Diverse Personalities Make for Wiser Crowds: How Personality Can Affect the Accuracy of Aggregated Judgments
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1 Diverse Personalities Make for Wiser Crowds: How Personality Can Affect the Accuracy of Aggregated Judgments Kriti JAIN J. Neil BEARDEN Allan FILIPOWICZ 2012/14/DS/OB (Revised version of 2011/17/DS/OB)
2 Diverse Personalities Make for Wiser Crowds: How Personality Can Affect the Accuracy of Aggregated Judgments Kriti Jain * J. Neil Bearden** Allan Filipowicz*** Revised version of 2011/17/DS/OB * PhD Candidate in Decision Sciences at INSEAD 1, Ayer Rajah Avenue, Singapore , Singapore. Kriti.jain@insead.edu ** Associate Professor of Decision Sciences at INSEAD 1, Ayer Rajah Avenue, Singapore , Singapore. neil.bearden@insead.edu *** Assistant Professor of Organisational Behaviour at INSEAD 1, Ayer Rajah Avenue, Singapore , Singapore. allan.filipowicz@insead.edu A Working Paper is the author s intellectual property. It is intended as a means to promote research to interested readers. Its content should not be copied or hosted on any server without written permission from publications.fb@insead.edu Find more INSEAD papers at
3 Abstract The aggregate judgment of multiple individuals is often superior to the individual judgments themselves because the aggregation can cancel out the individual level errors. Crucially, aggregation works best when the individuals errors are uncorrelated. This can happen when the individuals being aggregated have access to diverse, uncorrelated information. We propose that one important source of diversity between individuals is their personalities. Individuals personalities influence the way they seek, search, and process information. Across two studies, we show that averaging judgments of pairs of individuals with more diverse personalities improves accuracy more than averaging judgments of less diverse pairs. Using a bootstrap procedure, we also test for the robustness of our results. Our results show that one way to improve the wisdom of the crowd is to aggregate the judgments of individuals with diverse personality profiles. Keywords: Judgment; Diversity; Aggregation; Combining Opinions; Personality 2
4 Individual human judgment and forecasting is notoriously biased (Tversky & Kahneman, 1974). Fortunately, one can often generate highly accurate forecasts simply by averaging multiple individual forecasts (Hogarth, 1978; Clemen, 1989; Armstrong, 2001). Galton (1907), for example, examined the accuracy of judgments from a contest in which people estimated the weight of an ox. Remarkably, the average estimate was off by only 1 pound for a 1,198 pound ox, though the individual estimates varied substantially around the true weight. Galton took this finding as support for the soundness of democratic judgments, as evidence for the intelligence of the vox populi. More recently, the idea that aggregating the judgments of individuals can lead to high quality judgments and forecasts has come to be known as the wisdom of crowds (Surowiecki, 2004). How does aggregation improve accuracy? Larrick and Soll (2006) demonstrated the power of aggregation in terms of bracketing. Suppose that judges predicted the number of M&Ms in a jar where the true value is Assume that two judges predictions fell on the same side of the true value (i.e. did not bracket the true value), for example 700 and 900. On average, they were off by 200. Averaging the two estimates gives 800, which again is off by 200. Here, averaging the estimates is as good as randomly choosing between the two judges. Now, suppose that the two judges' predictions fell on opposite sides of the true value, bracketing it, for example 800 and On average, they were off by 250. However, averaging the two estimates gives us 1050, which has an error of 50, better than either of the two. Bracketing causes the errors to get cancelled out when judgments are averaged. For bracketing to work best, the errors of the individuals being aggregated should not be highly correlated. The correlation between individuals judgments and therefore their errors can be dampened when the individuals being aggregated form their judgments on the basis of diverse, uncorrelated information. Herzog and Hertwig (2009) showed that even 3
