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The authors have declared that no competing interests exist.

Conceived and designed the experiments: AS QJMH AK PS. Performed the experiments: AS AK. Analyzed the data: AS QJMH AK PS. Wrote the paper: QJMH PS.

Optimists hold positive

The optimism bias is regarded as one of the most prevalent and robust cognitive biases documented in psychology and behavioral economics. In individuals, trait optimism is usually measured using self-report questionnaires. However, choices in simple behavioral tasks can also be used to infer how optimistic people are in practice. We asked human subjects to fill in questionnaires about trait optimism, then to participate in a behavioral experiment where they needed to infer the likelihood of visual targets to be associated with a reward. Using modeling, we could then quantify the link between self-report trait optimism and decision or learning biases. We find that people who report that they are optimistic have a positive

Optimism is known to play an important role in human experience leading to more happiness, greater achievements and better health

Trait optimism is generally measured using questionnaires, the most common of which is the Life Orientation Test-Revised (LOT-R)

Optimism is thought to affect cognitive processes in at least two ways. First, it biases one's expectations in a positive direction: while optimists view the glass as being half-full, pessimists might perceive it as half-empty. Formally, such a divergence in the interpretation of the same object could result from the influence of different prior beliefs. Second, optimism also appears to impact learning: optimists sometimes maintain positive beliefs in defiance of what should be strong evidence, such as doctors underestimating the risks of treatments or people continuing to buy lottery tickets. Recent work has shown that this may be due to biases towards more readily learning from “good news” (i.e. outcomes that are better than expected) than from “bad news”

To approach these questions, we designed a behavioral task in which positive beliefs about future outcomes as well as learning biases could be quantified in individuals, independently from LOT-R scores and subjective introspection. This paradigm allowed us to disambiguate whether trait optimism functions as a prior belief on the likelihood of future outcomes, as a learning bias, or both.

Fifty-one subjects took part in the main study (30 males and 21 females, age range: 17–45 years old). They were first asked to answer a set of questionnaires assessing trait optimism and related personality traits: the LOT-R as a measure of trait optimism

The subjects then performed the behavioral task. Each trial started with the presentation of one of many fractal conditioned stimuli (CS). This was followed by a binary outcome (reward, depicted as a full treasure chest or no reward, empty chest) with a probability c_{i} drawn uniformly between 0 and 1, that was fixed for each fractal CS but unknown to the subjects (

Here the subject needs to choose between the yellow fractal and the square for which the reward probability is given by the number of blue dots (6 dots, indicating a probability of 60%).

Because subjects were given very little information about the true CS reward probability, we expected their reward expectations for fractal CSs (but not for the colored squares) to reflect both the information they had been exposed to, and subjects' prior beliefs about the probability of rewards. By varying the number of presentations before the instrumental choice point, we could probe the learning process at various time points. We asked three questions: i) Does trait optimism relate to a prior belief about the probability of reward c_{i} associated with each fractal stimulus? ii) Does this influence fade with increasing experience, as it should if optimism works as a prior belief, or is maintained or even amplified, as it should if optimism affects learning? iii) Are the effects about prior beliefs valence specific i.e. do they correspond only to an overestimation of the likelihood of positive events or also to an underestimation of the likelihood of aversive events?

Optimistic participants (i.e. with LOT-R>mean LOT-R) were biased towards overestimating the probability that rewards would follow fractal CSs (

To ascertain whether this bias was due to a prior belief related to optimism, we modeled the task as an optimal Bayesian inference process. Subjects were assumed to optimally combine the binary evidence p(D_{i}|c_{i}) regarding the probability of the observations D_{i} (number of rewards observed over trials) given some probability of reward for that fractal c_{i}, with their prior expectations p(c_{i}) that a reward would be given (see _{i}|D_{i}), which describes the subjective belief about a reward being associated with each fractal. The variability in the decision process was parameterized by a softmax temperature parameter γ. These parameters were estimated for each subject based on their performances at the task, using Maximum Likelihood. Each participant was thus described by 3 free parameters: α, β and γ.

