Research ArticlePSYCHOLOGY

Two sides of the same coin: Monetary incentives concurrently improve and bias confidence judgments

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Science Advances  30 May 2018:
Vol. 4, no. 5, eaaq0668
DOI: 10.1126/sciadv.aaq0668
  • Fig. 1 Behavioral task and hypotheses.

    Successive screens displayed in one trial are shown from left to right with durations in milliseconds. (A) Behavioral task—Common part. Participants viewed a couple of Gabor patches displayed on both sides of a computer screen, and judged which had the highest contrast. They were then presented with a monetary stake (in a green frame for gain, gray for neutral, and red for losses) and asked to report their confidence C in their answer on a scale from 50 to 100%. Then, a lottery number L was drawn in a uniform distribution between 50 and 100%, displayed as a scale under the confidence scale, and the scale with the highest number was highlighted. (B) Behavioral task—Lottery > Confidence. If L > C, then the lottery was implemented. A wheel of fortune, with an L% chance of winning, was displayed and played. Then, feedback informed whether the lottery resulted in a win or a loss. (C) Behavioral task—Confidence > Lottery. If C > L, then a clock was displayed together with the message “Please wait,” followed by feedback that depended on the correctness of the initial choice. Subjects would win (gain frame) or not lose (loss frame) the incentive in case of a winning trial, and they would not win (gain frame) or lose (loss frame) the incentive in case of a losing trial. (D) Behavioral task—Payoff matrix. Depending on the combination of a trial’s offered incentive and the trial’s final win or loss (regardless of whether the lottery or the correctness of the answer determined it), participants could receive various outcomes, from winning the proposed incentive to losing the proposed incentive. (E) Hypotheses. Expected biasing effects of incentives (−1€; 0€ or +1€) on confidence under different theoretical hypotheses. (Top) H0: No biasing effects of incentives. Participants are similarly overconfident in the three incentive conditions. (Middle top) H1: Rational decision-making. Under higher incentives, participants are more rational, that is, less biased. The absolute value of incentives therefore decreases confidence, if participants are generally overconfident. (Middle bottom) H2: Desirability bias. Participants are more inclined to believe that they are correct when higher incentives are at stake. The absolute value of incentives increases confidence. (Bottom) H3: Value-confidence interaction. The confidence judgment of participants is affected by the affective component of incentives. The net incentive value affects confidence.

  • Fig. 2 Experiment 1.

    (A) Incentive effects on behavior. Reported confidence (dots) and performance (diamonds)—that is, % correct—as a function of incentives. (B) Incentive effects on confidence (metacognitive) accuracy. Computed bias (top, dots) and meta-d′ (diamonds) as a function of incentives. The insets presented on the right-hand side of the graphs (A and B) depict the results of the linear mixed-effects model, estimated for each behavioral (A, top: confidence; bottom: performance) and metacognitive (B, top: bias; bottom: sensitivity) measure. (C) Incentive effects on confidence formation. Linking incentives, evidence, and confidence for correct (left) and incorrect (right) answers. In those two panels, the scatterplots display reported confidence as a function of evidence for the different incentive levels. The solid line represents the best linear regression fit at the population level. The histograms represent the intercepts (top) and slope for correct (middle) and incorrect (bottom) answers of this relationship, estimated at the individual level and averaged at the population level. The insets presented on the right-hand side of the graph depict the results of the linear mixed-effects model, estimated for each parameter of this regression, that is, intercept (top) and slope for correct answers (middle) and for incorrect answers (bottom). V, net incentive value; |V|, absolute incentive value. Error bars indicate intersubject SEM. *P < 0.05, **P < 0.01, ***P < 0.001.

  • Fig. 3 Experiment 2.

    (A) In experiment 2, participants performed two versions of the task: one in which confidence reports were incentivized (top row), and one in which the performance (that is, correctness of the binary choice) was incentivized (bottom row). See also table S1. Successive screens displayed in one trial are shown from left to right, with durations in milliseconds. Participants viewed a couple of Gabor patches displayed on both sides of a computer screen, and judged which had the highest contrast. They were then presented with a monetary stake (in a green frame for gain, gray for neutral, and red for losses) and asked to report their confidence C in their answer on a scale from 50 to 100%. (B) Incentive effects on behavior. Reported confidence (dots, leftmost scatterplot) and performance (diamonds, rightmost scatterplot)—that is % correct—as a function of incentives. (C) Incentive effects on confidence accuracy. Computed metacognitive bias (dots, leftmost scatterplots) and sensitivity (diamonds, rightmost scatterplots) as a function of incentives. The insets presented on the right-hand side of the graphs (A and B) depict the results of the linear mixed-effects model, estimated for each behavioral (A, top: confidence; bottom: performance) and metacognitive (B, top: bias; bottom: sensitivity) measure. Empty markers with thick edges indicate the performance rewarded task. (D) Incentive effects on confidence formation. Linking incentives, evidence, and confidence for the confidence incentivized (left half) and the performance rewarded (right half) tasks, for both correct (left scatterplot) and incorrect (right scatterplot) answers. In those two panels, the scatterplots display reported confidence as a function of evidence for the different incentive levels. The solid line represents the best linear regression fit at the population level. The histograms represent the intercepts (top) and slope for correct (middle) and incorrect answers (bottom) of this relationship, estimated at the individual level and averaged at the population level. The insets presented on the right-hand side of the graph depict the results of the linear mixed-effects model, estimated for each parameter of this regression, that is, intercept (top) and slope for correct answers (middle) and for incorrect answers (bottom). V, net incentive value; |V|, absolute incentive value. Error bars indicate intersubject SEM. ~P < 0.10; *P < 0.05; **P < 0.01; ***P < 0.001.