5 averaging multiple forecasts from the same person who has thought about a problem from multiple perspectives can improve accuracy. And, the accuracy of the average of two judgments from the same person taken at different points in time increases with the delay between the judgments (Vul & Pashler, 2008), that is, as the judgments become less dependent. One of the biggest sources of diversity in the way people experience, interpret and react to the world is their personality. People with different personality types tend to seek, search, and process information differently (Humphreys & Revelle, 1984; Wilson, 1997; Wilson, 2000; Heinström, 2003). For example, some people tend to gather information in a planned and structured manner, while others do so in a more flexible and spontaneous fashion (Solomon, 2002). Some get heavily influences by opinions of others while others confidently stick to their own assessments (e.g., Koestner et al., 1999). Personality is most commonly described and assessed as variations along five dimensions, extraversion, agreeableness, conscientiousness, emotional stability, and openness (Digman, 1990; John, & Srivastava, 1999). We hypothesized that averaging the judgments of pairs of individuals on the basis of the diversity of their personality profiles would affect the accuracy of the aggregate judgments. Specifically, if members of highly diverse pairs tend to rely on more diverse sets of information when forming their judgments (compared to low diversity pairs), then one should find that their averaged judgments are more accurate than the averaged judgments of low diversity pairs. Below, we describe two studies to test this hypothesis. Study 1 - M&M Task Method Participants and procedure. Two-hundred and forty MBA students at INSEAD first completed the 44-item Big Five Inventory (BFI) of personality (John, Donahue, & Kentle, 1991) a commonly used measure of personality (e.g., McCullough, Emmons, & Tsang, 4
6 2002). Next, they participated in a judgment task where they estimated the number of M&M candies in a jar. The BFI and the M&M task were administered separately, with two weeks in between. Pairing protocol. To construct two groups with high (low) diversity pairs, we first computed the correlations between all pairs of participants based on their BFI responses which gave us a 240 X 240 matrix of correlations. Next, we used this matrix to find the pair with the least (most) correlated personality profile. Specifically, we picked the most diverse pair (i.e., with the lowest correlation) and the least diverse pair (i.e., with highest correlation). Next, based on the correlations between the remaining 236 participants, we continued the above process of picking up most (least) diverse pairs repeatedly without replacement until all judges were paired. This gave us a total of 120 pairs with 60 each of high and low diversity pairs. 1 Results and Discussion As a check of the effectiveness of our pairing protocol, the average correlation between the BFI responses of high diversity pairs was significantly lower (M = -0.23, SD = 0.18) than for the low diversity pairs (M = 0.71, SD = 0.09), t(87.55) = 34.93, p < 0.001, d = Our pairing protocol gave us pairs with more diverse personalities in the high diversity group than in the low diversity group. 2 To measure bracketing, we created a binary variable which took the value 1 if the pair s estimates bracketed the true value and 0 otherwise. A greater proportion of high diversity pairs (27/60) bracketed the true value compared to the low diversity pairs (14/60), χ 2 (1, N = 120) = 5.91, p = Effects observed are robust to other pairing protocols (e.g., unidirectional search for pairs in an ascending or descending order of diversity). 2 Results on differences in correlations across groups also hold using Fisher s z transformations. However, we report untransformed averages for ease of interpretation. 5
7 Next, we computed two accuracy measures. First, for each pair, we computed the absolute error of their aggregated (averaged) estimates from the true value. Lower scores represent better accuracy. Absolute errors for the high diversity pairs were significantly smaller (M = , SD = , Mdn = ) than for low diversity pairs (M = , SD = , Mdn = ), t(118) = 2.78, p < 0.01, d = For comparison, we also computed the individual-level (unpaired) absolute errors across all 240 participants (M = , SD = , Mdn = ) and the pair-level absolute errors of the aggregated estimates across all possible pairs of participants (M = , SD = , Mdn = ). Aggregating judgments of more diverse individuals reduced errors more than aggregating judgments of less diverse individuals. Second, we computed a measure of gains in accuracy achieved through aggregation. For