A simple cognitive method improving prediction for matters of taste: exploiting the wisdom-of-crowd effect within-person

doi:10.21203/rs.3.rs-1497903/v1

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A simple cognitive method improving prediction for matters of taste: exploiting the wisdom-of-crowd effect within-person

https://doi.org/10.21203/rs.3.rs-1497903/v1

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We often need to predict how much others will be satisfied with something they have not experienced thus far. In such a situation, how can we accurately predict it? Previous studies have indicated that by referring to the extent to which people themselves have enjoyed something, they could predict others’ future satisfaction to some extent. In this study, we proposed a method that can further improve such predictions. This method is expected to allow the participants to exploit the Wisdom of crowd within a person for a matter of taste. Specifically, for a single target, the participants produced two opinions from different perspectives: the degree to which they preferred something and the estimated ‘public opinion’. Through two behavioural studies and computer simulations, we confirmed the effectiveness of our method; specifically, blending the two opinions could enhance individual’s predictions. Subsequently, we mathematically analysed how our method worked and identified several factors that influenced our method’s efficiency. Several contributions of the wisdom-of-crowd research were discussed.

In daily life, we are often asked by others, such as our friends, questions like ‘Do you feel I will like the restaurant you visited?’ or ‘Do you think I will be satisfied with the lecture you attended last year?’. In such situations^1–4, how can we accurately predict others’ future satisfaction? An intuitive way is to speculate on how much others would enjoy their experiences. However, previous studies^5–7 have pointed out that these speculations tend to be inaccurate, even though regarding fast friends. In contrast, some researchers^7–9 have revealed that our own impression can be a good predictor. Specifically, simply answering the extent to which we ourselves appreciated the experience (hereafter referred to as ‘Own’ opinion) can predict others’ future satisfaction to some extent.

This study proposed a method that can further improve these predictions by making people produce two opinions for an item from a different perspective, that is, in addition to the Own opinion, they estimated the public’s views (hereafter called the ‘Estimated’ opinion). Particularly, they would guess the extent to which average people like the item. Subsequently, the two opinions were averaged (hereafter referred to as ‘Blended’ opinion). This study’s central hypothesis was that the Blended opinion is a better predictor than the Own opinion; its basis has been explained as follows.

We developed a method primarily based on the wisdom-of-crowd research^10–24. It has been established that the aggregate of multiple judgments could have greater accuracy than individual ones. Note that the judgment problems are generally matters of fact, in which there is objective truth (for example, ‘What percent of the world’s airports are in the United States?’). Importantly, some previous studies^2,3,25 have shown that the wisdom-of-crowd effect can emerge for matters of taste, in which there is no objective, universal truth. Put simply, these studies have showed that as the number of people who give their opinions increases, the accuracy of the prediction (that is, provided by the aggregation of their opinions) also increases. In addition, recent studies^4,26−35 have demonstrated that an individual can harness the wisdom-of-crowd within-person (called ‘the wisdom-of-the-inner crowd’). In other words, an individual produced multiple responses for a problem (basically regarding the matters of fact, see ‘Discussion’), resulting in the fact that the aggregated answer was more accurate than a single one. Thus, we consider that an individual can improve their prediction if they can harness the wisdom-of-crowd even for matters of taste within-person.

In other words, we assume that a person can improve their prediction for the matters of taste by exploiting the wisdom-of-the-inner-crowd effect.

As mentioned above, in our method, the participants are requested to produce two evaluations for the same item: the Own and the Estimated opinion. Regarding the Estimated opinion, participants are instructed to examine the item differently from their own opinion; in other words, our method was expected to produce two quasi opinions of the participants. This approach is in line with the methods of previous studies^4,26−35 for the wisdom-of-the-inner crowd. For determining the details of the Estimated opinion —the simulated public opinion— we draw on the following findings from cognitive and social psychology. In these fields, many studies have examined how people can think differently from their own. In particular, it is well-known that to consider others’ perspectives, an individual can make diverse recognitions in various aspects, called as ‘perspective-taking’³⁶. For example, perspective-taking enables a person to decrease stereotypic biases³⁷, make coordinated behaviours³⁸, change preferential values³⁹, and reduce egocentric thinking⁴⁰. Thus, we primarily decided to follow the perspective-taking paradigm. Subsequently, among ‘others’, we adopted the general crowd’s viewpoint. Many studies have reported that people believe that the general crowd differ from themselves in several ways (e.g. the degree of intelligence^41–44, risk attitude^45,46, and judgmental estimations³²). Accordingly, we hypothesised that the participants could make evaluations different from their own opinions for the same target by considering the general crowd’s perspectives.

