When Unequals Compete: Where Do They Stand After the Competition?

When two unequals compete, the stronger, more able, richer competitor commonly stands a better chance of winning. If the stronger competitor does win, this worsens the relative status of the weaker competitor even further. Does this result depend on the type of competition? Does it depend on the size of the reward to be won? In the present paper, we report an experimental study of how a very simple competitive mechanism can affect the relative standing of the weaker, poorer of two competitors. In a lab experiment with 208 participants, we employed competitions with different levels of uncertainty in how a winner was determined and with different sizes of rewards to be won, to explore effects on the relative standing of the weaker and stronger competitors. We used an investment game in which participants differing in their endowed budgets competed against one another, forfeiting their investment whether they won or lost. Two versions of the game were used: a simple all-pay-auction contest and a non-constant-sum Colonel Blotto contest (Roberson & Kvasov, 2012), both with players that were unequal in their budgets. Results revealed that, in line with published game-theoretic solutions, the relative standing of the weaker agents worsened following competition, and increasingly so the higher the rewards. At the same time, the effect was mitigated in the variant of the Colonel Blotto game, which involved more uncertainty in how the winner was determined.

Age-related differences in strategic competition.

Understanding how people of different ages decide in competition is a question of theoretical and practical importance. Using an experimental laboratory approach, this research investigates the ability of younger and older adults to think and act strategically with equal or unequal resources. In zero-sum games of resource allocation, younger adults (19-35 years) and older adults (65-81 years) made strategic decisions in competition against opponents of a similar age (Study 1; N = 120) or different age (Study 2; N = 120). The findings highlight people's ability to make good interpersonal decisions in complex scenarios: Both younger and older adults were aware of their relative strength (in terms of material resources) and allocated their resources adaptively. When competing against opponents of a similar age, people's gains were in line with game-theoretic predictions. However, younger adults made superior strategic allocations and won more frequently when competing against older adults. Measures of fluid cognitive and numerical abilities correlated with strategic behavior in interpersonal competition.

Metacognitive myopia in change detection: A collective approach to overcome a persistent anomaly.

Going beyond the origins of cognitive biases, which have been the focus of continued research, the notion of metacognitive myopia refers to the failure to monitor, control, and correct for biased inferences at the metacognitive level. Judgments often follow the given information uncritically, even when it is easy to find out or explicitly explained that information samples are misleading or invalid. The present research is concerned with metacognitive myopia in judgments of change. Participants had to decide whether pairs of binomial samples were drawn from populations with decreasing, equal, or increasing proportions p of a critical feature. Judgments of p changes were strongly affected by changes in absolute sample size n, such that only increases (decreases) in p that came along with increasing (decreasing) n were readily detected. Across 4 experiments these anomalies persisted even though the distinction of p and n was strongly emphasized through outcome feedback and full debriefing (Experiment 1-4), simultaneous presentation (Experiments 2-4), and recoding of experienced samples into descriptive percentages (Experiment 3-4). In Experiment 4, a joint attempt was made by 10 scientists working in 7 different institutions to develop an effective debiasing training, suggesting how multilab-collaboration might improve the quality of science in the early stage of operational research designing. Despite significant improvements in change judgments, debiasing treatments did not eliminate the anomalies. Possible ways of dealing with the metacognitive deficit are discussed. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Myopic reactivity in repeated-choice: The case of competing with others for a scarce, unevenly distributed resource.

Foraging for a scarce resource takes place when fewer resource-units than agents are distributed among several locations and agents choose at which location to look for the resource. But how do foragers distribute themselves over the different locations? Optimal foraging theory postulates that the distribution of agents should match the distribution of resource units (ideal free distribution [IFD]), but research with animals and humans has revealed undermatching at the location at which the resource is most abundant. For the IFD to be reached, full information about other foragers' choices and outcomes is required, information that is usually not available. We conducted a theoretical analysis of the implications of relying on different levels of information: on the incomplete, but still valid information usually available in foraging scenarios and on full information. The analysis demonstrates that myopic reactivity to disappointment, or to regret, which are likely to arise in the wake of incomplete information, leads to undermatching, with either affect leading to different degrees of undermatching. Importantly, these analyses indicate that behavior would be sensitive not only to resource distribution (as in IFD), but also to its overall abundance. Three experiments employing incentivized repeated choices were conducted. The information provided to participants, the number of locations, and resource abundance were manipulated to test the predictions of the models. Analyses of aggregate choice probabilities and trial-to-trial choice dynamics indicate that myopic reactivity to regret provides the best explanation for the observed data. With more information available, behavior matches more closely the IFD predictions. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

How Endogenous Crowd Formation Undermines the Wisdom of the Crowd in Online Ratings.

