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Banking on a Bad Bet: Probability Matching in Risky Choice Is Linked to Expectation Generation
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Probability matching is the tendency to match choice probabilities to outcome probabilities in a binary prediction task. This tendency is a long-standing puzzle in the study of decision making under risk and uncertainty, because always predicting the more probable outcome across a series of trials (maximizing) would yield greater predictive accuracy and payoffs. In three experiments, we tied the predominance of probability matching over maximizing to a generally adaptive cognitive operation that generates expectations regarding the aggregate outcomes of an upcoming sequence of events. Under conditions designed to diminish the generation or perceived applicability of such expectations, we found that the frequency of probability-matching behavior dropped substantially and maximizing became the norm.
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... Therefore, the binary prediction in which one future outcome is less probable yet more desirable could work as a condition where individuals search for evidence or information that was less accessible initially. One possible aspect of the information that is useful for predicting a less probable outcome could be the stochastic nature of the outcome-the expectation that a less probable outcome would occur by chance (e.g., probability-matching; Gal, 1996;James & Koehler, 2011;Newell & Rakow, 2007). In general, understanding the stochastic nature of an outcome demands complex thought processes (Fischbein, Nello, & Marino, 1991;Jones, Langrall, & Mooney, 2007;Nilsson, 2013;Piaget & Inhelder, 1975) and less immediate information (Kahneman & Tversky, 1982, p.153). ...
... First, there could be a similarity between the current experimental paradigm and the experimental paradigm used in repeated binary-choice studies. The repeated binary-choices were analyzed through aggregating multiple responses made by a single individual (Friedman & Massaro, 1998;Gal, 1996;James & Koehler, 2011;Newell & Rakow, 2007;White & Koehler, 2007). However, in the current research, the data were collected through aggregating a single response made by multiple individuals in order to identify a typical pattern of behavior, since a proportion becomes conceptually identical to a mean if binary-predictions are made independently by multiple individuals. ...
... It has been observed that, when an individual makes several successive binary predictions, they also make predictions of a less probable outcome based on its actual probability. Namely, when one outcome is 10% probable (i.e., the other is 90% probable), an individual is likely to make a prediction of this outcome in roughly 10 out of 100 successive prediction attempts (Gal, 1996;James & Koehler, 2011;Newell & Rakow, 2007). This indicates that probability-matching is motivated by the probability information of the less probable outcome, which could also be an explanation for the different prediction pattern observed in Study 1, Condition 3. Consequently, it was hypothesized that the probability-matching motivation for a less probable outcome would significantly increase the number of individuals who predict a red ball in Condition 1. ...
... One possible interpretation of the conflicting results in the literature is that probability matching is not necessarily the product of a single process, but rather the result of a mosaic of mechanisms which produce similar behavioural outcomes even though they might operate in different circumstances 28,46,47 . However, the interpretation of the literature is complicated by the fact that behaviour on probability learning tasks is very sensitive to the details of the task and, for adults at least, its framing 3 . ...
... Instructions. Previous research has accentuated the role that instructions play on adult human's responses to prediction tasks: participants are more likely to maximise with instructions that emphasise single-trial predictions 46,62 , and more likely to probability match with instructions that emphasise sequence-based predictions 62 . These results suggest that the difference between human and non-human behaviour might lie in the fact that humans default to sequence-based expectations while other animals are more likely to make trialby-trial predictions. ...
Probability matching has long been taken as a prime example of irrational behaviour in human decision making; however, its nature and uniqueness in the animal world is still much debated. In this paper we report a set of four preregistered experiments testing adult humans and Guinea baboons on matched probability learning tasks, manipulating task complexity (binary or ternary prediction tasks) and reinforcement procedures (with and without corrective feedback). Our findings suggest that probability matching behaviour within primate species is restricted to humans and the simplest possible binary prediction tasks; utility-maximising is seen in more complex tasks for humans as pattern-search becomes more effortful, and we observe it across the board in baboons, altogether suggesting that it is a cognitively less demanding strategy. These results provide further evidence that neither human nor non-human primates default to probability matching; however, unlike other primates, adult humans probability match when the cost of pattern search is low.
... The occurrence of pattern matching is quite common and has shown to be influenced by the effort needed to implement a strategy 37 www.nature.com/scientificreports/ makes pattern matching less likely) 38 , and task expectations (for example setting a local focus to look at each trial separately makes the occurrence of pattern matching less likely) 39 . Cognitive load during the decision does not change the likelihood that participants use pattern matching 40,41 . ...