This is a broad background of our method. In the following section, we have comprehensively examined the effectiveness of the proposed method. We first conducted two experimental studies to collect the evaluation data (see details in ‘Methods’) that differed in the category of the stimuli presented: paintings and music in Studies 1 and 2, respectively. Both studies evaluated stimuli successively using our method. Subsequently, by utilising the evaluation data, we conducted a computer simulation to assess the effectiveness of our method.

Analysis.

In the analysis, we focused on the following situations: For a target, one person gave an opinion to another (hereafter referred to as the ‘Giver’ and ‘Receiver’, respectively). Figure 1a illustrates the definition of ‘helpfulness’ of the Giver’s opinion. The left side represents the following situation: a Giver has already experienced a target; thenceforward, s/he gives an opinion (for example, 70 in the figure) to a Receiver who has not experienced it thus far. The right side shows the results of opinion-giving. Here, the Receiver has also encountered the target and has formed his/her own judgement (that is, the Receiver’s own opinion). The upper row on the right side exemplifies the situations in which the Giver had a similar opinion (80) regarding the target. In this case, we assumed that the Giver’s opinion was ‘helpful’ since it accurately predicted the Receiver’s future satisfaction. Conversely, when the Receiver had an opinion different from the Giver (for example, 20 in the lower row), we supposed that the Giver’s opinion was relatively ‘Unhelpful’.

Note that this assumption is similar to those adopted in previous studies^3,4,7,8,25. As mentioned in the Introduction section, we simulated the opinion-giving on a computer using the evaluation data in Studies 1 and 2. The simulations could eliminate the possibility that the Receiver’s opinion formation was influenced by receiving the Giver’s opinion.

For the analysis, we mainly used the theoretical framework of the wisdom-of-crowd on the matters of taste (particularly, Müller-Trede et al.’s³), which enabled us to quantitatively investigate the efficacy of the proposed method.

Figure 1b illustrates our analysis. A Giver and a Receiver were independently selected from the participants whose behavioural data were obtained. Subsequently, we examined the helpfulness of the Giver’s three opinions (that is, the Own, Estimated, and Blended opinions). As shown in Fig. 1b, we employed the mean squared error (MSE) as an index for the helpfulness of opinions. In particular, we computed the value of the squared difference between a Giver’s opinion and the Receiver’s Own opinion. That is, a smaller MSE value indicated that the Giver’s opinion was more helpful. We conducted this analysis across all stimuli.

Using the simulation procedure, we examined all the Giver-Receiver combinations: (i) For a Giver, all participants except the Giver became her/his receivers and computed the MSE; (ii) The average MSE across all Receivers was allocated to the Giver’s value; (iii) For all participants, including the Giver, we computed the MSE.

-----Figure 1 about here-----

Main results.

Figure 2 shows the results of the analysis. Notably, the Blended opinion recorded a lower MSE than the Own opinion across the two studies (Study 1: Wilcoxon signed-rank test, p < .001, Cliff’s delta = 0.37; Study 2: paired t-test, p < .001, Cohen’s d = 1.36). That is, using our method, a Giver could improve his/her opinions. Thus, our main hypothesis was supported.

As mentioned in the Introduction section, the two studies differed in the stimulus categories. Moreover, the results indicated that they differed in terms of the data structure, as shown in Table 1; in Study 1, the average rating values were below half (i.e., 50) across all opinions. However, in Study 2, they were approximately half of them. Additionally, as Fig. 3 shows, none of the opinions followed a normal distribution in Study 1, while in Study 2, they did (Kolmogorov-Smirnov test; Study 1: ps < .001; Study 2: ps > .1). Taken together, our method was effective across different categories and data structures.

