Information risk aversion
Oliver Sugg (11889950), University of Amsterdam, 15ECTS
MSc. Economics (Behavioural Economics and Game Theory)
Abstract
Traditional economic theory values information only as much as it can im-prove expected utility, however, people have been found to avoid and ignore valuable information across a range of economic situations. This study uses a new theoretical framework and online pilot experiment to investigate in-formation selection in a risk environment. A series of binary choices between conditional probability information structures is used to evaluate whether sub-jects seek information that encourages (information risk-seeking) or discour-ages (information risk-averse) future risk after controlling for individual risk aversion. Subjects are found not to conform to expected utility theory predic-tions, consistently selecting less informative information structures. Subjects perform better than chance, however, indicating only a partial relationship be-tween expected utility and information selection. Subjects are also consistently found to be information risk-seeking or -averse, as they are significantly more likely to select information structures that encourage or discourage future risk at a subject level relative to random choices. After controlling for individual certainty equivalents, this effect remains correlated with elicited risk aversion: subjects with higher risk aversion are more likely to select a more informative information structure if it discourages risk in the second stage. Specific infor-mation structure or decision characteristics are not found to have significant effects on information selection. These results give preliminary evidence that information selection is driven by factors other than expected utility.
Acknowledgements
I am very grateful to Giorgia Romagnoli (University of Amsterdam, Economics de-partment) for the initial theoretical idea as well as her continued supervision and support throughout this thesis.
Statement of originality
This document is written by Oliver Sugg, who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents
1 Introduction 5
2 Literature Review 8
3 Theoretical framework 13
4 Experimental design 16
4.1 Certainty equivalent elicitation . . . 17
4.2 Binary information structure decisions . . . 17
4.2.1 First-stage . . . 17
4.2.2 Second-stage . . . 22
4.3 Elicitation of related characteristics . . . 23
4.3.2 Ambiguity aversion elicitation . . . 24 4.3.3 Questionnaire . . . 26 4.4 Hypotheses . . . 26 5 Results 29 5.1 Decision types . . . 30 5.2 Subject traits . . . 35 5.3 Decision features . . . 41 6 Discussion 44 7 Conclusion 47 References 48 Appendix A 52 Appendix B Instructions 54 B.1 Introduction . . . 54 B.2 PORU elicitation . . . 54
B.3 Risk aversion elicitation . . . 55
B.4 Second-stage decision instructions . . . 56
B.5 First-stage decision instructions . . . 56
B.6 Ambiguity aversion elicitation . . . 58
B.7 Questionnaire . . . 58
List of Figures
1 Information in alpha-beta space . . . 162 Elicitation of certainty equivalent . . . 17
3 Information structure diagrams . . . 18
5 Convention for information structure coordinates . . . 20 6 Structure of five decisions within each question block . . . 21 7 Information structure of D2 for each question block . . . 22 8 Task measuring preference for one-shot resolution of uncertainty . . . 25 9 Example question measuring ambiguity aversion . . . 25 10 Effect of decision type on correct first-stage decisions . . . 30 11 Distributions of sample and randomly generated directional indices . 34 12 Summary of subject trait measures elicited . . . 36
List of Tables
1 Effect of decision type on probability of correct first-stage decision . . 32 2 Correlations between subject traits . . . 35 3 Effect of subject traits and interactions on correct first-stage decisions 38 4 Effect of decision features on first-stage decisions . . . 42 5 D1 decisions for each question block . . . 52 6 Decision type balance table . . . 53
1
Introduction
From a traditional economic viewpoint, information is interpreted as a signal that reduces the uncertainty of a decision and thereby increases the resulting expected utility for an agent. Yet our interactions with the information available to us seem to tell a different story. When making any kind of decision, there is often a diverse range of information types and sources that can be useful. If we are thinking about where to spend our next vacation, we ask friends about their favourite places to visit, we look through travel magazines for recommendations or we look up online reviews of hotels and activities. These different types of information also intuitively seem to lead to different decisions being made: it is unlikely that you would end up in the same hotel using each of the above routes individually.
The extent to which people engage with these different types of information also varies, dependent on context. Sometimes people seek out more information to better inform their decision, but often they also ignore or even avoid useful information that they do not want to see. People have been found to trust information that goes against their current viewpoint less than information that supports it, as can frequently be seen in debates between politicians, colleagues, family members and even academic experts. We consistently avoid information if it holds negative per-sonal consequences, such as checking our investment portfolio less frequently if the market is down (Karlsson, Loewenstein, & Seppi, 2009), postponing medical check-ups if we know we are at risk of a transmitted disease (Ganguly & Tasoff, 2016) or even avoiding and ignoring information if we receive negative feedback about our appearance or ability (Eil & Rao, 2011). The above examples seem to indicate that the traditional economic view of information does not capture the full picture of how people interact with the information around them.
These situations often bear several similarities, however, so previous research has attempted to characterise how and why people fail to act ”rationally” when inter-acting with such information. A common theme throughout is that information can be said to hold intrinsic value beyond its expected value, falling into two main
cat-egories as suggested by Golman, Hagmann, and Loewenstein (2017). First, people may use information as a strategic tool in a game-theoretic setting, as discussed in the strategic communication strand of literature (Spence (1978); Grossman (1981); Milgrom (1981); Crawford and Sobel (1982); Kartik (2009)). For example, an in-formed second-hand car salesman may tactically restrict the information he decides to give less-informed potential buyers. Second, information may have an indirect effect on decisions through behavioural biases arising from our hedonic tendencies. If we know that seeking a certain type of information is likely to cause negative emotions, such as disappointment, regret or guilt, this anticipation factors into our decisions, rightly or wrongly (Loomes and Sugden (1982); Gul (1991); Wakker (1988)). In line with loss aversion, the equivalent positive emotions do not seem to carry the same weight.
Yet it also seems intuitively obvious that people may have intrinsic preferences for different types of information beyond simply expected value, strategic poten-tial and anticipated negative emotions, yet this idea has not been widely studied. Furthermore, there are few studies on how people choose between different types of information as opposed to interpreting or valuing information given, particularly when the information they receive is unambiguous. Therefore, this paper will focus on whether people have preferences over information in the domain of risk, with com-plete information and in addition to their risk aversion. The primary hypothesis for this research question is that if someone is choosing between two sets of information, they may be inclined to select the information that makes themselves more or less likely to take risk in the future.
A tangible example of this hypothesis might involve gambling: a person may be choosing whether or not to look up last week’s football scores while browsing the internet. They know that the information they gather from looking up the scores will make them more likely to bet on the following week’s matches, meaning their original decision to look up the scores will depend on their willingness to gamble in the future. Some people might avoid the information, some might seek it. This study
uses an equivalent, stylised experimental design to evaluate if people do consistently choose information in one direction or the other.