In natural environments, head movements are required to search for objects outside the field of view (FoV). Here we investigate the power of a salient target in an extended visual search array to facilitate faster detection once this item comes into the FoV by a head movement. We conducted two virtual reality experiments using spatially clustered sets of stimuli to observe target detection and head and eye movements during visual search. Participants completed search tasks with three conditions: (1) target in the initial FoV, (2) head movement needed to bring the target into the FoV, (3) same as condition 2 but the periphery was initially hidden and appeared after the head movement had brought the location of the target set into the FoV. We measured search time until participants found a more salient (O) or less salient (T) target among distractors (L). On average O’s were found faster than T’s. Gaze analysis showed that saliency facilitation occurred due to the target guiding the search only if it was within the initial FoV. When targets required a head movement to enter the FoV, participants followed the same search strategy as in trials without a visible target in the periphery. Moreover, faster search times for salient targets were only caused by the time required to find the target once the target set was reached. This suggests that the effect of stimulus saliency differs between visual search on fixed displays and when we are actively searching through an extended visual field.
... It still might be the case that for events that are purely stochastic, the reason why people predict a desirable but improbable outcome will occur is that the randomness of the event allows for arbitrary guesses in trying to specify what will happen. Research on people's tendency to match (i.e., exhibit prediction rates that match evidence proportions) rather than to maximize (i.e., always predict the more probable outcome) demonstrates people's willingness to occasionally make arbitrary predictions in favor of a lower probability outcome (James & Koehler, 2011;Schulze, James, Koehler, & Newell, 2019). Notably, the findings on matching vs. maximizing tend to come from paradigms that involve purely stochastic events. ...
The desirability bias (or wishful thinking effect) refers to when a person's desire regarding an event's occurrence has an unwarranted, optimistic influence on expectations about that event. Past experimental tests of this effect have been dominated by paradigms in which uncertainty about the target event is purely stochastic—i.e., involving only aleatory uncertainty. In six studies, we detected desirability biases using two new paradigms in which people made predictions about events for which their uncertainty was both aleatory and epistemic. We tested and meta-analyzed the impact of two potential moderators: the strength of evidence and the level of stochasticity. In support of the first moderator hypothesis, desirability biases were larger when people were making predictions about events for which the evidence for the possible outcomes was of similar strength (vs. not of similar strength). Regarding the second moderator hypothesis, the overall results did not support the notion that the desirability bias would be larger when the target event was higher vs. lower in stochasticity, although there was some significant evidence for moderation in one of the two paradigms. The findings broaden the generalizability of the desirability bias in predictions, yet they also reveal boundaries to an account of how stochasticity might provide affordances for optimistically biased predictions.
... In both cases, children ignore random variation to create a systematic pattern. Many researchers have concluded that age-related differences on probability learning tasks may help explain age-related differences in language learning (Hudson Kam & Chang, 2009;Hudson Kam & Newport, 2005James & Koehler, 2011;Perfors & Burns, 2010;Pitts Cochran et al., 1999;Ramscar & Gitcho, 2007;Singleton & Newport, 2004;Wonnacott, 2011;Yurovsky, Boyer, Smith, & Yu, 2013). One goal of the present review is to determine if this analogy between language learning and behavior on probability learning tasks is merited. ...
In probability learning experiments, a participant is typically presented with one of two alternatives to select, one of which will lead to a reward. For example, in a 70:30 task, one alternative will lead to a reward on 70% of trials while the other will yield a reward on the remaining 30% of trials. On probability learning tasks, adults are said to “probability match,” selecting each alternative with the relative frequency with which it has been reinforced. Children, on the other hand, are said to “maximize,” always guessing whichever alternative has been reinforced more often. The different patterns between adult and child behavior are thought to have implications for language learning, especially qualitative differences in child and adult language learning skills and developmental trajectories on a range of other cognitive tasks. However, a thorough review of the literature suggests that behavioral profiles of adults and children are not as straightforward as has been claimed. Crucially, there is little empirical support for a true probability matching strategy by any participants. Differences in features of the experimental task and in meta-task knowledge contribute to variability across tasks and participants in ways that only become evident when systematically reviewing the literature. Differences in probability learning across populations may not underlie or indicate causal differences in more complex cognitive behavior, but rather may themselves be another pattern of behavior that theories of learning and development must account for.