Table 1

The data structure across the two studies. This table showed a 95% confidence interval (CI) regarding the rating values. We computed the 95% CI by bootstrapping. In Study 1, the average rating values for all types of opinions were below half (that is, 50), while in Study 2, they were around half.
	Study 1	Study 2
Own	[21.05, 22.95]	[50.75, 53.53]
Estimated	[35.00, 36.88]	[53.00, 55.05]
Blended	[28.07, 29.83]	[51.99, 54.08]

-----Figures 2 and 3 about here-----

How did our method work across different data structures? Fig. 4 represents typical examples of the results. In Study 1 (Fig. 4a), the rating values of the Own opinion focused on 0. However, there were certain number of large rating values (for example, 100). In these cases, MSE on Own became quite large. On the contrary, fewer number of ratings were 0 in the Blended opinion. Especially, the rating value of the Blended opinion tended to be constantly distributed between 0 and 75. Put simply, this resulted in the Blended opinion recording lower MSE than the Own. Subsequently, in Study 2 (Fig. 4b), the mean rating value of the Own opinion was similar to that of the Blended (especially around 50). However, the distribution of rating values on the Own opinion was quite larger than that on the Blended. That is, there were certain cases where the rating values between a Giver and a Receiver were largely different (for example, the Giver’s rating value was 0 and the Receiver’s rating value was 100 and vice versa). In this respect, there were relatively fewer cases in the Blended than in the Own opinion since the Blended distribution was small. Thus, our method worked across different data structures.

-----Figure 4 about here-----

Notably, the results also indicated that the Blended opinion had a significantly lower MSE than the Estimated opinion in Study 1 (p < .001; Cliff’s delta = 0.52). Although we did not find such an effect in Study 2 (p = .55, Cohen’s d = 0.18), the findings were also in favour of the Blended opinion; we counted the number of participants who had a lower MSE in the Estimated (Blended) opinion than in the Own opinion. As a result, we found that in the Blended, more participants had a lower MSE than in the Estimated (55 for Blended and 44 for Estimated out of 56 participants; Fisher’s exact test: p < .005). Combined with the results of Study 1, it can be stated that the Blended opinion improves the Giver’s opinion more effectively than the Estimated opinion.

How our method worked: Analysis by decomposing MSE

How could our method reduce the error in Own opinion? In this respect, it is eminent^3,47,48 that the MSE was theoretically decomposed into different sources of error. By performing this decomposition, we could comprehensively observe how our method worked effectively. Several decompositions of the MSE have been suggested^3,42,43, among which we adopted the one proposed by Müller-Trede et al.³; this is because the decomposition consisted of psychologically meaningful factors. The MSE decomposition of Müller‐Trede et al.³ has been represented as follows:

MSE = Bias + Variability bias + Linear correspondence (1)

Firstly, the bias represents the degree to which the rating value of a Giver is higher or lower than that of a Receiver. Simply put, it was larger when the mean rating value of a Giver was more different from that of a Receiver. Secondly, the variability bias indicates how different the variability of the Giver opinions was from the optimal degree of regression to the mean. Specifically, the variability refers to the standard deviation of the Giver’s rating values across stimuli. Concerning the regression to the mean, we multiplied the variability of the Receiver opinions using a Giver-Receiver’s correlation coefficient across the stimuli. Lastly, linear correspondence denotes the extent to which a Giver-Receiver’s correlation deviates from a linear relation (see mathematical description in ‘Methods’).

Table 2 shows the MSE decomposition’s results. Remarkably, the Blended opinion recorded lower values in the variability bias than the Own opinion across the two studies (95% CI). We did not find such results concerning bias and linear correspondence (for figures, see also Fig. S1 of the Supplementary Information). The results indicated that our method worked effectively, owing to the improvement of the regression to the mean. Notably, the results were in line with the findings of the wisdom-of-crowds for matters of taste (Müller-Trede et al.³). As mentioned in the Introduction section, this study extended the wisdom-of-crowd phenomenon to the matters of taste from fact. In particular, it demonstrated that a crowd’s opinion mainly decreased the variability bias from an individual one, resulting in the emerging wisdom-of-crowd effect. Considering this viewpoint, we can regard our method as exploiting the wisdom-of-crowd effect for the matters of taste at the within-person level. In the Discussion section, we shall discuss this research’s contribution to the wisdom-of-crowd literature.

In Study 1, the Blended opinion had a lower bias in addition to the variability bias than the Estimated opinion. The results indicated that the rating values of the Estimated opinion were consistently farther from those of the Own than those of the Blended opinion (particularly, higher; see also Table 1). In Study 2, such a result was not found.