α/(α+β) | LOT-R | Ne | Ex | Op | Ag | Con | Att. | Motor | S-C | C-C | P | C-In | TI | DSAB | |

0.190 | −0.076 | 0.117 | −0.166 | −0.094 | 0.022 | −0.184 | 0.112 | 0.025 | 0.243 | 0.194 | 0.216 | 0.204 | 0.257 | −0.031 | |

−0.295 | 0.285 | 0.147 | 0.205 | 0.295 | −0.106 | 0.031 | −0.152 | 0.061 | 0.061 | −0.092 | −0.061 | −0.003 | |||

−0.065 | 0.287 | −0.126 | 0.007 | −0.205 | −0.128 | 0.106 | 0.047 | −0.110 |

To ascertain more directly whether optimism might also relate to the learning process, we fitted reinforcement learning models to the behavior. These models describe the learning process explicitly by assuming that subjects maintain an estimate of the value _{i}_{0} which plays a role similar to the prior mean belief _{+} for better than expected and _{0} (p = 0.002, r = 0.541 in Model RL_{b}), but not with either of the learning rates ε_{+} or ε_{−} or the difference between them (all p>0.1). Moreover, models that did not allow for subject-specific _{0} did not capture performance differences between optimists and pessimists. Thus, optimism is well described in terms of a positive prior belief on the likelihood of reward, and does not appear to affect the learning process.

If optimism really functions like a prior, then its influence should fade the more subjects are given evidence about the association of stimuli and reward. If the amount of evidence is sufficiently large then subjects' performance should become independent of their prior biases. For our Bayesian analysis, this means that the simplest model that would describe their performance is one with a non-informative prior. On the contrary, if optimism affects learning, the difference between optimists and pessimists should be maintained or even amplified with experience. We conducted a control experiment aimed at testing this directly. This experiment also excluded a potential confound in the previous experiment, namely that optimistic subjects might have an

The average number of times a given fractal was shown before a decision was requested was increased from 4 to 10;

Instead of being interleaved, the fractals were now presented in blocks.

A total of 51 new participants (28 males and 23 females, age range: 17–46 years old) participated in this version of the experiment. One subject (male) was post-hoc excluded from further analysis, because he did not achieve a 50% performance. In line with our hypothesis, we found that under those conditions, the difference of performance between optimistic and pessimistic subjects disappeared (

No correlation was found between the LOT-R score of individual subjects and the mean of their prior (r = 0.009, p = 0.95; a correlation significantly different from that of experiment 1: Fisher's Z = 2.26, p = 0.02; achieved power: 1−β = 0.87 assuming the effect size is the same as in experiment 1). The shape of the individual priors extracted from the subjects' performance was always close to a non-informative (i.e. Jeffrey's) prior (α = β = 0.5). In fact, in this control experiment, contrary to the main experiment, model comparison (BIC) shows that the performance of every single subject was better described by the simpler model in which the prior is chosen to be fixed and non-informative rather than by a prior with flexible α and β (vs. 45% of the subjects for experiment 1). This suggests that, in this case, subjects were able to correctly take into account the evidence and override their prior expectations: they now behave in a way indistinguishable from that of having unbiased prior beliefs.

Furthermore, the reinforcement learning models again failed to account for the data better than the Bayesian models, while supporting similar conclusions: the LOT-R score correlated neither with the learning rates _{0}

