subject's choosing each alternative about equally often. In conditions where the probability of reinforcement was five times higher on the green key, the green-key delay averaged about 12 s at the indifference point. In conditions where the probability of reinforcement was twice as high on the green key, the green-key delay at the indifference point was about 8 s with high probabilities and about 6 s with low probabilities. An analysis based on these results and those from studies on delay of reinforcement suggests that pigeons' choices are relatively insensitive to variations in the probability of reinforcement between .2 and 1.0, but quite sensitive to variations in probability between .2 and 0.     

Signal detection and matching: analyzing choice on concurrent variable-interval schedules.

Pigeons' pecks on a red key and a green key were followed by access to grain according to pairs of concurrent independent variable-interval schedules in a combined signal detection/matching law paradigm. Pecks on the red key were reinforced by the richer variable-interval schedule if a short-duration tone had been presented; pecks on the green key were reinforced by the richer variable-interval schedule if a long-duration tone had been presented. Pecks on the green key given a short-duration tone, or on the red key given a long-duration tone, were reinforced by the leaner variable-interval schedule. The data were analyzed according to both signal detection's and the matching law's separate measures of, first, the discrimination of the choices and, second, the bias to make one response or another. Increasing the difficulty of the tone-duration discrimination decreased both methods' measures of the discrimination of the choices and did not change both methods' measures of the bias to make one response or another. Changing the leaner variable-interval schedule so that it approached the richer variable-interval schedule decreased signal detection's measure of discrimination but left its measure of response bias and the matching law measures unchanged. Data collected only until a subject's first changeover response following presentation of a long or a short tone showed higher values for both methods' measures of discrimination, no change in signal detection's measure of response bias, and lower values for the matching law's measure of response bias. Relationships between the matching law's and signal detection's methods of analyzing choice are discussed. It is concluded that a signal detection analysis is more efficient for examining changes in the difficulty of a discrimination, whereas a matching law analysis is more effective for examining the effects of changes in relative reinforcer frequency.     

Delayed reinforcement and delayed choice in symbolic matching to sample: Effects on stimulus discriminability

Six pigeons were trained to peck a red side key when the brighter of two white lights (S₁) had been presented on the center key, and to peck a green side key when the dimmer of two white lights (S₂) had been presented on the center key. Equal frequencies of reinforcers were provided for the two types of correct choice. Incorrect choices, red side-key pecks following S₂ presentations and green side-key pecks following S₁ presentations, resulted in blackout. With 0-s delay between choice and reinforcement, the delay between sample presentation and choice was varied from 0 to 20 s. Then, with 0-s delay between sample presentation and choice, the delay between choice and reinforcement was varied from 0 to 20 s. Both types of delay resulted in decreased discriminability (defined in terms of a signal-detection analysis) of the center-key stimuli, but delayed choice had more effect on discriminability than did delayed reinforcement. These data are consistent with the view that the two kinds of delay operate differently. The effect of a sample-choice delay may result from a degradation of the conditional discriminative stimuli during the delay; the effect of a choice-reinforcer delay may result from a decrement in control by differential reinforcement.     

Beyond gains and losses: the effect of need on risky choice in framed decisions

Substantial evidence suggests people are risk-averse when making decisions described in terms of gains and risk-prone when making decisions described in terms of losses, a phenomenon known as the framing effect. Little research, however, has examined whether framing effects are a product of normative risk-sensitive cognitive processes. In 5 experiments, it is demonstrated that framing effects in the Asian disease problem can be explained by risk-sensitivity theory, which predicts that decision makers adjust risk acceptance on the basis of minimal acceptable thresholds, or need. Both explicit and self-determined need requirements eliminated framing effects and affected risk acceptance consistent with risk-sensitivity theory. Furthermore, negative language choice in loss frames conferred the perception of high need and led to the construction of higher minimal acceptable thresholds. The results of this study suggest that risk-sensitivity theory provides a normative rationale for framing effects based on sensitivity to minimal acceptable thresholds, or needs.     