An online pilot experiment is used as a proof of concept, investigating whether people consistently select less valuable information in the first stage of a task if it makes them more or less likely to take on a risky investment in the second stage. Subjects first state their certainty equivalent value for an investment that gives e20 with 50% probability ande0 with 50% probability. They are then provided truthful but probabilistic signals, or information structures, about whether the investment will pay out. If they are given a “positive” signal, the investment will be more likely to pay out than 50% and vice versa for a “negative” signal. Once they receive this signal, they then decide whether to take the investment or to receive their certainty equivalent for sure. Before this decision, subjects first make a series of binary deci-sions between information structures, which are used to infer subjects comparative valuations of the various information structures. This experimental design is used for several reasons. First, Bayesian inference only restricts the expectation of poste-riors, so the value of the different information structures given can be manipulated by changing the conditional probabilities of a good signal given the investment pays out and a bad signal given the investment does not pay out. Second, the signals are all verifiable and given to the subjects, meaning Bayesian calculation biases as found in many other studies (Ambuehl & Li, 2018; Eil & Rao, 2011) will not be able to explain the decisions made. Third, by eliciting and controlling for each subject’s certainty equivalent, any effects found cannot only be attributed to risk aversion and must arise from additional preferences over the information itself. Fourth, as the subject’s certainty equivalent represents indifference between that amount with cer-tainty and the investment, it is clear that they should prefer the investment after a positive signal and the certainty equivalent after a negative signal, meaning only the binary decisions between information structures in the first stage are necessary to answer the research question. Therefore, as subjects do not receive feedback on the uncertainty resolving in the second stage, the effect of anticipatory emotions should
be minimised.
Within this design, subjects were found to consistently select information struc-tures that have a lower expected value than the alternative, similarly to many pre-vious studies’ results counter to expected utility theory. Furthermore, evidence was found suggesting that subjects may be information risk-seeking or -averse, as the like-lihood of selecting the less informative structure is linked to whether the structure increases or decreases the probability of a positive signal, and therefore of taking the risky investment in the second stage. This tendency is correlated with risk aversion over and above the risk aversion elicited by the lottery certainty equivalent, and does not depend on the specific characteristics of the information structures.
2
Literature Review
Golman et al. (2017) summarise considerable evidence that people avoid and ignore information in certain circumstances, particularly when there are opportunities to act in a self-serving way. For example, Dana, Weber, and Kuang (2007) use a simple yet compelling experimental design to show that selfish motives can lead to people avoiding socially valuable information. When subjects have the choice of whether to costlessly reveal information on whether an action benefits another person, they often choose not to while selecting the selfish option. Similarly, Eil and Rao (2011) investigate how Bayesian updating depends on the nature of the information subjects are given. They found that people who initially receive negative information about their appearance or intelligence, relative to their expectations, are more likely to avoid obtaining the full information. They also argue that people’s inferences reflect Bayes’ Rule more accurately if they are given information with good news regarding personal qualities. Peysakhovich and Karmarkar (2015) find the same effect of favourable and unfavourable information with respect to the valuation of an ambiguous gamble, suggesting that favourable information increases people’s valuations but unfavourable information does not decrease valuations in the same
manner. Numerous other papers, including Babcock, Loewenstein, Issacharoff, and Camerer (1995), Glaeser and Sunstein (2013) and Lord, Ross, and Lepper (1979) apply this concept at a more psychological level considering how and why people interpret information and evidence in ways that support what they are motivated to believe. These studies, and many others, show how people’s valuations of information are influenced by a self-serving bias. Although this study also looks at how people may have self-serving preferences over information above and beyond expected value, subjects are given the full Bayesian calculations and information required for their decision, so they are not easily able to avoid or misinterpret information as such.
Beyond a self-serving bias, Ambuehl and Li (2018) consider how Bayesian-updating biases affect people’s demand for information. They use a similar experimental de-sign to this study, suggesting that the information valuation biases found are well explained by non-Bayesian belief updating and that there is consistent heterogene-ity determined by individual responsiveness to information. They acknowledge that biases may also occur because of non-standard valuations of information, though their data did not support this explanation. However, they did not focus on this hypothesis in their experimental approach, meaning every decision subjects made involved risk. Therefore, they did not consider that risk may be a determinant of non-standard valuation of information. The current research ensures that all Bayesian updating is made clear for each trial and therefore that the choices made can be attributed to information preferences as opposed to biased Bayesian infer-ence. Furthermore, subjects have a riskless option in every second-stage decision they make, which potentially impacts their initial choice of information structure via non-standard valuations. Ambuehl and Li also reach two specific conclusions regarding how subjects valued and responded to information. First, they find a sig-nificant border effect where subjects disproportionately value information structures situated on the border, which thereby have some degree of certainty. Second, they find that mathematical and cognitive ability do not correlate with individual biases or responsiveness to information. The closely-related experimental design implies
that these effects might be relevant to the results of this study.
This study’s experimental design is also partially based on the uncertainty and ambiguity experiments proposed by Ellsberg (1961), where subjects place bets on the colour of a ball from a box with known or unknown proportions of coloured balls. Halevy (2007) uses this approach to investigate attitudes to ambiguity and compound objective lotteries by subjects betting on the colour of balls drawn from each of four urns. The same approach is used to determine both risk and ambiguity aversion in this research.
There has also been considerable research on how information acquisition de-cisions can impact utility and therefore why people may avoid information. This research may help to inform the reasons for subjects’ decisions within the current research. Golman et al. (2017) suggest that there are two types of reasons people may avoid information: the direct impact of anticipation or realisation (hedonic) and that the information received may influence subsequent decisions (strategic). The current research focuses on the latter, as the hypothesised driver of information structure choice beyond expected utility is that it affects the likelihood of themselves making a risky decision in the second stage. Furthermore, subjects do not realise outcomes during the experiment, so they are unlikely to experience the hedonic ef-fects of decision-making, such as disappointment aversion arising from finding out the result of the first-stage signals or second-stage outcomes, as in Gul (1991). If outcomes were realised, people may use the information structure decision as an internal commitment device for risk preferences that violate dynamic consistency. Wakker (1988) demonstrates how people may avoid information about a first lottery in anticipation that it may affect their decision in a second lottery. In the current research, although someone’s second-stage decision to take on risk after a positive signal is unlikely to change, choice of information structure impacts that probability that they will have to make the decision that they may wish to commit themselves to ex-ante.
some kind of dynamic inconsistency in decision-making and is therefore strongly theoretically linked to a“dual-self” model, as proposed by Fudenberg and Levine (2006). They argue that several empirical economic regularities can be explained by modelling individual decision-making as the interaction between two selves. The decision facing the subjects in the current research can be modelled as a similar interaction between a long-run self, who chooses the information structure, and a short-run self, who chooses between the investment and the certainty equivalent and (hypothetically) experiences the outcome. For example, if the long-run self is more risk-averse than the short-run self, they may choose a less informative information structure, but one that reduces the possibility of the short-run self taking a risky action in the second stage.