People frequently consult average ratings on online recommendation platforms before making consumption decisions. Research on the wisdom-of-the-crowd phenomenon suggests that average ratings provide unbiased quality estimates. Yet we argue that the process by which average ratings are updated creates a systematic bias. In analyses of more than 80 million online ratings, we found that items with high average ratings tend to attract more additional ratings than items with low average ratings. We call this asymmetry in how average ratings are updated endogenous crowd formation. Using computer simulations, we showed that it implies the emergence of a negative bias in average ratings. This bias affects items with few ratings particularly strongly, which leads to ranking mistakes. The average-rating rankings of items with few ratings are worse than their quality rankings. We found evidence for the predicted pattern of biases in an experiment and in analyses of large online-rating data sets.

The dynamics of choice in a changing world: Effects of full and partial feedback.

We explored the dynamics of choice behavior while the values of the options changed, unannounced, several times. In particular, choice dynamics were compared when the outcome values of all available options were known (full feedback) and when the outcome value of only the chosen option was known (partial feedback). The frequency of change, the values of the options, and the difference between them were also manipulated. In an experiment with N = 427, we found that the patterns of choices were different for the two levels of feedback. Whereas behavior in the full-feedback condition showed a tendency to switch choices following a missed opportunity-replicating previous findings-the behavior in the partial-feedback condition was different. It was sensitive to the outcome value of the chosen option in comparison to some memory of the last-experienced outcome value of the unchosen option. However, the comparison of these two values influenced choice behavior only when the outcome of the currently chosen option was satisfactory and the last outcome of the unchosen one was not. As expected, the other manipulated variables (change frequency, the options' values, and the difference between them) had no effect on the dynamics of behavior.

Anomalies in the detection of change: When changes in sample size are mistaken for changes in proportions.

Detecting changes, in performance, sales, markets, risks, social relations, or public opinions, constitutes an important adaptive function. In a sequential paradigm devised to investigate detection of change, every trial provides a sample of binary outcomes (e.g., correct vs. incorrect student responses). Participants have to decide whether the proportion of a focal feature (e.g., correct responses) in the population from which the sample is drawn has decreased, remained constant, or increased. Strong and persistent anomalies in change detection arise when changes in proportional quantities vary orthogonally to changes in absolute sample size. Proportional increases are readily detected and nonchanges are erroneously perceived as increases when absolute sample size increases. Conversely, decreasing sample size facilitates the correct detection of proportional decreases and the erroneous perception of nonchanges as decreases. These anomalies are however confined to experienced samples of elementary raw events from which proportions have to be inferred inductively. They disappear when sample proportions are described as percentages in a normalized probability format. To explain these challenging findings, it is essential to understand the inductive-learning constraints imposed on decisions from experience.

The Evaluative Advantage of Novel Alternatives: An Information-Sampling Account.

New products, services, and ideas are often evaluated more favorably than similar but older ones. Although several explanations of this phenomenon have been proposed, we identify an overlooked asymmetry in information about new and old items that emerges when people seek positive experiences and learn about the qualities of (noisy) alternatives by experiencing them. The reason for the asymmetry is that people avoid rechoosing alternatives that previously led to poor outcomes; hence, additional feedback on their qualities is precluded. Negative quality estimates, even when caused by noise, thus tend to persist. This negative bias takes time to develop, and affects old alternatives more strongly than similar but newer alternatives. We analyze a simple learning model and demonstrate the process by which people would tend to evaluate a new alternative more positively than an older alternative with the same payoff distribution. The results from two experimental studies (Ns = 769 and 805) support the predictions of our model.

Binding lies.

Do we feel bound by our own misrepresentations? Does one act of cheating compel the cheater to make subsequent choices that maintain the false image even at a cost? To answer these questions we employed a two-task paradigm such that in the first task the participants could benefit from false reporting of private observations whereas in the second they could benefit from making a prediction in line with their actual, rather than their previously reported observations. Thus, for those participants who inflated their report during the first task, sticking with that report for the second task was likely to lead to a loss, whereas deviating from it would imply that they had lied. Data from three experiments (total N = 116) indicate that, having lied, participants were ready to suffer future loss rather than admit, even if implicitly, that they had lied.