Table 2

The results of the MSE decomposition (95% CI; in Study 1, all types of opinions did not follow a normal distribution, *Kolmogorov–Smirnov* test: ps < .001). It can be observed that the Blended opinion had a smaller *variability bias* than the Own opinion across the two studies. In addition, in Study 1, the Blended opinion had a smaller *bias* than the Estimated opinion.
Study 1	Bias	Variability bias	Linear correspondence
Own	[641.79, 727.88]	[351.34, 415.41]	[283.72, 300.39]
Estimated	[787.48, 884.64]	[350.01, 407.73]	[275.79, 291.46]
Blended	[609.26, 690.30]	[274.15, 315.90]	[270.67, 286.38]
Study 2	Bias	Variability bias	Linear correspondence
Own	[118.91, 179.41]	[207.32, 303.39]	[449.15, 479.40]
Estimated	[98.52, 124.97]	[86.37, 162.80]	[447.09, 472.86]
Blended	[95.76, 126.20]	[88.53, 145.54]	[432.29, 454.59]

Further analysis: when does our method works better (or worse).

For further analysis, we investigated the conditions under which our method worked better or worse. Particularly, we focused on two factors: individual differences and taste discrimination.

Individual differences. There are diverse types of taste among people^3,25,49,50: Some have considerably different tastes from the general public, while others have ordinary ones. Here, we examined how individual differences concerning taste typicality influenced the efficacy of our method.

Figure 5 illustrates our analysis. (1) For the typicality of the taste of a Giver, we calculated the absolute distance between the Giver’s and all participants’ Own opinions (particularly, the averages of all participants; called ‘distance from average’), that is, a small value on the distance from average represents high typicality of the taste of a Giver. (2) Subsequently, we analysed the reduction in the MSE. It was computed by subtracting the case when the Giver’s opinion was a Blended opinion from when it was an Own opinion; the larger the reduction in the MSE, the better the performance of our method. (3) We conducted this analysis across all stimuli and examined the relationship between the distance from the average and the reduction of the MSE. In particular, we calculated the correlation coefficient between them.

The following procedure was the same as in the final paragraph of the ‘Analysis’ section: for a Giver, we performed this analysis across the Receivers (all participants except the Giver). Thenceforward, the averages of the reduction in the MSE were assigned to the Giver’s value. Finally, we conducted this procedure for all the participants.

Figure 6 shows the results of the analysis. Each plot indicates the Giver’s value. The x-axis represents distance from average while the y-axis represents the reduction in the MSE. Across the two studies, we found a significant positive relationship between them (Study 1: rho = 0.42, p < .001; Study 2: r = 0.67, p < .001). That is, for a Giver with an atypical taste, our method worked better (for further analysis, see Section S2 of the Supplementary Information).

-----Figures 5 and 6 about here-----

Taste discrimination. When assessing an item, we have different feelings concerning our evaluations. For some items, we can make distinctive judgments whether we like them or not (for example, pop and metal music); however, for other items, we can only make vague judgments (for example, ambient and experimental music). Previous studies^1,3 have indicated that the distinctiveness of judgments (called ‘taste discrimination’) plays a critical role in opinion-giving. Notably, Müller-Trede et al.³ showed that taste discrimination affected the helpfulness of opinions in our context. They primarily provided a theoretical model and pointed out the effects of taste discrimination; briefly, they defined taste discrimination based on signal-to-noise ratios on judgments. Subsequently, they performed behavioural research and empirically confirmed its influences. Specifically, familiarity with the stimulus to which participants responded was used as an index of taste discrimination.

Therefore, we investigated the effect of taste discrimination on the effectiveness of our method. In this section, we only utilised the behavioural data from Study 2, in which the participants indicated their Own opinion and familiarity, identical to the study of Müller-Trede et al.³. In addition, we provided ‘Difficulty’ as a new index for taste discrimination: The participants also directly answered how challenging they found it to answer the Own opinion (see more details in ‘Methods’).