Group | LOT-R | Bayesian Model | Sig. | ||

α/(α+β) | γ | ||||

14.70 (4.42) | 0.42 (0.23) | 7.88 (3.93) | |||

17.30 (2.36) | 0.47 (0.21) | 8.01 (4.09) | |||

10.60 (3.69) | 0.33 (0.25) | 7.75 (3.78) | |||

15.65 (4.27) | 0.49 (0.37) | 4.03 (1.64) | |||

18.96 (2.30) | 0.50 (0.40) | 3.82 (1.69) | |||

12.33 (4.02) | 0.48 (0.38) | 4.18 (1.61) | |||

15.44 (3.60) | 0.56 (0.32) | 6.71 (5.30) | |||

18.32 (3.13) | 0.56 (0.37) | 6.76 (4.62) | |||

12.55 (3.87) | 0.55 (0.31) | 6.67 (5.40) |

Group | LOT-R | RL Models | Sig. | ||||

ε_{+} |
ε_{−} |
V_{0} |
τ | ||||

14.70 | 0.09/0.08/0.09/X | X/0.12/0.13/X | X/X/0.46/0.42 | 3.63/3.64/3.65/3.57 | |||

17.30 | 0.09/0.11/0.08/X | X/0.14/0.14/X | X/X/0.54/0.47 | 3.79/3.80/3.77/3.76 | |||

10.60 | 0.09/0.07/0.10/X | X/0.08/0.11/X | X/X/0.35/0.33 | 3.34/3.38/3.49/3.46 | |||

15.65 | 0.27/0.25/0.22/X | X/0.30/0.27/X | X/X/0.61/0.56 | 2.21/2.31/2.48/2.44 | |||

18.96 | 0.27/0.24/0.21/X | X/0.27/0.24/X | X/X/0.64/0.59 | 2.28/2.37/2.52/2.51 | |||

12.33 | 0.26/0.26/0.22/X | X/0.32/0.29/X | X/X/0.59/0.54 | 2.15/2.24/2.46/2.39 | |||

15.44 | 0.50/0.51/0.48/X | X/0.50/0.42/X | X/X/0.59/0.57 | 0.38/0.53/0.52/0.51 | |||

18.32 | 0.46/0.50/0.45/X | X/0.49/0.39/X | X/X/0.68/0.65 | 0.48/0.61/0.63/0.59 | |||

12.55 | 0.52/0.51/0.49/X | X/0.52/0.44/X | X/X/0.53/0.52 | 0.33/0.48/0.47/0.41 |

In view of these results and so as to test whether the dependency of the bias with level of uncertainty could also be observed in the same group of participants (vs. between two different groups), we also re-analyzed the data of experiment 1. We compared performances (% choices) for the fractals that were “over-observed” (observed more than 4 times) compared to the fractals that were “under-observed” (less than 4 times). We tested whether optimists and pessimists differed in their “under-observed” and “over-observed” biases using two sample t-tests. Consistent with our hypothesis, we found that the differences in performances between optimists and pessimists was statistically significant for “under-observed” fractals (p<0.01), but not for the “over-observed” ones (p = 0.135). We used a two-sample, one-tailed t-test to test if one effect is significantly greater than the other, and found that this was the case (p = 0.0017).

We finally asked whether optimism could also predict prior beliefs about the likelihood of losses, by repeating the experiment with punishments (i.e. losses of points) rather than rewards. The experimental procedure was the same as in Experiment 1, except for the fact that, here, both the CS and the square stimuli were associated with a probability of punishment (instead of reward), depicted by a cartoon of a sad face. Subjects were now asked to estimate the probability of punishment c_{i} associated with the CS and to avoid punishment when choosing between the CS and the square stimulus.

A total of 51 subjects (29 males and 22 females, age range: 17–38 years old) participated in this version of the experiment. Four subjects (1 female and 3 males) were post-hoc excluded from further analysis, because they did not achieve a 50% performance. We found that under those conditions, optimistic and pessimistic subjects had similar performances (

In conclusion, trait optimism as measured by the LOT-R questionnaire is found to correlate with performance biases in a simple Pavlovian conditioning task: optimistic subjects over-estimate the probability of reward associated with the uncertain target. This bias affects the estimation of future rewards but not of future losses in our task. It conforms to Bayesian principles of optimal inference and disappears when the level of uncertainty decreases.

Our findings are consistent with intuition about the nature of optimism in humans, as well as evidence that optimistic people are more likely than pessimists to have positive gambling expectations

Second, in our experiment, participants don't seem to be biased in the learning process itself. Optimists and pessimists differ in their initial biases but not in how they accumulate new information. Moreover, fitting the data with reinforcement models showed that they learned similarly from positive prediction errors (“good news”) and negative prediction errors (“bad news”). Studies looking at updating of beliefs related to one's personal qualities or future life events

There are many important differences between the current paradigm and those studies, which makes the comparison difficult. As stated above, a crucial difference is whether the quantity to be estimated concerns the self or a neutral stimulus. This can lead to large differences in motivation in the learning process: when information is personally relevant, participants have a motive to disregard negative information so that they can keep a rosy view of the future. In our task, on the other hand, there is no intrinsic advantage of keeping a biased estimate for the probability of rewards associated with the fractals. Consistent with this idea, Eil and Rao found that participants conformed Bayesian rationality in their control (neutral) condition

Other differences in experimental design between these studies and ours are worth mentioning. In

The experimental paradigm opens the door to a number of investigations. For example, our experimental paradigm offers new routes to the differentiation between optimism and pessimism, and optimism and hope, which are sometimes believed to be different constructs

Finally, optimistic biases have also been reported in animals and it has been proposed that those biases could be used as an indicator of affective state

All participants gave informed written consent and the University of Edinburgh Ethics Committee approved the methods used in this study, which was conducted in accordance with the principles expressed in the Declaration of Helsinki.