each pair, we computed the percentage decrease in error of the average of the two judges estimates relative to the average of the two judges errors (similar index was used by Herzog and Hertwig, 2009). Higher scores represent greater improvement. We found that the high diversity pairs achieved significantly higher accuracy gains (M = 26%, SD = 34%, Mdn = 0%) than the low diversity pairs (M = 11%, SD = 22%, Mdn = 0%), Mann-Whitney U = 1366, z = -2.70, p < The more diverse pairs gained higher accuracy improvements than the less diverse pairs. Mediation analysis (Baron & Kenny, 1986) confirmed that bracketing mediated the relationship between diversity and absolute error (Sobel test, z = 2.40, p = 0.02) and between diversity and accuracy gain (Sobel test, z = 2.53, p = 0.01). Study 1 demonstrated that aggregating the judgments of individuals with more diverse personalities led to more accurate aggregate judgments than aggregating individuals with less diverse personalities. 6
8 Study 2 World Cup Prediction Task In Study 2, we replicate the findings of Study 1 using a larger set of stimuli where participants made predictions for real-world events for which the true values were not known ex ante. Specifically, we invited cricket fans to participate in a large-scale study in which they predicted the outcomes of the 2011 Cricket World Cup. The Cricket World Cup is a One-Day matches cricket tournament held every four years. The tournament consists of a series of group stage matches and knockout matches until a single winner remains. In 2011, fourteen national teams from around the world competed in the tournament held in the Indian subcontinent. Method Participants and procedure. Three-hundred and forty cricket fans from various educational institutions in India and from INSEAD first completed the 44-item Big Five Inventory (BFI) of personality. Next, they were asked to make predictions about the total runs scored across 10 qualifying matches for the 2011 Cricket World Cup. Specifically, participants were asked to predict how many runs they expected the two corresponding teams would make conditional on the team batting first. (The batting order is not decided until the day of the match.) Since in each match only one of the two teams batted first, we only used participants predictions for those 10 teams that actually batted first. Participants were informed that the most accurate predictor would be paid SGD 100 (US$ 75). Pairing protocol. We used the same pairing protocol as in Study 1. This gave us a total of 170 pairs with 85 each of high and low diversity pairs. Results and Discussion As a check of the effectiveness of our pairing protocol, we found that the average correlation between paired individuals BFI responses was significantly less for high 7
9 diversity pairs (M = -0.13, SD = 0.21) than for low diversity pairs (M = 0.79, SD = 0.08), t(107.43) = 38.31, p < 0.001, d = Next, we computed similar measures as used in Study 1. First, we computed the bracketing rate as the percentage of pair s predictions that bracketed the true value across the 10 predictions. The bracketing rate was significantly greater for high diversity pairs (M = 31%, SD = 21%, Mdn = 30%) than for the low diversity pairs (M = 22%, SD = 14%, Mdn = 20%), t(149.12) = 2.91, p < 0.01, d = The predictions of the high diversity pairs fell on opposite sides of the true value more often than the predictions of the low diversity pairs. For each pair, we also computed the median absolute error between their aggregated estimates and the actual runs across the 10 estimates. Lower scores represent better accuracy. The median absolute error for the high diversity pairs was significantly lower (M = 32.27, SD = 10.33, Mdn = 32.25) than for the low diversity pairs (M = 35.66, SD = 9.43, Mdn = 36.00), t(168) = 2.23, p = 0.03, d = For comparison, we also computed the individual-level (unpaired) median absolute errors across all 340 participants (M = 38.92, SD = 13.23, Mdn = 37.00) and the pair-level median absolute errors of the aggregated estimates across all possible pairs of participants (M = 34.47, SD = 9.70, Mdn = 34.25). As hypothesized, we found that the aggregate forecasts of the high diversity pairs were more accurate than those of the low diversity pairs. Finally, we computed accuracy gain as the average percent decrease in the error of a pairs averaged forecasts relative to the average error of their individual forecasts taken over the ten estimates. Higher scores represent greater improvement. Accuracy gain was significantly higher for the high diversity pairs (M = 16%, SD = 12%, Mdn = 14%) than for the low diversity pairs (M = 12%, SD = 9%, Mdn = 11%), t(156.15) = 2.49, p = 0.01, d = In short, aggregation led to greater accuracy improvement for high diversity pairs than for low diversity pairs. 8