We conducted mixed effects analyses that included the ‘Reduction of the MSE’ as a dependent variable, while Familiarity, Difficulty, and the interaction term as independent variables (Table 3). Consequently, the impact of Difficulty was significant (F(1, 1123.7) = 48.32, p < .001). Further, we found no effect of Familiarity or interaction (Familiarity: F(1, 427.1) = 0.13, p = .72; the interaction term: F(1, 1311.3) = 0.90, p = .34). Thus, concerning our experimental settings, only Difficulty influenced the effectiveness of our method. The findings showed that the lower the Difficulty, the higher the efficiency of our method: reduction of the MSE = − 3.23 × Difficulty + intercept (= 288.21).

How did the lower difficulty enhance our method? To examine this issue, we performed additional mixed-effects analyses separately for the Own and the Blended opinions (Tables 4 and 5, respectively). These analyses used the same independent variables as our last analysis: Familiarity, Difficulty, and interaction term. However, this analysis included a different dependent variable: the MSE (not the reduction of the MSE).

The results showed that the effects of Difficulty were significant (ps < .001), and neither Familiarity nor the interactions were significant (all ps > .1) for the Own and the Blended opinions. Concerning Difficulty, the MSEs both in Own and Blended opinions had inverse relationships: as the Difficulty increased, the MSE decreased. Importantly, the Own opinion had larger slopes than the Blended: Own = − 6.48 × Difficulty + intercept (= 1034.49), and Blended = − 3.03 × Difficulty + intercept (= 739.58). That is, as the Difficulty increased, the Own opinion rapidly became an accurate prediction. Consequently, the merits of using our method were relatively low when people found it challenging to answer their own opinions.

Table 3

Results of the GLMM.
Independent variable	Statistics
Difficulty	F(1, 1123.7) = 48.32, p < .001
Familiarity	F(1, 427.1) = 0.13, p = .72
Difficulty * Familiarity	F(1, 1311.3) = 0.90, p = .34

Table 4

Results of the additional GLMM for the Own opinion.
Independent variable	Statistics
Difficulty	F(1, 1298.4) = 92.16, p < .001
Familiarity	F(1, 1211.0) = 1.28, p = .26
Difficulty * Familiarity	F(1, 1329.5) = 1.96, p = .16

Table 5

Results of the additional GLMM for the Blended opinion.
Independent variable	Statistics
Difficulty	F(1, 1286.1) = 58.01, p < .001
Familiarity	F(1, 1245.0) = 0.16, p = .69
Difficulty * Familiarity	F(1, 1326.8) = 3.11, p = .078

This research proposed a method to improve an individual’s prediction of others’ future satisfaction. This method requires a person to evaluate an item twice from different viewpoints: one is stating their preferences and the other is estimating the public opinions^32,41−46. Through two behavioural studies and computer simulations, we comprehensively examined our method. Consequently, we first confirmed its effectiveness: by averaging the two opinions, an individual could improve her/his predictions (concerning optimal weightings on the opinions, see Section S4 of the Supplementary Information). Subsequently, we mathematically analysed³ how our method worked effectively and identified multiple factors that influenced the efficiency of our method.

Throughout the analyses, we considered that this study clarified the efficacy of our method. In daily situations, people can provide better opinions for matter of taste^1–4 by using our method. Furthermore, the findings from the further analysis indicated when to use our method in detail. For example, when individuals think they have an atypical taste, they should use our method since its efficacy is high.

As mentioned in the ‘Introduction’, previous studies^2,3,25 have demonstrated that the wisdom-of-crowd effect could emerge for the matters of taste within-group. In contrast, this is the first study showing that the wisdom-of-crowd for the matter of taste can emerge even within-person (a related study⁴ focused on the performance evaluation, as a kind of wisdom-of-crows for matter of taste and extended it to within-person level).

Particularly, the analysis on decomposing MSE indicated that the same mechanism worked for the wisdom-of-crowd for matters of taste both within-group and within-person: by mainly reducing the variability bias (in other words, improving the regression to the mean), the effect emerged.

Importantly, in our daily life, we usually cannot gather many others’ opinions^{2, 25} as is assumed in the wisdom-of-crowd research. Thus, we consider that our method has not only theoretical contributions but also practical implications.

Overall, we can consider that this study highlights the generality of the wisdom-of-crowd phenomenon. That is, without objective criteria and multiple people, we can exploit the wisdom-of-crowd effect.

(1) Details of the experiment in Study 1.