Rivals in the dark: how competition influences search in decisions under uncertainty.

In choices between uncertain options, information search can increase the chances of distinguishing good from bad options. However, many choices are made in the presence of other choosers who may seize the better option while one is still engaged in search. How long do (and should) people search before choosing between uncertain options in the presence of such competition? To address this question, we introduce a new experimental paradigm called the competitive sampling game. We use both simulation and empirical data to compare search and choice between competitive and solitary environments. Simulation results show that minimal search is adaptive when one expects competitors to choose quickly or is uncertain about how long competitors will search. Descriptively, we observe that competition drastically reduces information search prior to choice.

Strategic interactions, affective reactions, and fast adaptations.

We studied repeated choices under uncertainty in situations in which the source of uncertainty is the choice of an interaction partner. In 1 experiment the participants engaged in repeated decisions in a mixed motive game; in another experiment the options and outcomes were identical to those in the 1st, but periods of the mixed-motive game alternated with periods of a coordination game, with the change in period not announced. We analyzed choice dynamics-the relationship between an outcome and the choice that followed-and aggregate choice probabilities to gauge the relative merit of reward-based or affect-based accounts (the affects considered being disappointment and regret). In both experiments choice dynamics were essentially identical and were compatible with only the regret-based account. This was true irrespective of the game played or the stage (early or late) of the game. Moreover, the same dynamics explained the very different aggregate probabilities with which the 2 options were chosen in the 2 games and the remarkably fast adaptations to unannounced changes in the game played.

Judge for yourself: reply to Evans and Buehner (2011).

In their comment, Evans and Buehner (2011) maintained that Fiedler and Kareev's (2006) conclusion that decision quality does not always increase with the size of information sample is wrong in every respect. They claimed, first, that the decision model proposed by Fiedler and Kareev is normatively incorrect and is not supported by earlier findings; second, that Fiedler and Kareev misinterpreted or misrepresented their own data, which show in fact a large-sample advantage; and third, that it is not true that small samples lead to clear data; rather, when clear data are observed people make do with small samples. In this rebuttal, we refute all these claims. First, the issue is whether the model is descriptively, not normatively, correct. Furthermore, earlier data are commensurate with our, not Evans and Buehner's, model. Second, our data do support our conclusion; it is Evans and Buehner's dismissal of some of our data that led them to their conclusions. Finally, Evans and Buehner's third point is discussed explicitly and at length in the original article. However, whereas Evans and Buehner only reiterate this point (and present it as novel), we continue from there and show that small samples are likely to result in clear data.

Clarifying the advantage of small samples: as it relates to statistical Wisdom and Cahan's (2010) normative intuitions.

On the basis of earlier findings, we (Fiedler & Kareev, 2006) presented a statistical decision model that explains the conditions under which small samples of information about choice alternatives inform more correct choices than large samples. Such a small-sample advantage (SSA) is predicted for choices, not estimations. It is contingent on high constant decision thresholds. The model was harshly criticized by Cahan (2010), who argued that the SSA disappears when the threshold decreases with increasing sample size and when the costs of incorrect decisions are higher than the benefits of correct decisions. We refute Cahan's critique, which confuses normative and descriptive arguments. He neither questioned our theoretical reasoning nor presented empirical counterevidence. Instead, he discarded our model as statistically invalid because the threshold does not decrease with increasing sample size. Contrary to this normative intuition, which presupposes a significance-testing rationale, we point out that decisions are often insensitive to sample size. We also refute Cahan's intuition that ignoring the potential asymmetry of gains and losses creates a serious bias in favor of the SSA. We regret any misunderstandings resulting from our linking the SSA to Bernoulli's law of large numbers.

Correct acceptance weighs more than correct rejection: a decision bias induced by question framing.

We propose that in attempting to detect whether an effect exists or not, people set their decision criterion so as to increase the number of hits and decrease the number of misses, at the cost of increasing false alarms and decreasing correct rejections. As a result, we argue, if one of two complementary events is framed as the positive response to a question and the other as the negative response, people will tend to predict the former more often than the latter. Performance in a prediction task with symmetric payoffs and equal base rates supported our proposal. Positive responses were indeed more prevalent than negative responses, irrespective of the phrasing of the question. The bias, slight but consistent and significant, was evident from early in a session and then remained unchanged to the end. A regression analysis revealed that, in addition, individuals' decision criteria reflected their learning experiences, with the weight of hits being greater than that of correct rejections.

The effects of problem content and scientific background on information search and the assessment and valuation of correlations.