There is a considerable body of research studying strategic communication be-tween two parties in ways that could be applied to a dual-self model. However, the majority of these papers focus on market interactions where the party sending infor-mation is able to conceal inforinfor-mation or lie about its realisation (Spence, 1978; Gross-man, 1981; Milgrom, 1981; Crawford & Sobel, 1982; Kartik, 2009). The model of Bayesian persuasion proposed by Kamenica and Gentzkow (2011), however, focuses on strategic communication where the signal realisation is truthfully communicated, such that both parties are simply solving a straightforward, game-theoretic decision problem. Using the observation that Bayesian updating only restricts the expecta-tion of posteriors, they outline the condiexpecta-tions under which a Sender can benefit from choosing an informative signal to send a Receiver, who then takes a noncontractible action that impacts both parties. In general, they find that the Sender benefits from persuasion when the Receiver does not take their preferred action by default, and the Receiver’s action is constant in some neighbourhood of beliefs around the prior. This model closely resembles how behaviour in the current research might be viewed within a dual-self framework where information is the variable of interaction between the selves.
and why subjects may have preferences beyond simply expected utility. For example, Kreps and Porteus (1978) (and subsequently Grant, Kajii, and Polak (1998)) propose a framework emphasising the importance of timings when valuing lotteries, suggest-ing that people have a preference for earlier (or later) resolution of uncertainty. If someone has such a preference, they would prefer to have the same lottery resolve in one stage as opposed to two. In addition to preferences over time, Palacios-Huerta (1999) and Dillenberger (2010) suggest that people may have a preference for uncer-tainty resolved gradually or all at once, supported by the finding of Zimmermann (2014) that people have heterogeneous preferences in this regard. In the context of this study, subjects who have these preferences are likely to reflect them in their choice of information structure. By choosing an information structure with a higher probability of a negative signal, the uncertainty is more likely to be resolved in one stage, as the optimal second-stage decision is to take the certainty equivalent after a negative signal. Although subjects do not experience this resolution of uncertainty during the experiment, they may still use this preference as a basis for decision-making.
Another explanation may involve the role of ambiguity aversion. Bleaney and Humphrey (2006) find that people value lotteries more when they are presented with frequencies as opposed to probabilities. They interpret the difference as one of ambi-guity aversion, suggesting that people are more easily able to understand information as frequencies than probabilities and therefore that valuation of probabilities is likely to incorporate more cognitive processing of ambiguity. In the current research, if people are given the correct Bayesian probabilities but still mentally interpret them as ambiguous, it may help to explain if their decision-making is inconsistent with predictions based purely on risk aversion.
Existing non-expected utility models may also help us to understand people’s decision-making if it violates the traditional expected utility theory. For example, regret aversion, as suggested by Loomes and Sugden (1982), describes the effect of anticipated regret on current decision-making, where the utility of a decision is
modulated by the potential utility if the unchosen option was experienced, without having chosen it. As subjects do not directly experience the result of their decisions during the experiment, it is unlikely to play an important role in choices between information structure. Yet subjects may to some degree take into account the pos-sibility that they receive a bad signal when the investment would have paid out, over and above its expected value. The subjective expected utility theory proposed by Savage (1972) may also help to explain how people do not use the probabilistic information they are given objectively, leading to inconsistent choices.
3
Theoretical framework
To test the hypothesis that subjects value information in ways beyond simply the expected utility of their decisions, it is necessary to establish a theoretical framework. Suppose there are two states of the world, Good (G) and Bad (B), each occurring with equal probability, and one action, INVEST, whose outcome is larger in the G state than in the B state. For example, assume:
20 = IN V EST (G) > IN V EST (B) = 0 (1) There is an agent with well-defined utility function u(.), normalised such that u(0) = 0. Ex-ante, the certainty equivalent (CE) of the action of investing is elicited. That is, the CE is such that:
u(CE) = 0.5 · u(20). (2)
Before taking any action, the agent can observe a signal whose distribution is conditional on the true state. The signal can be of two types, a good (g) signal or a bad (b) signal, and we define α = pr(g|G) and β = pr(b|B) as the base conditional probabilities used for reference throughout the framework. As Bayesian inference only places restrictions on the expectation of posteriors being 0.5, the only additional assumption required is α > 1 − β, simply to ensure G is more likely after a g signal
than a b signal. We call {α, β} an information structure. From Bayes rule we also derive: P r(G|g) = P r(g|G)P r(G) P r(g) = α 1 + α − β (3) P r(B|b) = P r(b|B)P r(B) P r(b) = β 1 + β − α (4) P r(g) = 0.5(1 + α − β) (5) P r(b) = 0.5(1 + β − α) (6) After receiving the signal, the decision-maker decides whether to invest or to take her certainty equivalent reported in equation 2. As the agent, by definition, is indifferent between their certainty equivalent and the lottery with 50% probability of G, she will clearly decide to invest after a g signal, as the probability of state G is greater than 50%. Similarly, she will decide to take her certainty equivalent after a b signal, as the probability of state G is less than 50%. Formally:
u(IN V EST |g) = α
1 + α − β · u(20) > u(CE) (7) u(IN V EST |b) = (1 − β
1 + β − α) · u(20) < u(CE) (8) It follows that the agent will invest with probability P r(g) = 0.5(1 + α − β). The value of an information structure, V (α, β), can be defined as the expected utility of receiving a signal and taking the optimal action described above. Therefore:
V (α, β) = P r(g) · u(IN V EST |g) + P r(b) · u(CE) (9)
= 0.5(1 + α − β) α
= 0.5[α(u(20) − u(CE)) + (1 + β)u(CE)] (11) As can be seen, the value of the information structure is increasing in both α and β. Fixing the value of the information structure (V ) gives an iso-value curve where combinations of α and β give equal expected value:
V = 0.5[α(u(20) − u(CE)) + (1 + β)u(CE)] (12)
α = V − u(CE) u(20) − u(CE)− β
u(CE)
u(20) − u(CE) (13) As u(20) = 2u(CE), the iso-value curve can be re-expressed as:
α + β = V − u(CE)
u(CE) (14)
In principle, as the right-hand side of the equation is constant, for any degree of risk aversion or shape of utility curve, the decision-maker will be indifferent among all information structures with equal sums of α and β, as demonstrated in Figure 1a.
Importantly, however, different points on the iso-value curve will generate dif-ferent probabilities of taking up risk, as P r(g) = 0.5(1 + α − β) = P r(IN V EST ). Therefore, when α = β, the agent will invest with an ex-ante probability of 50%; when α > β she invests with probability larger than 50%, and vice versa when α < β. For example, if α is high, there will be a greater probability of a g signal, however, this will be balanced by a relatively lower chance of investment success should the signal occur. If the agent wants a reason to take up risk, she will prefer the in-formation structures with larger α and smaller β (we call this agent “inin-formation risk-seeking”). Conversely, an agent who wants a reason to be safe will prefer in-formation structures with larger β and smaller α (“inin-formation risk-averse”). These definitions can be seen in Figure 1b. The traits are distinct from the agent’s risk
(a) Increasing isovalue curves (b) Information risk-averse and -seeking
Figure 1: Information in alpha-beta space
aversion, which has already been controlled for through elicitation of the certainty equivalent.