10 Figure 1 summarizes these results. Figure 2 plots the distributions of the three measures across all pairs in both groups. Clearly, the high diversity pairs had better bracketing rates, lower median errors, and higher accuracy gains than the low diversity pairs. Mediation analysis confirmed that the bracketing rate mediated the relationship between diversity and median absolute errors (Sobel test, z = 2.63, p < 0.01) and also between diversity and accuracy gains (Sobel test, z = 2.89, p < 0.01). See Figure 3. Robustness Check. To check the robustness of our results, we conducted a bootstrap procedure based on 10,000 simulations. In each simulation, we randomly sampled two nonoverlapping groups from the 340 participants, giving us 170 judges in each group. In the first group, based on the correlations of BFI scores between all pairs of 170 judges, we paired judges in a decreasing order of diversity, starting from the most diverse pair. In the second group, we paired participants based on an increasing order of diversity, starting from the least diverse pair. This gave us a high and a low diversity group respectively. For the 85 pairs each in the two groups, we computed bracketing rates, median errors of their averaged estimates, and accuracy gains. Based on 10,000 simulations, in Figure 4, we plot the cumulative distributions of several measures for the two groups. The plots clearly show that before generating the high and low diversity pairs through our pairing protocol, the two groups were similar in terms of personalities (panel a) and in terms of accuracy of the averaged estimate (panel b). Our pairing protocol gave us two personality-wise distinct groups, one with high and the other with low diversity of pairs (panel c). In terms of accuracy, the distribution of average median error for the low diversity groups first-order stochastically dominates the distribution for the high diversity groups (panel d). And, the distributions of average bracketing rate (panel e) and of average accuracy gain (panel f) for the high diversity groups first-order stochastically dominate the distributions for the low diversity groups. Clearly, high 9
11 diversity pairs were more accurate than low diversity pairs. Hence, the conclusions are robust with respect to the pairing procedure. General Discussion Previous research has shown that simple pooling of people s estimates can give surprisingly accurate estimates (Wolfers & Zitzewitz, 2004; Armstrong, 2001). Across two studies, our results now demonstrate that aggregating judgments of personality-wise more diverse individuals improves accuracy more than aggregating judgments of less diverse individuals. Research on teams has shown that heterogeneity within groups can lead to better performance due to the possibility of sharing diverse information within them. For example, Hoffman and Maier (1960) showed that heterogeneous teams (with respect to personality) came up with higher quality results in a problem solving task than homogenous teams. However, heterogeneity can also lead to process losses due to biases such as stereotyping and subgroup formation (see Van Knippenberg, & Schippers, 2007, for a review). Simply pooling judgments from personality-wise diverse individuals can be one easy way for groups to reap the benefits of heterogeneous opinions without incurring any process losses. Crucially, personality can be measured ex ante before judgments are made. Hence, one way to improve the wisdom of the crowd is to ask for forecasts from personality-wise diverse individuals and then pool them together. 10