  • Fig. 4 Experiment 3.

    (A) Incentive effects on behavior. Reported confidence (dots) and performance (diamonds)—that is, % correct—as a function of incentives. (B) Incentive effects on confidence (metacognitive) accuracy. Computed bias (top, dots) and meta-d′ (diamonds) as a function of incentives. The insets presented on the right-hand side of the graphs (A and B) depict the results of the linear mixed-effects model, estimated for each behavioral (A, top: confidence; bottom: performance) and metacognitive (B, top: bias; bottom: sensitivity) measure. (C) Incentive effects on confidence formation. Linking incentives, evidence, and confidence for correct (left) and incorrect (right) answers. In those two panels, the scatterplots display reported confidence as a function of evidence for the different incentive levels. The solid line represents the best linear regression fit at the population level. The histograms represent the intercepts (top) and slope for correct (middle) and incorrect answers (bottom) of this relationship, estimated at the individual level and averaged at the population level. The insets presented on the right-hand side of the graph depict the results of the linear mixed-effects model, estimated for each parameter of this regression, that is, intercept (top) and slope for correct answers (middle) and for incorrect answers (bottom). V, net incentive value; |V|, absolute incentive value; +/−, incentive valence. Error bars indicate intersubject SEM. **P < 0.01; ***P < 0.001.

  • Fig. 5 Experiment 4.

    (A) Incentive effects on behavior. Reported confidence (dots) and performance (diamonds)—that is, % correct—as a function of incentives. (B) Incentive effects on confidence (metacognitive) accuracy. Computed bias (top, dots) and meta-d′ (diamonds) as a function of incentives. The insets presented on the right-hand side of the graphs (A and B) depict the results of the linear mixed-effects model, estimated for each behavioral (A, top: confidence; bottom: performance) and metacognitive (B, top: bias; bottom: sensitivity) measure. (C) Incentive effects on confidence formation, linking incentives, evidence, and confidence for correct (left) and incorrect (right) answers. In those two panels, the scatterplots display reported confidence as a function of evidence for the different incentive levels. The solid line represents the best linear regression fit at the population level. The histograms represent the intercepts (top) and slope for correct (middle) and incorrect answers (bottom) of this relationship, estimated at the individual level and averaged at the population level. The insets presented on the right-hand side of the graph depict the results of the linear mixed-effects model, estimated for each parameter of this regression, that is, intercept (top) and slope for correct answers (middle) and for incorrect answers (bottom). V+, net incentive value for gains; V−, net incentive value for losses; +/−, incentive valence. Error bars indicate intersubject SEM. ~P < 0.10, *P < 0.05, **P < 0.01, ***P < 0.001.

  • Fig. 6 Incentive bias costs.

    (A) Expected probability of winning E(x) induced by the MP mechanism, as a function of the chosen rating x for several levels of underlying confidence c. The dots indicate the highest point of each curve, which correspond to x = c. (B) Effects of a combination of biases (11% overconfidence + 3% extra bias due, for example, to an incentive of 1€) on the expected probability of winning E(x). The values of the overconfidence and incentive biases correspond to the values observed in experiment 1. (C) Expected loss induced by a combination of an overconfidence bias (x axis) and an additional incentive bias (βV = 3%) for several levels of incentives (y axis). Note that incentivizing confidence with gains (or losses) decreases the losses induced by underconfidence (or overconfidence) (top left and bottom right corners). On the contrary, incentivizing confidence with gains (or losses) increases losses induced by overconfidence (or underconfidence) (top left and bottom right corners). The markers (dot, diamond, and square) correspond to the parameters used in (B).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/5/eaaq0668/DC1

    section S1. Demographics and experimental design

    section S2. Calibration and staircase procedure

    section S3. Preliminary analyses

    section S4. Mixed-linear effects results

    section S5. Reaction-time analysis

    table S1. Demographics and experimental design.

    table S2. Results of linear mixed-effects models for preliminary analyses.

    table S3. Results of linear mixed-effects models for experiment 1 analyses.

    table S4. Results of linear mixed-effects models for experiment 2 analyses.

    table S5. Results of linear mixed-effects models for experiment 3 analyses.

    table S6. Results of linear mixed-effects models for experiment 4 analyses.

    table S7. Results of linear mixed-effects models for reaction time analyses.

    fig. S1. General behavior for experiments 1 to 4.

    fig. S2. Reaction times.

    References (69, 70)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Demographics and experimental design
    • section S2. Calibration and staircase procedure
    • section S3. Preliminary analyses
    • section S4. Mixed-linear effects results
    • section S5. Reaction-time analysis
    • table S1. Demographics and experimental design.
    • table S2. Results of linear mixed-effects models for preliminary analyses.
    • table S3. Results of linear mixed-effects models for experiment 1 analyses.
    • table S4. Results of linear mixed-effects models for experiment 2 analyses.
    • table S5. Results of linear mixed-effects models for experiment 3 analyses.
    • table S6. Results of linear mixed-effects models for experiment 4 analyses.
    • table S7. Results of linear mixed-effects models for reaction time analyses.
    • fig. S1. General behavior for experiments 1 to 4.
    • fig. S2. Reaction times.
    • References (69, 70)

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