Seeking Advice – Endogenous Communication

In a first step, I examine where people tend to seek advice when given the choice. To in-vestigate this issue, I implemented treatment Advice, which constitutes a simple variation of the Selected treatment. Subjects first completed three of the tasks in Selected so as to enable me to determine their naïvetéχ. Then, they were unexpectedly interrupted by a computer screen which informed them that in the subsequent four tasks they would get access to the decisions of subject Y or Z (“advisors”) prior to making their own decisions.

More precisely, subjects would see the group entrance decision of the respective ad-visor (red or blue), then enter a group themselves, and finally observe the belief of the chosen advisor on the belief formation decision screen, along with the signals of the

computer players.¹⁴The instructions clarified that the two potential advisors completed the same seven tasks a few weeks earlier while having access to the same information.

In other words, participants knew that the two candidate advisors obtained the same private signal and communicated with the same computer players as subjects in Advice, implying symmetric information between advisors and advisees. In order to be able to make an informed choice between Y and Z, subjects were provided with a computer screen which contained all decisions from the first three tasks of themselves as well as of Y and Z.¹⁵Thus, subjects could evaluate how their own decisions compared to those of the potential advisors. Y and Z were selected such that one of them was fully naïve in all seven tasks and the other one rational in all tasks.¹⁶All subjects in Advice had access to the same two candidate advisors. After subjects had chosen their preferred advisor, they completed an additional four tasks. 59 subjects took part in this treatment, which lasted 50 minutes and yielded average earnings of 10.80 euros including a 6 euros show-up fee.¹⁷

In this treatment, subjects usually faced the beliefs of an advisor who stated similar beliefs to themselves and of another advisor who reported different beliefs. A perhaps natural conjecture is that the rational types understand that they are rational and hence choose the rational subject as advisor so as to reduce cognitive effort in the remaining four tasks, or to double-ckeck their own calculations against random computational er-rors. On the other hand, rational subjects may be uncertain about whether they pursued the correct problem-solving approach. Even more so, two competing hypotheses come to mind regarding the naïve subjects. First, just like the rational types, the naïfs may believe that they are rational and hence opt for the naïve advisor for the reasons discussed above.

Second, however, the naïfs may have an intuitive feeling that their problem-solving strat-egy is somehow incorrect even though they weren’t able to work out the correct solution themselves. Then, seeing someone state different beliefs may lead subjects to assume that (for whatever reason) this must be the correct solution.

Result 12. Subjects overwhelmingly choose advisors whose decisions reflect their own belief formation rule. Thus, under endogenous communication, beliefs between the rational and naïve types do not converge in a meaningful way.

Columns (1) and (2) of Table 3.3 show marginal effects at means in probit esti-mations of subjects’ choice of advisor on their (median) naïveté parameter. Both with and without additional controls, higher naïveté is significantly associated with a higher

14Subjects saw the advisor’s belief provided that the subject opted for the same group as the advisor. This restriction was put in place so as to ensure that subjects had no strategic incentives to opt for a group that contradicted their private signal.

15On this screen, the labeling of Y and Z and their location on the screen (left / right) were randomized across sessions. To investigate differences between fast and slow reasoning, I implemented two conditions in which subjects could not make a decision until 30 or 90 seconds after they had entered the “advisor choice” decision screen. The corresponding results are very similar, so I pool the data in what follows.

16No deception was used in the experimental instructions. In particular, the instructions informed sub-jects that Y and Z were two participants in a previous session, but it was never indicated that they were drawn at random.

17The show-up fee in all “interaction” treatments was 6 euros because they took slightly longer than the treatments reported above.

Table 3.3. Naïveté and choice of advisor

Probit estimates, robust standard errors in parentheses. The table reports partial effects at means. The base rate for the choice of the naïve advisor is 52.5% in Advice and 58.3% in Advice only. Additional controls include age, gender, log monthly income, marital status fixed effects, and high school grades.^∗p< 0.10,^∗∗p< 0.05,

∗∗∗p< 0.01.

probability of choosing the naïve advisor. The left panel of Figure3.3illustrates these results by splitting the sample into subjects with χ ≤ 0.5 (“rationals”) and χ > 0.5 (“naïfs”). Here, the raw difference in the fraction who chose the naïve advisor is 39 percentage points, a statistically highly significant difference (p= 0.0030, two-sample test of proportions).¹⁸

Robustness and Extension

In treatment Advice, subjects have the option of choosing an advisor who states the same beliefs as them. It is conceivable that the naïve subjects seek advice in an assortative manner not because they believe that the naïve advisor is right, but rather because they may feel good if someone confirms their own assessments. Likewise, it is possible that the naïve types feel that their problem-solving strategy is incorrect, yet that they have no way of assessing how much better the strategy of the rational subject is. After all, if subjects only understand that they got it wrong, but do not know how to adequately solve the problem, they may not know whether the advisor who states different beliefs is actually superior.