... According to the broad frameworks of cognitive processing, learning, and decision making, the processing of new information and the formation of expectations about future events are guided by inferences based on prior experiences (e.g., Daw, Gershman, Seymour, Dayan, & Dolan, 2011;Friston, 2005;Friston, 2010;Friston, Stephan, Montague, & Dolan, 2014;Griffiths, Kemp, & Tenenbaum, 2008;Shohamy & Daw, 2015). This also pertains to randomness perception (Hahn & Warren, 2009;Sun et al., 2015;Sun & Wang, 2010;Teigen & Keren, 2020;Warren, Gostoli, Farmer, El-Deredy, & Hahn, 2018), binary choice behavior (Feher da Silva & Baldo, 2012;Gaissmaier & Schooler, 2008;James & Koehler, 2011) as well as implicit statistical learning (Conway, 2020;Qian, Jaeger, & Aslin, 2012). The persistence of the primarily learned statistical structure and its influence on further processing have been evidenced by behavioral (e.g., Gebhart, Aslin, & Newport, 2009;Lany, Gómez, & Gerken, 2007) as well as neurocognitive measures (e.g., Honbolygó & Csépe, 2013;Karuza et al., 2016;Mullens et al., 2014;Todd, Frost, Fitzgerald, & Winkler, 2020;Todd, Provost, & Cooper, 2011). ...
It is unclear how implicit prior knowledge is involved and remains persistent in the extraction of the statistical structure underlying sensory input. Therefore, this study investigated whether the implicit knowledge of second-order transitional probabilities characterizing a stream of visual stimuli impacts the processing of unpredictable transitional probabilities embedded in a similar input stream. Young adults (N = 50) performed a four-choice reaction time (RT) task that consisted of structured and unstructured blocks. In the structured blocks, more probable and less probable short-range nonadjacent transitional probabilities were present. In the unstructured blocks, the unique combinations of the short-range transitional probabilities occurred with equal probability; therefore, they were unpredictable. All task blocks were visually identical at the surface level. While one-half of the participants completed the structured blocks first followed by the unstructured blocks, this was reversed in the other half of them. The change in the structure was not explicitly denoted, and no feedback was provided on the correctness of each response. Participants completing the structured blocks first showed faster RTs to more probable than to less probable short-range transitional probabilities in both the structured and unstructured blocks, indicating the persistent effect of prior knowledge. However, after extended exposure to the unstructured blocks, they updated this prior knowledge. Participants completing the unstructured blocks first showed the RT difference only in the structured blocks, which was not constrained by the preceding exposure to unpredictable stimuli. The results altogether suggest that implicitly acquired prior knowledge of predictable stimuli influences the processing of subsequent unpredictable stimuli. Updating this prior knowledge seems to require a longer stretch of time than its initial acquisition.
... In sum, providing a fuller description of the outcome contingencies and information about the task structure did not enhance value learning despite leading to an overall improvement in explicit knowledge of the learned associations. The null effect of instruction on value learning is consistent with previous evidence that participants use probability matching strategies even when outcome information and occurrence probabilities are fully available (James & Koehler, 2011;Koehler & James, 2009, 2010. The fact that explicit VLT instructions decreased rather than increased the explicit knowledge advantage for the optimal loss scene is somewhat paradoxical. ...
Neutral stimuli can acquire value when people learn to associate them with positive or negative outcomes (i.e., gain versus loss associations). Acquired value has been shown to affect how gain and loss associated stimuli are attended, remembered, and acted upon. Here we investigate a potential and previously unreported learning asymmetry in the acquisition of gain and loss associations that may have consequences for subsequent cognitive processing. In our first study, we provide meta-analytic evidence that in probabilistic learning tasks that pair neutral stimuli with intermixed win, loss, and no-change outcomes, people learn win-associations better than loss-associations despite the symmetrical task structure and symmetrical outcome probabilities. Then in two empirical studies, we demonstrate that this learning asymmetry is evident when acquiring gain versus loss associations to gray-scale landscape images whether participants earn points or money (Study 2), and whether or not they receive explicit instructions about the outcome contingencies (Study 3). Furthermore, performance on a post-learning source recognition task was also asymmetrical: explicit knowledge of associated outcomes was superior for optimal gain than optimal loss scenes. These findings indicate the acquisition of gain and loss associations need not be equivalent, despite symmetrical outcome probabilities, equivalent numbers of learning trials, and a constant learning criterion. Consequently, learning asymmetries could contribute to valence and optimality differences in subsequent cognitive processing.