12 References Armstrong, J. S. (2001). Combining forecasts. In J. S. Armstrong (Eds.), Principles of forecasting: A handbook for researchers and practitioners (pp ). Norwell, MA: Kluwer Academic. Baron, R. M., & Kenny, D. A. (1986). The moderator mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51, Clemen, R.T. (1989). Combining forecasts: A review and annotated bibliography. International Journal of Forecasting, 5, Digman, J.M. (1990). Personality structure: Emergence of the five-factor model. Annual Review of Psychology, 41, Galton, F. (1907). Vox populi. Nature, 75, Heinström, J. (2003). Five personality dimensions and their influence on information behaviour. Information Research, 9, paper 165. Herzog, S.M., & Hertwig, R. (2009). The wisdom of many in one mind: Improving individual judgments with dialectical bootstrapping. Psychological Science, 20, Hoffman, L. R. & Maier, N. R. F. (1961). Quality and acceptance of problem solutions by members of homogenous and heterogeneous groups. Journal of Abnormal and Social Psychology, 62, Hogarth, R.M. (1978). A note on aggregating opinions. Organizational Behavior and Human Performance, 21, Humphreys, M.S., & Revelle, W. (1984). Personality, motivation, and performance: A theory of the relationship between individual differences and information processing. Psychological Review, 91,
13 John, O.P., Donahue, E.M., & Kentle, R.L. (1991). The Big Five Inventory--Versions 4a and 54. Berkeley, CA: University of California, Berkeley, Institute of Personality and Social Research. John, O. P., & Srivastava, S. (1999). The Big Five Trait taxonomy: History, measurement and theoretical perspectives. In L. A. Pervin and O. P. John (Eds.) Handbook of Personality: Theory and Research (2nd ed., pp ). New York: Guilford. Koestner, R., Gingras, I., Abutaa, R., Losier, G.F., DiDio, L., & Gagné, M. (1999). To follow expert advice when making a decision: an examination of reactive versus reflective autonomy, Journal of Personality, 65, Larrick, R.P., & Soll, J.B. (2006). Intuitions about combining opinions: Misappreciation of the averaging principle. Management Science, 52, McCullough, M.E., Emmons, R.A., & Tsang, J. (2002). The grateful disposition: A conceptual and empirical topography. Journal of Personality and Social Psychology, 82, Solomon, P. (2002). Discovering information in context. In B. Cronin, (Ed.). Annual Review of Information Science and Technology, 36, Surowiecki, J. (2004). The Wisdom of Crowds. New York: Random House. Tversky, A., & Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science, 185, Van Knippenberg, D. & Schippers, M. C. (2007). Work group diversity. Annual Review of Psychology, 58, Vul, E., & Pashler, H. (2008). Measuring the crowd within: Probabilistic representations within individuals. Psychological Science, 19, Wilson, T. D. (2000). Human Information Behavior. Informing Science, 3,
14 Wilson, T. D. (1997). Information behavior: An interdisciplinary perspective. Information Processing and Management, 33, Wolfers, J., & Zitzewitz, E. (2004). Prediction Markets. Journal of Economic Perspectives, 18,
15 Bracketing Rate (%) Median Error Average Accuracy Gain (%) Figure 1. Plots showing the average of (a) Bracketing rate, (b) Median error of the aggregated estimate, and (c) Average accuracy gain, in Study 2. The dotted line in (b) shows average individual (unpaired) median absolute error. Error bars represent standard errors of the mean. a 35 b 40 c High Diversity Pairs Low Diversity Pairs High Diversity Pairs Low Diversity Pairs High Diversity Pairs Low Diversity Pairs 14
16 Accuracy Gain Median Error Bracketing rate Figure 2. Distribution of magnitudes across pairs for (a) Bracketing rate, (b) Median error of the aggregated estimate, and (c) Average accuracy gain, in Study 2. Each point on the lines represents a pair s score (sorted in descending order). a 100% High Diversity Low Diversity 80% 60% 40% 20% b 0% c % 50% 40% 30% 20% 10% 0% 15
17 Figure 3. Mediation analysis of (a) median absolute error of the aggregated estimate and (b) average accuracy gain, for Study 2. Standardized regression coefficients and their significance are reported above each arrow, indicating the effect of one variable in predicting another. For the effect of diversity on the dependent variable, the total effect is reported above the arrows, and the coefficient computed when the mediator is included in the regression is reported below the base arrow in parentheses. *p < **p < a Bracketing 0.22** -0.45** Diversity (1 = High; 0 = Low) -0.17* (-0.07) Median Error b Bracketing 0.22** 0.91** Diversity (1 = High; 0 = Low) 0.19* (-0.01) Average Accuracy Gain 16
18 Figure 4. Results from bootstrapped groups based on 10,000 simulations. Plots show cumulative distributions of (a) average BFI correlation before pairing protocol, (b) average pair-level median error before pairing protocol, (c) average BFI correlation after pairing protocol, (d) average median error after pairing protocol, (e) average bracketing rate after pairing protocol, and (f) average accuracy gain after pairing protocol. a b c d e f 17
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