Dolphin pointing is linked to the attentional behavior of a receiver

In 2001, Xitco et al. (Anim Cogn 4:115–123) described spontaneous behaviors in two bottlenose dolphins (Tursiops truncatus) that resembled pointing and gaze alternation. The dolphins spontaneous behavior was influenced by the presence of a potential receiver, and the distance between the dolphin and the receiver. The present study adapted the technique of Call and Tomasello [(1994) J Comp Psychol 108:307–317], used with orangutans to test the effect of the receivers orientation on pointing in these same dolphins. The dolphins directed more points and monitoring behavior at receivers whose orientation was consistent with attending to the dolphins. The results demonstrated that the dolphins pointing and monitoring behavior, like that of apes and infants, was linked to the attentional behavior of the receiver.     

Learning mechanisms in matching to sample.

A model system and an experiment on early learning and decision processes in matching-to-sample and oddity-from-sample tasks are presented. The model system is based, in part, on videotaped records of pigeons' looking responses before they chose 1 of 2 comparison stimuli. In order to see the wavelength stimuli recessed behind the pecking keys, the pigeons had to move in front of them. Although there were slight increases in the acceptance probability with switches between the stimuli before a choice response, the overall decision strategy was close to a Markov choice process in which choice proportions could be predicted by the product of each rejection probability and the final acceptance probability. Learning involved learning to discriminate rather than learning to adopt a stricter criterion for an acceptable sample match.     

One-sided limb preference is linked to alternating-limb locomotion in anuran amphibians

Amphibians provide a unique opportunity for identifying possible links between lateralized behaviors, locomotion, and phylogeny and for addressing the origin of lateralized behaviors of higher vertebrates. Five anuran species with different locomotive habits were tested for forelimb and hind limb preferences during 2 stereotyped behavior sequences--wiping a foreign object off their snout and righting themselves from the overturned position. The experiments were analyzed in a broader context of previous findings on anuran lateralization involving 11 anuran species that were studied within the same experimental paradigms. This analysis shows that one-sided forelimb and hind limb motor lateralization in anurans is strongly associated with alternating-limb locomotion and other unilateral limb activity. Conclusions reached for anuran amphibians may be applicable to other vertebrates possessing paired appendages-the degree of lateralization in motor response depends on the mode of locomotion used by a species.     

Human risky choice in a repeated-gambles procedure: an up-linkage replication of Lakshminarayanan, Chen and Santos (2011)

Lakshminarayanan et al. (J Exp Soc Psychol 47: 689–693, 2011) showed that when choice is between variable (risky) and fixed (safe) food amounts with the same expected values, capuchins prefer the safe alternative if choice is framed as a gain, but the risky alternative if it is framed as a loss. These results seem similar to those seen in human prospect-theory tests in choice between variable and fixed gains or losses. Based on this similarity, they interpreted their results as identifying a between-species commonality in cognitive function. In this report, we repeat their experiment with humans as subjects (an up-linkage replication). Whether choices were rewarded with candy or nickels, choice approximated indifference whether framed as gains or losses. Our data mirror those of others who found that when humans make risky choices within a repeated-trials procedure without verbal instruction about outcome likelihoods, preference biases seen in one-shot, language-guided, prospect-theory tests such as Tversky and Kahneman’s (Science 211:453–458, 1981) reflection effect may not appear. The disparity between our findings and those of Lakshminarayanan et al. suggests their study does not evidence a cognitive process shared by humans and capuchins.     

Cetacean responses to violation of expectation paradigm in a free-swim context

Animal Cognition - The investigation of individual responses to unexpected stimuli or outcomes provides insights into basic cognitive processes, such as mental representations, emotional states of...     

Probability matching, accuracy maximization, and a test of the optimal classifier's independence assumption in perceptual categorization

Observers completed perceptual categorization tasks that included 25 base-rate/payoff conditions constructed from the factorial combination of five base-rate ratios (1:3, 1:2, 1:1, 2:1, and 3:1) with five 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 flat-maxima hypothesis with the independence assumption of the optimal classifier. Model-based 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 for the COBRA instantiation later in learning. This pattern held in the present study and in a reanalysis of Bohil and Maddox (2003). Strong support was obtained for the flat-maxima hypothesis over the independence assumption, especially as the observers gained experience with the task. Model parameters indicated that observers' reward-maximizing decision criterion rapidly approaches the optimal value and that more weight is placed on accuracy maximization in separate base-rate/payoff conditions than in simultaneous base-rate/payoff conditions. The superiority of the flat-maxima hypothesis suggests that violations of the independence assumption are to be expected, and are well captured by the flat-maxima hypothesis, with no need for any additional assumptions.     