Overall, 543 Japanese adults (273 females and 270 males, M_age = 45.23 years, SD_age = 11.01 years) participated in the experiment through a web research company. All participants provided informed consent prior to study enrolment. The experimental protocol was approved by the University of Tokyo Research Ethics Committee and conducted in accordance with the latest version of the Declaration of Helsinki. They received certain cash-equivalent points as an incentive that could be employed for online shopping in Japan.

We set five conditions for this research. In each condition, five different paintings were utilised as stimuli. Their contents varied among the five conditions. As a result, the stimulus consisted of 25 paintings in total (= 5 conditions × 5 paintings; see Table S1 in the Supplementary Information). Regarding the selection of the paintings, we followed a previous study⁵⁵ that included various paintings such as Gothic, Renaissance, Surrealism, and Modern art. In the experiments, the participants were randomly assigned to one of the five conditions and asked to evaluate the paintings. Specifically, they were asked the following two questions: ‘How much would you like to hang this picture on your wall?’⁵⁶ (Own opinion) and ‘How much would the average people like to hang this picture on their wall?’ (Estimated opinion). We randomized the order of the paintings’ presentation for each participant. Moreover, for convenience, we primarily analysed each condition, followed by combining the results across the conditions.

(2) Details of the experiment in Study 2.

Overall, 56 Japanese undergraduate and graduate students (22 females and 34 males, M _age = 19.61, SD _age = 1.40) partook in the laboratory experiment. All participants provided informed consent prior to study enrolment. The experimental protocol was approved by the University of Tokyo Research Ethics Committee and conducted in accordance with the latest version of the Declaration of Helsinki. On its completion, they received a flat fee of 1,000 Japanese yen (approximately $9.17).

The experimental settings were the same as those employed by Müller-Trede et al.³. In this study, we set only a single condition: All participants followed the same experimental procedure and evaluated identical stimuli. They were asked the following two questions: ‘How much do you like the musical piece?’ (Own opinion) and ‘How much would the average people like the musical piece?’ (Estimated opinion).

We selected songs from various music genres, such as classic, folk, hip-hop, and ethnic. Specifically, we selected 2 songs from 12 musicians (for example, 2 songs by Oasis from the same album ‘What’s The Story Morning Glory?’; see Table S2 in the Supplementary Information). Thus, the stimuli consisted of 24 songs in total (12 musicians × 2 songs). Each song was cut into a one-minute musical piece. We randomised the order of the musical pieces for each participant.

Furthermore, this research involved two additional questions: Difficulty in answering the Own opinion (‘How difficult was it for you to state your preference?’) and Familiarity with the song’s genre (‘How familiar are you with the genre of this musical piece?’). The participants responded to these questions on a scale ranging from 0–100.

(3) A formula of MSE decomposition.

As mentioned in the Results section, the MSE decomposition proposed by Müller-Trede et al.³ has been represented as follows:

MSE = Bias + Variability bias + Linear correspondence (1)

Mathematically, in our context, the MSE decomposition was represented as follows:

MSE _{Giver, Receiver} = (M_Giver − M_Receiver)² + (σ_Giver − ρ_{Giver, Receiver} × σ_Receiver)²

+ (1 − ρ_{Giver, Receiver}²)σ_Receiver² (2)

M is the mean of the rating value, σ is its standard deviation, and ρ is the correlation between a Giver’s and a Receiver’s ratings. On the equation’s right-hand side, the first, second, and third terms correspond to bias, variability bias, and linear correspondence, respectively.

(4) Assumptions in our analysis.

The analysis supposed that we could measure the difference in the tastes between the Givers and Receivers on a discrete scale. Further, many studies^{3,4,8,57−59} that explored preference predictions have also made similar assumptions.

(5) Mixed effects analysis.

We performed all mixed-effects analyses using the R packages lme4 and lmerTest⁶⁰. In particular, we selected the best model and computed all statistical values using the step() function for the full model with random participants and stimulus intercepts.

Data availability

The R-code during the current study and the two datasets analysed during the current study (including data for making Figures) are available in the Mendeley Data: http://dx.doi.org/10.17632/tr952fsrpx.1.

Competing of interests

The authors declare no competing interests.

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No competing interests reported.

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A simple cognitive method improving prediction for matters of taste: exploiting the wisdom-of-crowd effect within-person

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