All experiments took place at the

Visual stimuli were generated using the Matlab programming language and displayed using Psychophysics Toolbox

The experiment contained two types of screens (

More precisely, there were 60 different fractal stimuli in total. They were generated using Matlab code available from the C.I.R.A.M. Research center in Applied Mathematics at the University of Bologna. The probability c_{i} for each fractal CS to lead to a reward was drawn randomly between 0 and 1 at the start of the experiment and kept unknown to the subject. As described above, CSs were then shown in random sequences of observation and decision screens. More precisely, in the main experiment, each CS was assigned to a group of 5 fractals and those were presented in randomly interleaved observation screens before they were shown in decision screens (

Feedback was not given after each decision screen but each subject was given a final score at the end of the experiment. Due to funding changes, the first 42 subjects of experiment 1 were unpaid but participated in a draw with a £20 voucher prize, while subjects of experiment 2 and 3 and the last 11 subjects in the main experiment were paid £6 for participation (unrelated to their performance at the task). No significant differences were found between paid and unpaid participants' performances.

We assumed that subjects behave as Bayesian observers, and estimated the probability of reward, denoted c_{i}, associated with a given fractal i by computing the posterior distribution p(c_{i} |D_{i}), using Bayes rule:_{i} denotes the series of observations related to fractal _{i})

We further assumed that subjects formed their decision by extracting the mean of this posterior distribution so as to obtain an estimate ĉ_{i} of c_{i}:_{i})_{i} is:_{i}_{i}

We assumed that subjects' decision results from a ‘softmax’ comparison between their estimate _{i}_{i}

We also fitted various reinforcement learning (RL) models to our data. Our idea was to assess whether RL models could capture the differences in performance between optimists and pessimists in experiment 1, and if so, to identify the parameters which would explain those differences. We were particularly interested in assessing whether optimists and pessimists would differ most in the parameters governing value update as a function of the sign of the prediction error or in those parameters setting the initial biases (consistent with the alternative account of optimism as a prior belief). We used a simple temporal-difference (TD) learning algorithm. In these models, subjects learn a value V(s_{i}) for each CS _{o} (identical for each CS) and then updated after each observation of that CS, according to:_{t} = r_{t}−V_{t}(s_{i}) denotes the prediction error, r_{t} denotes the binary reward, t represents the observation number, and the learning rate ε(δ_{t}) is set to hold either the same value (ε+ = ε−) for better-than-expected (i.e. δ_{t}>0) and worse-than-expected outcomes (δ_{t}<0), or different values (ε+≠ε−). The selection between targets 1 and 2 is governed by a softmax action selection, with additional parameter τ._{i} corresponds to the reward probability of the colored square. We first examined model RL_{2b} which had 2 free learning rates ε+, ε− and free v_{o}. We additionally examined simplified versions of this model, which differed in the number of parameters kept free in addition to τ:

RL_{ε} has only one learning rate ε ( = ε+ = ε−) as free parameter, v_{o} is set to 0.5;

RL_{2} has 2 free learning rates ε+, ε−, v_{o} is set to 0.5;

RL_{2b} has 2 free learning rates ε+, ε−, and free v_{o};

RL_{b} has only free v_{0}, the learning rate ε ( = ε+ = ε−) is set to 0.1.

Each model was fitted to the data of each participant using maximum-likelihood estimation.

We found that: i) only the models with free bias term v_{o} captured the difference in performance between optimists and pessimists in experiment 1 (i.e. led to significantly different parameters for optimists and pessimists); ii) in line with the hypothesis that optimism functions as a initial bias, the bias v_{o} correlated with LOT-R scores in experiment 1 (significantly so for RL_{b};: r = 0.541, p = 0.002); iii) the RL models were worse at fitting the data than the Bayesian models, both in terms of log likelihood and BIC values in all experiments (BIC for experiment 1: RL_{ε} = 71.83; RL_{2} = 74.57; RL_{2b} = 77.83; RL_{b} = 75.53, Bayesian model = 60.92; BIC for experiment 2: RL_{ε} = 80.71; RL_{2} = 83.36; RL_{2b} = 86.71;RL_{b} = 81.16, Bayesian model = 71.38; BIC for experiment 3: RL_{ε} = 90.52; RL_{2} = 93.88; RL_{2b} = 97.49;RL_{b} = 90.14, Bayesian model = 83.12). We concluded that, in our data, optimism is well described in terms of a positive prior belief on the likelihood of reward and is not significantly accompanied by selective updating during the learning process.

We are grateful to Tali Sharot and the anonymous reviewers for very helpful comments on a previous version of this manuscript.