As the slope of the iso-value curve is -1, it is possible to make a prediction about how a risk-neutral agent should behave. Given a choice of two information structures, the agent should prefer the information structure with a greater sum of α and β. For example, if the line between the information structures is steeper than -1, the agent will prefer the structure with a lower α.
This experiment tests this prediction, in particular, by examining whether sub-jects do consistently select the more valuable information structures as predicted by the above theoretical framework.
4
Experimental design
As a preliminary proof of concept, an incentivised, online experiment was conducted with 40 subjects. Subjects were primarily recruited through the author’s network of
Figure 2: Elicitation of certainty equivalent
Master’s and Bachelor’s students. The instructions for each section are provided in Appendix B.
4.1
Certainty equivalent elicitation
A Becker-DeGroot-Marschak mechanism was used to elicit each subject’s certainty equivalent for an investment that gives e20 with 50% likelihood and e0 with 50% likelihood. It was made clear to the subjects that their answer was equivalent to their valuation of the investment, and that this would be used in the remainder of the experiment.
A single bid was used in combination with an explanation of why the subject should bid their valuation of the lottery, as opposed to a series of binary decisions, to limit the time required to ensure understanding and reflect the methodology used by Ambuehl and Li (2018).
The input mechanism used is shown in Figure 2.
4.2
Binary information structure decisions
4.2.1 First-stage
The main section of the experiment involved subjects making a series of binary de-cisions between two of the information structures discussed in the theoretical frame-work. Subjects were explicitly shown diagrams of the information structures with all probabilities, such as in Figure 3, where the positive signal represents g, the negative signal represents b, X represents their certainty equivalent and the probabilities on
(a) Calculation of Bayesian probabilities (b) Example of diagram shown to subjects
Figure 3: Information structure diagrams
the final branches represent the conditional probabilities of the investment succeed-ing. The Bayesian calculations using alpha and beta are shown in Figure 3a, while an example of a diagram the subject might see in the experiment is shown in Figure 3b, where α = 0.54 and β = 0.9.
Each choice between information structures was described to subjects as though the diagrams represent experts who focus on different aspects of the economic en-vironment to give accurate but differing signals about the probability of investment success. An example of how the binary choice was presented to subjects is shown in Figure 4. This decision is referred to as a first-stage decision.
Each first-stage decision can be displayed as a comparison of two points plotted in alpha-beta space. With generality, let (α1, β1) be the coordinates of the information
structure closer to the bottom-right corner (i.e. higher alpha and lower beta value), referred to as Option 1 in this paper, or Expert A to subjects during the experiment. Similarly, let (α2, β2) be the coordinates of the information structure closer to the
top-left corner of the alpha-beta graph (i.e. lower alpha and higher beta value), referred to as Option 2 or Expert B. These coordinates are shown in Figure 5.
Figure 4: Example of binary decision between information structures
Each subject receives one first-stage decision randomly selected from each of 16 question blocks. Each question block contains five binary decisions that varied in the alpha-beta coordinates of the information structures. If the coordinates of Decision 1 (D1) were (a1, b1) for Option 1 and (a2, b2) for Option 2, then the five decisions
consisted of the following sets of coordinates, as shown in Figure 6:
D1: (a1, b1), (a2, b2); where a1+ b1 = a2+ b2
D2: (a1− 0.05, b1− 0.05), (a2, b2)
D3: (a1− 0.1, b1− 0.1), (a2, b2)
D4: (a1, b1), (a2 − 0.05, b2− 0.05)
D5: (a1, b1), (a2 − 0.1, b2− 0.1)1
1When D1 includes an information structure on the border, the sum of alpha and beta is reduced
such that the structure remains on the border. For example, if (a2, b2) lies on the right-hand border
Figure 5: Convention for information structure coordinates
In D1, α1+ β1 = α2+ β2. D2 and D3 decisions lie in the same “direction”, where
Option 2 is more informative than Option 1 , meaning α1+ β1 < α2+ β2. On the
other hand, in D4 and D5 decisions, Option 1 is more informative than Option 2, meaning α1+ β1 > α2+ β2.
Subjects were randomly given only one decision from each question block to ensure they were not influenced by previous decisions over closely related information structures.
These first-stage decisions were designed to check whether subjects made them as predicted by the theoretical framework. For example, if the subject receives D2 and they are a rational agent as previously described, then they should select Option 2 at (a2, b2), as a2+ b2 > (a1− 0.05) + (b1− 0.05). If they consistently select the less
infor-mative information structure in D2 to D5 decisions, then there is some evidence that the traditional expected utility theory is not able to explain subjects’ information
Figure 6: Structure of five decisions within each question block
selection. In particular, if people consistently select the information structures in a certain direction, then it indicates information risk-seeking or -avoiding preferences in addition to risk aversion. For example, as Option 1 structures have a greater value of alpha than Option 2, they are more likely to give a positive signal, meaning the subject is more likely to take on the risky investment in the second-stage. Therefore, information risk-seeking would mean subjects would be more likely to select Option 2 than the theory suggests in a given decision.
The 16 question blocks were then presented to the subjects in a random order, such that each subject made 16 first-stage decisions in total. Looking at the alpha-beta space, there are several characteristics of information structures that feasibly may have an effect on the decisions subjects make between them. For example, previous literature in related areas (Ambuehl & Li, 2018) has found a certainty effect associated with structures located on the border. The values of a and b were varied between question blocks in order to span the alpha-beta space and to test whether such characteristics correlate with first-stage decisions made. The characteristics considered include alpha-beta sum, structure symmetry, location along isovalue curve
Figure 7: Information structure of D2 for each question block
and whether structures lie on a border. Figure 7 shows the information structures for D2 of each question block for some clarity. The detailed list of information structures used can be found in Appendix A.
Furthermore, as each subject received only one first-stage decision selected at random from each question block, the different effects found between choices cannot be attributed only to the location of the information structures. For example, the instances of D5 each subject received will be randomly distributed across the combi-nations of alpha and beta, so the specific values of alpha and beta can be controlled for.
4.2.2 Second-stage
Following each first-stage decision, subjects were then given either a positive or negative signal based on the conditional probabilities of their selected information
structure.2 Given the signal received and the resulting probability of investment
suc-cess, subjects were then asked to choose between the investment and their certainty equivalent X. This decision is referred to as a second-stage decision.
As explained in the theoretical framework above, the subject selected their cer-tainty equivalent to the 50/50 lottery between e20 and e0 such that they should prefer the investment after a positive signal and their certainty equivalent after a negative signal. Subjects were still asked to make these second-stage decisions, how-ever, to check consistency in their decisions and their elicited certainty equivalents. If subjects were shown to consistently select against these predictions, it may indicate that their certainty equivalent had changed over the course of the experiment or that they demonstrate a fundamental lack of understanding around the task.