People often need to predict the outcomes of future events. We investigate the influence of order on such forecasts. Six preregistered studies (n = 7,955) show that people are more likely to forecast improbable outcomes (e.g., that an “underdog” will win a game) for predictions they make later versus earlier within a sequence of multiple predictions. This effect generalizes across several contexts and persists when participants are able to revise their predictions as well as when they are incentivized to make correct predictions. We propose that this effect is driven by people’s assumption that improbable outcomes are bound to occur at some point within small sets of independent events (i.e., “belief in the law of small numbers”). Accordingly, we find that the effect is attenuated when the statistical independence of events is made salient to forecasters both through the nature of the predictions themselves (i.e., when the events are from distinct domains) and through directly informing them about statistical independence. These findings have notable practical implications, as policy makers and businesses have the ability to control the order in which people evaluate and predict future events.
This paper was accepted by Yuval Rottenstreich, behavioral economics and decision analysis.
Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2022.01175 .
Erwartungen spielen eine zentrale Rolle in der menschlichen Handlungssteuerung. Trotz ihrer Rolle in verschiedenen psychologischen Theorien, werden Erwartungen unterschiedlich operationalisiert (was zu teilweise widersprüchlichen Ergebnissen führt) und dabei oft nur indirekt über Hinweisreize(Cues) gemessen bzw. induziert. Diese Dissertation beschäftigt sich mit der Frage, wie sich selbst-generierte und cue-induzierte Erwartungen qualitativ unterscheiden, wie die beiden Erwartungsformen interagieren und welche Art der Operationalisierung zur Messung von Erwartungen zielführender ist. In den beschriebenen Experimenten hatten Proband_innen die Aufgabe, eine Erwartung zu verbalisieren und so schnell und akkurat wie möglich auf einen Stimulus zu reagieren, der diese Erwartung entweder erfüllt(match) oder davon abweicht(mismatch). Die Erwartung konnte dabei durch Vorlesen eines Cues oder die Benennung einer selbst-generierten Erwartung verbalisiert werden. Dabei wurden das Abstraktionslevel der Erwartung, die Art der Reaktion und der Vergleich der beiden Erwartungsformen (innerhalb vs. zwischen verschiedenen Trials) variiert. Bei einem Experiment, das einen genaueren Vergleich von cue-induzierten zu selbst-generierten Erwartungen erlaubt, konnte der größere Effekt von selbst-generierten Erwartungen bestätigt werden. Es wird gezeigt und diskutiert, dass und wie sich selbst-generierte Erwartungseffekte qualitativ von cue-induzierten Effekten unterscheiden. Am konkreten Beispiel von Konflikterwartungen können verbalisierte selbst-generierte Erwartungen eine zuvor widersprüchliche Forschungslage zum Einfluss von Erwartungen auf sequentielle Konflikteffekte konsolidieren. Die Effekte von selbst-generierten und cue-induzierten Erwartungen sind nicht additiv und der Effekt eines Cues wird nicht durch eine abweichende selbst-generierte Erwartung zunichte gemacht. In Anbetracht dieser Ergebnisse diskutiere ich kritisch die Operationalisierung von Erwartungen als Cues.