In order to address these issues, I implemented treatment Advice only. This condition was identical to Advice except for three variations. First, in the advisor selection phase, subjects were not provided with the advisors’ decisions from the first three tasks. Rather, subjects in Advice only were presented with the advisors’ decisions in two belief formation tasks from the baseline Selected condition which subjects in Advice only did not complete themselves. That is, out of the seven tasks in Selected, subjects in Advice only completed three tasks without advice, two with advice, and two not at all. Accordingly, when making their decision among the advisors, they could not compare their own beliefs to the ones of the advisors (where again one advisor was essentially fully rational and one fully

18Subjects’ propensity to choose an advisor of the their own type may depend on their confidence. To investigate this issue, I make use of a qualitative question that was asked after the first three tasks, i.e., before the choice of the advisor was introduced: “On a scale from 1 (not certain at all) to 10 (very certain), how certain are you that your previous estimates (and the underlying strategy) were correct?”. In Appendix3.E, I discuss this variable and its relationship to subjects’ decisions in detail. I find that there is a moderate, statistically significant, correlation between subjects’ naiïveté and their confidence (ρ = −0.16, p = 0.0227).

However, the relationship between subjects’ confidence and their choice of advisor is weak at best, for both rationals and naïfs.

0.25.5.751Fraction chose naive

Naïveté ≤ 0.5 Naïveté > 0.5

Treatment Advice

0.25.5.751Fraction chose naive

Naïveté ≤ 0.5 Naïveté > 0.5

Treatment Advice only

Figure 3.3. Fraction of naïve and rational subjects that chose the naïve advisor. The left panel illustrates the results from treatment Advice and the right panel those in treatment Advice only.

In both panels, subjects are split according to whether their median naïvetéχin the first three tasks was larger or smaller than0.5.

naïve). Rather, they had to work through the two tasks which they did not complete themselves in order to be able to assess the respective belief statements of the advisors.

Second, and relatedly, subjects were told that the advisors’ decisions would be the only piece of information in the subsequent tasks. In other words, in the remaining two tasks, subjects neither saw their own private signal nor did they communicate with any of the computer players. Thus, once they had chosen an advisor, subjects were essentially left only with following the group entrance decisions and belief statements of the chosen advisor. Importantly, note how these two changes to the design ensure that subjects indeed choose the advisor whom they assess to be superior, rather than someone whom they suspect to confirm their own assessments; after all, subjects did not state any beliefs when the advisors did, so that such affective reasons could play no role. Third, and finally, the instructions explicitly stated that one of the advisors solved all problems correctly.

Thus, if the naïve types conjectured that their own strategy was wrong, they should immediately pick the rational advisor, even if they did not understand how the rational advisor developed their beliefs. 60 subjects participated in this treatment and earned 11.40 euros on average.

Columns (3) and (4) of Table 3.3present the results, while the right panel of Fig-ure3.3provides a graphical illustration. In short, the results are even stronger than those in Advice. Again, there is a strong and significant relationship between subjects’ naïveté and their propensity to choose the naïve advisor. For instance, when I again split the sample into subjects withχ ≤ 0.5 and χ > 0.5, the difference in the fraction who chose the naïve advisor is 62 percentage points (p< 0.0001, two-sample test of proportions).

In sum, across both treatments, subjects choose advisors in an assortative manner. I proceed by visualizing the resulting belief patterns, pooled across treatments Advice and Advice only. Figure3.4depicts the distribution of naïveté implied in all beliefs subjects stated when they had access to an advisor, partitioned by subjects’ inherent naïveté type (as determined by the first three tasks without advice). The figure reveals that little belief convergence took place through the introduction of the advisors: the majority of rationals

still states approximately rational beliefs, while the majority of naïfs remains naïve.¹⁹ This suggests that, if people can choose whom to communicate with, pronounced belief heterogeneity may persist over time. Notably, this pattern obtains in the absence of he-donic motives, but rather because people talk to those they believe to have the correct problem-solving approach. At the same time, the relationship between subjects’ beliefs with and without advice ought to be interpreted with care because subjects chose these advisors themselves. The following section discusses how subjects respond when they are confronted with the beliefs of others whom they did not select themselves.

0.25.5

-.5 0 .5 1 1.5 -.5 0 .5 1 1.5

Rationals Naïfs

Fraction

Implied naïveté

Distribution of naïveté with advice

Figure 3.4. Distribution of decisions in the last four tasks (i.e., with advice), conditional on subjects’ naïveté type in the first three tasks. Rationals are defined asχ ≤ 0.5and naïfs as

χ > 0.5. The histograms exclude observations outside [-1,1.5].