To minimise the possibility of the latter, before starting their series of decisions, subjects were made aware that the certainty equivalent they previously reported im-plied the second-stage decision they should make, as well as the underlying reasoning. They then completed four practice second-stage decisions before beginning the main series of decisions. Subjects on average answered 3.5 out of 4 practice questions correctly, indicating a significant level of consistency and understanding.
4.3
Elicitation of related characteristics
Two further tests were carried out to elicit measures of related subject characteristics that may help to explain the pattern of decisions between information structures, followed by a basic information questionnaire.
4.3.1 Preference for one-shot resolution of uncertainty
A preference for one-shot resolution of uncertainty (PORU) has been found by Kreps and Porteus (1978) and Grant et al. (1998), and may help to explain the direction of people’s decisions. For first-stage decisions in this experiment, a preference for
2These probabilities were used to calculate randomly generated signals ex-ante for each possible
Option 2 information structures (with a higher probability of a negative signal) would intuitively relate to a preference for one-shot resolution of uncertainty, as the subject is more likely to select the certainty equivalent in the second stage, resolving uncertainty sooner.
To measure this effect, subjects completed a choice list between two risky options. In the first option, subjects are told that a coin will be flipped once. If it lands heads, they have a 75% chance of receiving e20 and 25% chance of receiving nothing. If it lands tails, they have a 25% chance of receivinge20 and 75% chance of receiving nothing. In the second option, a coin is also flipped once, but if it lands heads, they receiveeZ with certainty, and if it lands tails, they receive e0 with certainty.
Subjects then had to decide for values of Z frome15 to e25 which of the options they would rather play. When Z =e20, the two options have the same expected value of e10, so people with a stronger preference for one-shot resolution of uncertainty would switch from Option 1 to Option 2 at a lower value of Z.
A measure of this preference was calculated by subtracting from 20 the first value for Z at which a subject switched from Option 1 to Option 2. If a subject switched more than once, in order to maintain a reasonable sample size, the subject was assigned a proxy switching point as if all Option 1 selections were grouped for the lowest values of Z.
As a preference for one-shot resolution of uncertainty is a related characteristic that seems likely to impact the decisions between information structures, the subjects were given the question at the start of the experiment.
The choices used for the elicitation task are shown in Figure 8. 4.3.2 Ambiguity aversion elicitation
Ambiguity aversion may help to explain the decisions people make between informa-tion structures, as subjects may view the investment as ambiguous despite knowing the probabilities. If a subject is more ambiguity averse, they may be more likely to select information structures that give a higher probability of a negative signal.
Figure 8: Task measuring preference for one-shot resolution of uncertainty
Figure 9: Example question measuring ambiguity aversion
To elicit a measure of ambiguity aversion, subjects valued an investment using the same BDM mechanism from Part 1, however, the probability of the investment pay-ing out was unknown both to the subject and the experimenter. The valuation of this investment can then be compared to the valuation of the investment where the probability is known in order to generate averse the subject is to ambiguity, above and beyond their risk aversion. The measure is calculated by subtracting the risk aversion task valuation from the ambiguity aversion task valuation to find the dif-ference. If a subject submitted a lower valuation for the ambiguity task than the risk aversion task, the measure will be the positive difference between the two. The mechanism closely mirrors that used by Halevy (2007).
This elicitation was carried out after the main block of information structure decisions such that their valuation was not anchored by the similar elicitation of risk aversion. The valuation input is shown in Figure 9.
4.3.3 Questionnaire
Finally, subjects were given a questionnaire asking for basic personal characteristics including age, gender, employment status, likelihood of starting a business in the future and their perceived level of understanding. They were also asked to describe how they made their decisions throughout the experiment, and whether they used any rules-of-thumb.
4.4
Hypotheses
The theoretical prediction for first-stage decisions is that subjects should choose the information structure with the highest expected utility. In line with the findings of Ambuehl and Li (2018), I expect that subjects will not accurately value information structures. As valuations tend to vary insufficiently with informativeness, the per-ceived difference between information structures is likely to be diminished, meaning subjects are more likely to end up selecting the less informative information struc-ture. However, the greater the difference in expected utility, the more subjects will begin to notice the discrepancy, increasing the proportion of decisions for the higher utility option.
Hypothesis 1: Subjects will select less informative information structures a sig-nificant proportion of the time for decision types other than D1.
Hypothesis 2: Subjects will select less informative information structures with lower expected utility more frequently for D2 than D3, and for D4 than D5 decisions.
The core research question underlying this experiment is to investigate whether subjects are information risk-seeking or averse, meaning they would consistently choose information structures that encourage them to take on, or not to take on, risk. This effect may outweigh the expected utility difference if it is not too large or
obvious. If a subject wishes to take on risk, then they will be more willing to choose an information structure with a lower expected utility if that structure has a higher value of alpha. This willingness is likely to be consistent throughout the experiment, in the same way that their elicited risk aversion is expected to be.
Hypothesis 3: Subjects will be consistently information risk-seeking or -averse, selecting less informative information structures more in one direction than the other (i.e. for D2 and D3, or for D4 and D5).
Subjects were described the reasoning behind why they should select the invest-ment after a positive signal and the certain amount after a negative signal. Therefore, when making second-stage decisions, I expect to find that subjects select the less in-formative option in only 10-15% of decisions, in line with the proportion of noisy subjects found previously in other risky decision-making studies (Ambuehl & Li, 2018; Holt & Laury, 2002).
Hypothesis 4: For the majority of second-stage decisions, subjects will select investment after a positive signal and the certainty equivalent after a negative signal.
It is expected to be difficult predicting the direction of individual subjects’ de-cisions using related traits and characteristics, as the within-subject sample size is small and little work has been done in this area to date. However, there are several related factors that may reasonably be predicted to correlate with this direction. For example, preference for one-shot resolution of uncertainty has been shown to be heterogeneous between people by Zimmermann (2014) and is closely linked with the decisions at hand. Choosing an information structure with a higher beta value can be interpreted as seeking a one-shot resolution of uncertainty through a higher probability of a negative signal. Therefore, it seems reasonable to suggest that this trait may correlate with the direction of first-stage decisions.
The same may also be true of ambiguity aversion, as if subjects interpret the con-ditional probabilities ambiguously, as discussed by Bleaney and Humphrey (2006), and are ambiguity averse, they may be more likely to select the information structure with a higher likelihood of giving a negative signal.
Risk aversion may also correlate with first-stage decisions, over and beyond their elicited certainty equivalent, as people with a higher risk aversion may still be more willing to select information with a higher likelihood of giving a negative signal. This tendency may feasibly represent the outcomes of a dual-self mechanism, or a self-serving bias to make decisions consistent with self-image.
Other personal characteristics may also feasibly correlate with decision direction.
Hypothesis 5: The direction in which people select less informative informa-tion structures will be correlated with measures of risk aversion, ambiguity aversion, preference for one-shot resolution of uncertainty and/or personal characteristics.