When being a model minority is good . . . and bad: realistic threat explains negativity toward Asian Americans

The current research explores the hypothesis that realistic threat is one psychological mechanism that can explain how individuals can hold positive stereotypical beliefs toward Asian Americans yet also express negative attitudes and emotions toward them. Study 1 demonstrates that in a realistic threat context, attitudes and emotions toward an anonymous group described by only positive, "model minority" attributes are significantly more negative than when the group was described using other positive attributes. Study 2 demonstrates that realistic threat significantly mediates the relationship between (a) the endorsement of the both the positive and negative stereotypes of Asian Americans and (b) subsequent negative attitudes and emotions toward them. Studies 3 and 4 conceptually replicate this effect in experimental situations involving interactions with Asian Americans in realistic threat contexts. Implications for understanding the nature of stereotyping and prejudice toward Asian Americans and other minority groups are discussed.     

Time is on my side: optimism in intertemporal choice

The present research examines the role of optimism on time preferences for both losses and gains. It is argued that optimism has asymmetric effects on time preferences for gains versus losses: one reason why decision makers prefer immediate gains is because they are optimistic that these gains will be followed by additional gains in future. In contrast, decision makers prefer to delay losses because they are optimistic that losses are avoidable in the future. Optimism about outcomes affects time preferences for both gains and losses, such that low optimism reduces the discount rates while increased optimism is associated with higher discount rates. This prediction was supported in two different domains: monetary outcomes (Study 1), and health (Study 2). Implications of these results for both research practice and time preferences in the real world are discussed.     

Evidence that thesame-different disparity in letter matching is not attributable to response bias

When pairs of letters or letter strings are judged assame ordifferent, correctsame responses are usually faster than correctdifferent responses. Recently, Ratcliff and Hacker (1981, 1982) have argued that thissame-different disparity is likely attributable solely to a bias to respondsame. The present article reports an experiment in which the relative bias to respondsame ordifferent was varied for matches of single-letter pairs. Bias was manipulated by having 80, 60, 40, or 20 pairs in a block of 100 besame, with the remainder beingdifferent. For both sequential and simultaneous presentation of the letters,same reaction times had an overall advantage overdifferent reaction times that could not be attributed to response bias. Moreover, consistent with Proctor’s (1981) facilitation principle, this reaction time disparity was greater with sequential presentation than with simultaneous presentation. The larger reaction time advantage forsame pairs with sequential presentation was obtained without an increase in the relative number of false-same responses, supporting the view that the facilitation is attributable to changes in sensitivity and not to changes in encoding criteria.     

Making the transition: How finding a good job is a risky business for military Veterans in Northern Ireland

ABSTRACT

Veterans transitioning from the military to civilian life may encounter difficulties in different domains of functioning. Most research in this area comes from the US and Israel, with Veterans in Northern Ireland (NI) in the United Kingdom, remaining an understudied population. This qualitative study aimed to examine the nature of transition experiences of NI Veterans by analyzing responses (N = 252) to an open-ended question related to the transition process, in a self-report survey. Thematic analysis highlighted both positive and negative experiences across high-level themes. These were related to (1a) how good the military life had been, (1b) the transition had been easy for some Veterans, and (1c) the skills gained in the military have been valuable; (2) it was hard to adjust to civilian life/still adjusting; (3) negative employment experiences; (4) lack of trust; (5) transitioning is hard in NI; and (6) inadequate support, post-service. The findings highlight that NI Veterans share some of the same challenges as other Veterans; however, the challenges in NI are compounded by ongoing security concerns and political tensions, which means living under the radar is a reality for many, making finding meaningful work and community integration difficult. The findings indicate that preparation for civilian life and the acculturation process needs to start many months before discharge. Perhaps more crucially, regiments should work closely with and support civilian employers to equip them to recognize and value the skills ex-Services Veterans can offer, and find a good fit for their skills within their organizations.