The effects of problem contents and one's scientific background on the detection of correlations and the assessment of their strength were studied using a task that required active data search, assessment of the strength of a correlation, and monetary valuation of the correlation's predictive utility. Participants (N = 72) who were trained either in the natural sciences or in the social sciences and humanities explored data sets differing in contents and actual strength of correlation. Data search was consistent across all variables: Participants drew relatively small samples whose relative sizes would favor the detection of a correlation, if one existed. In contrast, the assessment of the correlation strength and the valuation of its predictive utility were strongly related not only to its objective strength, but also to the correspondence between problem contents and one's scientific background: When the two matched, correlations were judged to be stronger and more valuable than when they did not.

Base rates, contingencies, and prediction behavior.

A skew in the base rate of upcoming events can often provide a better cue for accurate predictions than a contingency between signals and events. The authors study prediction behavior and test people's sensitivity to both base rate and contingency; they also examine people's ability to compare the benefits of both for prediction. They formalize these notions and propose a new measure of the regularity in the environment (ExpPA). In two experiments they test whether the notions underlying this measure capture prediction behavior. In the first experiment, they compare participants' prediction behavior, preference, and assessment of contingencies in two data sets that differ only in their base rate. In the second, in which the contribution of contingency over base rate is manipulated, they study participants' willingness to forgo a costly predictor. Results indicate a close correspondence between ExpPA and behavior.

Do the weak stand a chance? Distribution of resources in a competitive environment.

When two agents of unequal strength compete, the stronger one is expected to always win the competition. This expectation is based on the assumption that evaluation of performance is complete, hence flawless. If, however, the agents are evaluated on the basis of only a small sample of their performance, the weaker agent still stands a chance of winning occasionally. A theoretical analysis indicates that, to increase the chance of this happening the weaker agent ought to give up on enough occasions so that he or she can match the stronger agent on the remaining ones. We model such a competition in a game, present its game-theoretic solution, and report an experiment, involving 144 individuals, in which we tested whether players (both weak and strong) are actually sensitive to their relative strengths and know how to allocate their resources accordingly. Our results indicate that they do.

Choosing between adaptive agents: some unexpected implications of level of scrutiny.

Even with ample time and opportunity to use extensive data, people often make do with small samples, which increases their risk of making the wrong decision. A theoretical analysis indicates, however, that when the decision involves continually selecting among competing, adaptive agents who are eager to be selected, an error-prone evaluation may be beneficial to the decision maker. In this case, the chance of an error can motivate competitors to exert greater effort, improving their level of performance--which is the prime concern of the decision maker. This theoretical argument was tested empirically by comparing the effects of two levels of scrutiny of performance. Results show that minimal scrutiny can indeed lead to better performance than full scrutiny, and that the effect is conditional on a bridgeable difference between the competitors. We conclude by pointing out that small-sample-based, error-prone decisions may also maintain competition and diversity in the environment.

Nonproportional sampling and the amplification of correlations.

A theoretical analysis shows that sample correlations between two binary variables will be inflated when the frequency distributions of the two variables are flatter (i.e., closer to equal frequencies for the two values) in the sample than in the population. A correlation-assessment study in which participants were free to choose their own sample revealed an overwhelming preference for samples that included roughly the same number of observations for the two values of dichotomous variables, irrespective of their actual distribution in the population. Subjective estimates of observed correlations followed the sample correlations--which were inflated, as predicted--more closely than the true correlations. People's sampling behavior thus resembles that of a research designer who maximizes the chance of detecting a relationship, at the cost of diminished accuracy in estimating its strength.

Does decision quality (always) increase with the size of information samples? Some vicissitudes in applying the law of large numbers.

Adaptive decision making requires that contingencies between decision options and their relative assets be assessed accurately and quickly. The present research addresses the challenging notion that contingencies may be more visible from small than from large samples of observations. An algorithmic account for such a seemingly paradoxical effect is offered within a satisficing-choice framework. Accordingly, a choice is only made when the sample contingency describing the relative evaluation of the 2 options exceeds a critical threshold. Small samples, because of the high dispersion of their sampling distribution, facilitate above-threshold contingencies. Across a broad range of parameters, the resulting small-sample advantage in terms of hits is stronger than their disadvantage in false alarms. Computer simulations and experiments support the model predictions. The relative advantage of small samples is most apparent when information loss is low, when the threshold is high relative to the ecological contingency, and when the sampling process is self-truncated.