Other characteristics about the location of the information structures in alpha-beta space may also influence first-stage decisions.
Ambuehl and Li (2018) find a significant border effect and an insignificant sym-metry effect in their experiment, where subjects disproportionately prefer structures that give certainty in the second-stage, but are not influenced by structures lying on the 45 degree line where alpha is equal to beta. Although subjects were not given the Bayesian calculations for these previous results, similarity in experimental design suggests that they might also occur in the current study. Similarly, as Ambuehl and Li (2018) find single structure asymmetry not to influence valuation, the location of structures along isovalue lines, including decision symmetry should not affect first-stage choices. Although Ambuehl and Li (2018) find that people undervalue more informative information, the differences in alpha-beta sum (and therefore informa-tional value) between information structures in this study are fixed (i.e. 0, 0.1 or 0.2) regardless of location. Therefore, the sum size in any decision should not correlate
with which option is chosen.
Hypothesis 6: Subjects will select information structures that lie on a border more frequently than interior information structures giving the same expected utility. Isovalue curve location, alpha-beta sum and structure symmetry will not significantly affect the probability of a subject selecting less informative information structures.
5
Results
40 subjects completed the survey, each completing 16 first- and second-stage deci-sions. 3 observations were not recorded due to subjects failing to submit decideci-sions.
The theoretical framework describes a distinct prediction for how subjects should choose between information structures: choose the most informative structure that has the highest alpha-beta sum. Therefore, excluding D1 decisions, one of the two options was optimal given that subjects followed an expected utility model. For D2 and D3, subjects would be expected to select Option 2, as the alpha-beta sum is greater than Option 1, and vice versa for D4 and D5. For D1, as the alpha-beta sums are equal, subjects would be expected to be indifferent between the two options, resulting on average in subjects selecting Option 1 and Option 2 with equal probability. A first-stage decision in line with this theoretical prediction will be referred to as “correct” for ease of exposition. However, for first-stage decisions, this is not to imply that subjects are otherwise making wrong decisions: they are simply not in line with the predicted behaviour. The same terminology will be used for second-stage decisions if the subject chooses the investment after a positive signal or the certain amount after a negative signal. These decisions are more clear-cut than first-stage, however, as subjects were explicitly given the reasoning behind why they should select these choices for each signal.
Figure 10: Effect of decision type on correct first-stage decisions made a correct first-stage decision, selecting the most informative option.
5.1
Decision types
Figure 10 plots the proportion of correct first-stage decisions by decision type. If subjects follow the expected utility model, the null hypothesis is that subjects should make 100% correct decisions. This null hypothesis is rejected for all decision types except D1, as the proportion of decisions in line with the prediction is signifi-cantly below 100%. The null hypothesis cannot be rejected for D1, as all decisions are technically correct and the proportion of Option 1 choices (57%) is not significantly different from random selection, or 50% (p-value = 0.28).
However, the proportion of correct responses was significantly higher than 50% for D2, D3 and D5, indicating that subjects were able to answer better than chance for all decision types other than D4.
These results provide evidence that subjects can identify which is the better op-tion, but that they consistently do not make decisions in line with expected utility theory, supporting Hypothesis 1.
Result 1: Subjects select less informative information structures a significant proportion of the time for decision types other than D1.
A balance table of decision types presented to subjects is provided in Table 6 in Appendix A.
Table 1 shows that these decision type effects are robust to controlling for other relevant decision and subject characteristics, as the decision type coefficients remain consistent between regressions (1) and (2). This robustness was expected, as decision types were randomly allocated for each subject within each question block making it unlikely for there to be strong correlations with other characteristics.
Testing for differences between coefficients in regression (1) also shows, however, that the likelihood of a correct decision is not significantly higher for D3 than D2, or for D4 than D5. In particular, the proportion of correct decisions is actually lower for D3 than for D2, in the opposite direction to that hypothesised (Chi-squared p-value = 0.76). The proportion of incorrect decisions for D4 is greater than D5, in line with Hypothesis 2, however, the result is not significant (Chi-squared p-value = 0.13). The results are also insignificant if D2 and D4 are combined and compared to D3 and D5. Interestingly, subjects also selected Option 1 less often in D4 than D1 decisions, despite the reduced information value of Option 2 in D4 decisions.
Similar tests also show that the effect on correct decisions is not significantly different in aggregate between D2 and D4 (Chi-squared p-value = 0.29), or D3 and D5 (Chi-squared p-value = 0.95). The results are also insignificant if D2 and D3 are combined and compared to D4 and D5.
Probit margins (1) (2) (3) D2 0.67∗∗∗ 0.67∗∗∗ (0.065) (0.067) D3 0.65∗∗∗ 0.66∗∗∗ (0.061) (0.058) D4 0.56∗∗∗ 0.55∗∗∗ (0.058) (0.059) D5 0.66∗∗∗ 0.67∗∗∗ (0.064) (0.058) D2D3 0.66∗∗∗ (0.052) D4D5 0.61∗∗∗ (0.052) Controls No Yes No N 511 511 511
Standard errors in parentheses. Clustered by subject.
∗ p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001
Significance relative to D1, where proportion correct = 1. Controls include all subject traits and decision features.
frequently for D2 than D3 decisions, or for D4 than D5 decisions.
To evaluate Hypothesis 3, a directional index was calculated for each subject based on the difference in percentage of incorrect first stage decisions for D2D3 and D4D5 decision types. This index gives an indication whether each subject is more likely to select the less informative structure more in one direction than the other. For example, if a subject chose incorrectly for all D2D3 decisions but correctly for all D4D5 decisions, they would be given a directional index of +1. A positive index indicates a subject is more information risk-seeking, as they select the less informative information structure more often for D2D3 decisions. Similarly, a negative index indicates a subject is more information risk-averse. Using proportions of incorrect decisions means the index accounts for the number of decision types answered by each subject.
Subsequently, a dummy dataset was created by generating random decisions for each of the decisions subjects made. The same indices were then calculated for each of the dummy subjects. Figure 11 graphs the directional indices for each dataset ordered by subject from lowest to highest.
The graph shows that the sample distribution is weighted more towards the ex-tremes of the distribution than if choices are generated randomly. Equivalently, sam-ple subjects are likely to be more information risk-seeking or -averse than random selection. A two sample Kolmogorov-Smirnov test indicates that the two distribu-tions are significantly different at the 10% level (p-value = 0.097).
More qualitatively, a significant proportion of the subjects backed up this con-clusion when asked how they made decisions between information structures. Some insightful responses included:
“I was happy going with the sure amount every time, so I mostly took risk by choosing Expert B.”
“Primarily a risk-averse investor, and therefore chose the highest return on a positive outcome.”
Directional index = % D2D3 incorrect - % D4D5 incorrect. Column = 1 subject. Figure 11: Distributions of sample and randomly generated directional indices
“Tried to choose the expert that would give me a strong chance of success following a positive decision.”