8 GROUPS OF SS, FROM NURSERY SCHOOL (3-5 YR.) TO COLLEGE (18-25 YR.) PREDICTED 200 EVENTS OF A CONSTRAINED 75:25 SCHEDULE. OVERALL RESPONSE PROBABILITIES AND SELECTED SEQUENTIAL DEPENDENCIES WERE EXAMINED FOR GROUPS AND INDIVIDUALS. VERY YOUNG SS BOTH MAXIMIZED (NURSERY) AND ALTERNATED RESPONSES (KINDERGARTEN, 5-6 YR.) WHILE INDIVIDUAL PROBABILITY MATCHING INCREASED WITH GRADE. ANALYSIS OF BOTH GROUP AND INDIVIDUAL DATA SHOWED A DECREASE IN POSITIVE RECENCY, AN INCREASE IN NEGATIVE RECENCY, AND THE "GAMBLER'S FALLACY" WITH INCREASED GRADE STANDING (THE 3RD GRADE DID NOT CONFORM TO THIS TREND). THE INCREASE IN GROUP "GAMBLER'S FALLACY" BEHAVIOR WAS DUE TO A PROGRESSIVE INCREASE IN THE PREDICTION OF SEQUENCES OF INTERMEDIATE RUNS. ABOVE NURSERY SCHOOL, RESPONSE PERSEVERATION INCREASED WITH GRADE. HOWEVER, WITH PRACTICE SS BEGAN TO ADJUST TO THE SCHEDULE EVENT PERSEVERATION. THE ACCURACY OF THE ADJUSTMENT IN THE 200 TRIALS WAS AGAIN A FUNCTION OF GRADE. (20 REF.) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
In three experiments involving over 1,500 university students (n=1,557) and two different probabilistic choice tasks, we found that the utility-maximizing strategy of choosing the most probable
alternative was not the majority response. In a story problem version of a probabilistic choice task in which participants
chose from among five different strategies, the maximizing response and the probabilitymatching response were each selected
by a similar number of students (roughly 35% of the sample selected each). In a more continuous, or trial-by-trial, task,
the utility-maximizing response was chosen by only one half as many students as the probability-matching response. More important,
in both versions of the task, the participants preferring the utility-maximizing response were significantly higher in cognitive
ability than were the participants showing a probability-matching tendency. Critiques of the traditional interpretation of
probability matching as nonoptimal may well help explain why some humans are drawn to the nonmaximizing behavior of probability
matching, but the traditional heuristics and biases interpretation can most easily accommodate the finding that participants
high in computational ability are more likely to carry out the rule-based cognitive procedures that lead to maximizing behavior.
Findings from two experiments indicate that probability matching in sequential choice arises from an asymmetry in strategy availability: The matching strategy comes readily to mind, whereas a superior alternative strategy, maximizing, does not. First, compared with the minority who spontaneously engage in maximizing, the majority of participants endorse maximizing as superior to matching in a direct comparison when both strategies are described. Second, when the maximizing strategy is brought to their attention, more participants subsequently engage in maximizing. Third, matchers are more likely than maximizers to base decisions in other tasks on their initial intuitions, suggesting that they are more inclined to use a choice strategy that comes to mind quickly. These results indicate that a substantial subset of probability matchers are victims of "underthinking" rather than "overthinking": They fail to engage in sufficient deliberation to generate a superior alternative to the matching strategy that comes so readily to mind.
Rats were trained on a T-maze under either a 50:50 or a 85:15 reinforcement schedule and then shifted to a 30:70 schedule. With noncorrection training, preshift choices approached an asymptote at 100% to the more likely alternative. Postshift choices dropped considerably below the 30% pay-off level without special resistance to readjustment by the rats shifted from the 50:50 schedule. Noncorrection training proved more efficient than correction training, and the rats made a higher percentage of successful choices than humans run under analogous conditions." From Psyc Abstracts 36:01:1EL92P.
Ten monkeys were trained in a probability learning situation, one response being rewarded on 75% of the trials, and the alternative response on the remaining 25% of the trials. After each response, S also could see whether the response he did not make would have been rewarded if it had been made." When correction of an unrewarded response was not permitted, all Ss reached an asymptote of 100% choice on the .75 side. When immediate correction was allowed, the data did not support the conclusion that all Ss were approaching an asymptote of 75% choice of the .75 side. "The behavior of monkeys in this situation is not compatible with either an "information' or a "secondary reinforcement' model.
The author regrets that there was a mistake in reference [37] in the above article. The correct reference is:Oliva, A. and Torralba, A. (2001) Modeling the shape of the scene: a holistic representation of the spatial envelope. Int. J. Comput. Vis. 42, 145–175.The author sincerely apologizes for any problems that this error may have caused.
Dual-system models of reasoning attribute errors of judgment to two failures: the automatic operations of a 'System 1' generate a faulty intuition, which the controlled operations of a 'System 2' fail to detect and correct. We identify System 1 with the automatic operations of associative memory and draw on research in the priming paradigm to describe how it operates. We explain how three features of associative memory--associative coherence, attribute substitution and processing fluency--give rise to major biases of intuitive judgment. Our article highlights both the ability of System 1 to create complex and skilled judgments and the role of the system as a source of judgment errors.
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.