“Expert A seemed the most viable option in most scenarios.”
“The worst outcome was a positive indication from the expert then a negative result, so I tried to minimise this.”
“I prefer someone who doesn’t give a positive signal too often.”
A common theme throughout these quotes is that subjects would use specific, asymmetric rules-of-thumb when deciding between information structures. They might specifically focus on the relative probabilities of signals in one direction, or on the probability of investment success given a positive signal. These rules-of-thumb lead subjects to prefer Option 1 or 2 (i.e. Expert A or B) throughout the decisions, leading to the weighted-tail distribution shown in Figure 11.
Risk av. Amb. av. PORU Underst. Risk av. 1 Amb. av. -0.52∗∗∗ 1 PORU 0.19∗∗∗ 0.050 1 Underst. 0.14∗∗∗ -0.031 -0.091∗ 1 ∗ p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001
Table 2: Correlations between subject traits
Result 3: Subjects are consistently information risk-seeking or -averse, selecting less informative information structures more in one direction than the other (i.e. for D2 and D3, or for D4 and D5).
5.2
Subject traits
Subject traits include the elicited subject-specific measures, understanding as well as background characteristics. The latter, including age, gender, employment and self-reported likelihood of starting a business in the future, were uncorrelated with the relevant variables and not central to the research question, so are excluded from analysis. Therefore, the remaining variables considered are elicited measures of risk aversion, ambiguity aversion, PORU and decision understanding. Understanding is proxied by the number of correct second-stage decisions made by the subject, where complete understanding is normalised to 0: a more negative score indicates fewer decisions made correctly and therefore a lower measure of understanding.
Figure 12 and Table 2 summarise the elicited measures of subject traits. Sub-jects were risk neutral on average, and slightly ambiguity averse, although there was a considerable variance in individual measures. Interestingly, subjects on average had a negative preference for one-shot resolution of uncertainty, contrary to the results
Figure 12: Summary of subject trait measures elicited
found by previous literature. The high proportion of significantly negative PORU measures seems anomalous when compared to the expected outcome, and the need for caution when interpreting the results. With respect to understanding, the aver-age subject made 2.2 errors in the second staver-age, with a median value of 1. 13% of second-stage decisions were incorrect, which is significantly different from the null hypothesis of 0% (t-stat = 9.83), however, this result is in line with Hypothesis 1 and the 10-15% of noisy subjects found in other risky decision-making studies (Ambuehl & Li, 2018; Holt & Laury, 2002). When the 12 subjects who made more than three second-stage mistakes are excluded from the analysis, all results remain significant.
Result 4: For the majority of second-stage decisions, subjects select investment after a positive signal and the certainty equivalent after a negative signal.
Table 2 shows the correlations between subject trait variables for reference. As the first column suggests, risk aversion is significantly correlated with the other
subject traits. If a subject is more risk averse, they are also likely to have a lower measure of ambiguity aversion, higher PORU and greater understanding of second-stage decisions. A negative correlation with ambiguity aversion fits intuitively if risk aversion is measured with error, as ambiguity aversion is calculated in relation to risk aversion for each subject. A positive correlation between risk aversion and PORU was expected, reflecting similarity in underlying concepts, notwithstanding the caution in interpreting the measure as suggested above. The adjusted R-squared when regressing these three traits on risk aversion indicates that they can explain 34% of variation.
(1) (2) (3)
S1 correct S1 correct Directional index Risk aversion -0.049∗ -0.17∗∗ -0.063 (0.022) (0.054) (0.034) Ambiguity aversion -0.018 -0.028 -0.0053 (0.021) (0.040) (0.022) PORU -0.022 0.13∗ 0.091∗∗ (0.031) (0.058) (0.031) Understanding 0.062∗ 0.097∗ 0.019 (0.027) (0.048) (0.030) Risk aversion*D2D3 0.24∗∗ (0.088) Ambig. aversion*D2D3 0.0081 (0.068) PORU*D2D3 -0.30∗∗∗ (0.081) Understanding*D2D3 -0.066 (0.072) Constant -0.39 -0.58 1.02 (0.43) (0.63) (0.79) N 511 511 40 R2 0.340
Standard errors in parentheses. Clustered by subject.
∗ p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001
(1), (2): probit regressions at decision level, controlling for decision type.
(3): linear regression at subject level, controlling for proportions of decision types faced. Directional index = %D2D3 incorrect - %D4D5 incorrect by subject.
Table 3 summarises the results of three regressions evaluating Hypothesis 5. Regression (1) is a probit regression looking at the impact of subject traits on first-stage decisions, controlling for decision type. Regression (2) adds interaction variables to this regression, as the initial hypotheses indicate that it may also be important to consider how these subject traits may interact with decision types. As discussed in Hypothesis 5, the risk and uncertainty attitudes may feasibly correlate with decisions in each direction, cancelling out to some extent in aggregate. For this purpose, D2 and D3 are grouped together, as are D4 and D5, as these decisions lie in the same direction in alpha-beta space. As all D1 decisions are classified as correct, the interaction terms used in regression (2) indicate the effect for D2 and D3 decisions relative to D4 and D5.
Regression (1) suggests that the more risk averse a subject is, the less likely they are to choose the correct first-stage option. This effect increases in magnitude once you include an interaction term with decision type in regression (2), such that it is significant at the 1% significance level. Interestingly, however, the interaction term between risk aversion and D2D3 itself also becomes significant in the opposite direction, indicating an asymmetrical effect by decision type. If a subject is more risk averse, then they are specifically more likely to choose the correct first-stage option if the decision is of type D2 or D3. In these decisions, Option 2 is more informative, which has a higher value of beta and therefore a higher probability of giving a negative signal. This provides evidence in support of Hypothesis 5, suggesting that even after accounting for individual risk aversion, subjects with a higher risk aversion are more likely to select more informative information if it is less risky in the second stage.
The pure PORU coefficient and the interaction term with D2D3 are also sig-nificant in regression (2), however, in the opposite directions to those expected. A higher PORU leads to subjects selecting the less informative option more often when the decision is D2 or D3. This suggests a confusing result where subjects are less likely to select Option 2, which is both more informative and with higher probabil-ity of earlier uncertainty resolution, if they have a stronger PORU. If subjects who
switched more than once or did not switch at all are omitted from the regression, the pure PORU term increases in significance, while the interaction term becomes insignificant. When taken together with the high proportion of negative measures elicited, these coefficients suggest an inconsistent elicitation method compared to previous studies. These results do not appear have a coherent explanation within this experimental design, so they should be taken with caution.
Understanding has a significantly positive correlation with proportion of correct first-stage decisions in both regressions, as would be expected. Ambiguity aversion is insignificant in both regressions.
Regression (3) also evaluates Hypothesis 5 at the subject level, showing how the directional index discussed previously is correlated with subject traits using a linear regression. Directional index value is negatively correlated with the elicited measure of risk aversion, significant at the 10% significance level after controlling for the proportions of decision types faced by each subject (p-value = 0.084). This result suggests that subjects with a higher risk aversion are less likely to choose the correct option for D2 and D3 decisions, reflecting the interaction effect from regression (2). The index is also significantly positively correlated with the elicited measure of PORU at the 1% significance level, controlling for decision types faced. Again, this gives the counterintuitive result that subjects with a higher PORU are more likely to choose the less informative option for D2 and D3 decisions, in which uncertainty is more likely to be resolved in the second stage. Directional index is uncorrelated with ambiguity aversion or subject understanding.
These results provide evidence supporting the conclusion that subject traits are correlated with subject tendencies to select information structures encouraging or discouraging risk.
Result 5: The direction in which people select less informative information struc-tures is correlated with risk aversion and preference for one-shot resolution of un-certainty, but is uncorrelated with ambiguity aversion and understanding. (Subjects
with a higher risk aversion are less likely to choose the correct option for D2 and D3 decisions, while subjects with a greater preference for one-shot resolution of uncer-tainty are less likely to choose the correct option for D4 and D5 decisions.)
5.3
Decision features
Decision features describe the characteristics of the individual decisions that subjects made. Information structure locations within alpha-beta space can be represented along isovalue curves by an α − β difference, where a more positive value indicates an option closer to the right border. By including both Option 1 and 2 locations, any effects involving distance between options would also be captured. When α1 = 1 and
β2 6= 1, a decision lies on the right border only, meaning Option 1 lies on the right
border and Option 2 lies in the interior. Similarly, if it is top border only, α1 6= 1 and
β2 = 1, and if both borders, α1 = 1 and β2 = 1. The alpha-beta sum identifies which
isovalue curve the equivalent D1 decision lies on, and decision symmetry is satisfied when α1 = β2 and α2 = β1. The effects of these decision features on first-stage
S1 correct (1) Option locations α1− β1 -0.47 (0.44) α2− β2 0.57 (0.34) Border options α1 = 1, β2 6= 1 0.27 (0.25) α1 6= 1, β2 = 1 0.28 (0.22) α1 = 1, β2 = 1 0.37 (0.31) Sum size α + β = 1.5 -0.16 (0.12) α + β = 1.8 -0.069 (0.35) Symmetry α1 = β2 & α2 = β1 0.037 (0.20) Constant 0.65 (0.24) N 511 R2 ∗ p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001
Standard errors in parentheses. Clustered by subject. Equations refer to equivalent D1 decision.
Decision type included as control.
Regarding Hypotheses 6, decision characteristics have an insignificant effect on the likelihood of selecting the more informative option. Option 2 location is the most significant coefficient, with a positive effect (p-value = 0.097) suggesting that the closer Option 2 lies to the right border, the more likely the subject is to choose the correct option.
This insignificance was hypothesised for option location, sum size and symmetry, as they were not expected to vary by decision type or by subject traits. However, given the border effect found by Ambuehl and Li (2018), border decision features might have been expected to have some effect on first-stage decisions, yet these were also found to be insignificant. A potential explanation for this result is that the primary result found by Ambuehl and Li (2018) suggests that information valuation is driven primarily by non-Bayesian belief updating. As this study gives subjects the Bayesian probabilities, updating is not required. Therefore, this result suggests that the information border effect found by Ambuehl and Li (2018) results from non-Bayesian belief updating as opposed to a valuation anomaly.
The results remain largely insignificant when interaction terms between decision characteristics with both decision types and subject traits are included. The Option 2 location coefficient becomes marginally more significant when interaction terms are included with decision types and PORU, and medium sum size becomes significant when including interaction terms with ambiguity aversion, however, these results do not seem to have relevant interpretations, and are likely to reflect the number of variables included in regressions increasing the probability of false significance.
However, several variables do become significant if interaction variables are in-cluded with decision understanding. For example, pure sum size variables become significantly negative, while their interaction terms become significantly positive, and the effect is stronger for a sum size of 1.8 than 1.5. This indicates that subjects with a better decision understanding are more likely to select the more informative information structure as sum size increases. The same result is found for Option 1 location, meaning subjects with greater understanding are more likely to select the
more informative information structure the closer Option 1 lies to the right border. Conversely, they are less likely to choose the more informative option if Option 1 lies on the right border.
These results indicate the effect of decision characteristics on first-stage decisions may depend asymmetrically on the level of subject understanding. However,if sub-jects who made more than three second-mistakes are excluded from the analysis, the significance of variables in the overall regression in Table 4 do not change, indicat-ing a binary division of subjects in understandindicat-ing is not sufficient to explain these interactions.
Nonetheless, these results should be interpreted as suggestive towards future re-search, rather than specific and conclusive, for two reasons. First, the relatively small sample size and the considerable number of possible interaction variables increase the possibility of these interaction terms bearing false significance. Second, any potential explanations of these interaction variables do not have meaningful interpretations. Given the large number of possible interaction variables, these regressions are not included in analysis.
Result 6: Decision characteristics, including border structures, do not signifi-cantly affect the probability of a subject selecting less informative information struc-tures.
6
Discussion
The findings of this study provide some first steps towards studying how people’s preferences over information may differ from expected utility theory. The overall tendency of subjects to select less informative information structures indicates the potential for future studies with larger sample sizes and designs focused on achieving more statistical power to isolate the effects of different decision types. For example,
the difference between D4 and D5 decisions was found to be insignificant in Figure 10, but intuitively one would expect difference in informativeness to impact the likelihood of selecting the less informative structure.
The finding that subjects are more information risk-seeking or -averse than ran-dom selection represents initial evidence in support of this study’s primary research question. A point to consider in these results, however, is that although decision types were randomised for each subject, Option 1 was always presented to subjects as the option with a greater probability of a good signal. The results may therefore be partially explained by subjects developing a default bias for one option, which manifests in information risk-seeking or -averse behaviour. However, the example quotes presented in the Results section demonstrated the importance of the risk component of decisions to subjects when creating these rules-of-thumb. Therefore, the results presented still indicate that the underlying decision process is based on the concept of information risk-aversion, at least at the start of the decisions. Fur-ther research might try to limit the possibility of default options in order to more clearly differentiate between these two effects.
Another central finding of this study is that risk aversion is not fully captured by the initial certainty equivalent elicitation, as it retains explanatory power at the information structure level: a subject’s risk aversion can help to explain the like-lihood of choosing the more informative information structure, depending on the type of decision they face. PORU, however, is correlated with decisions in the op-posite direction, indicating that its effect on information selection may differ to risk aversion. This difference suggests that preferences over lotteries and choice of in-formation structures may be driven by different underlying mechanisms, in a new departure from expected utility. Further research will be required to understand these mechanisms and their relation to information selection in risky environments. However, the PORU elicitation demonstrated some inconsistency in its measure-ment, indicating some lack of subject understanding. The method used gave a sig-nificant proportion of negative measures where previous research had found positive
