Introduction
Decision-making is influenced by the value of outcomes, the probability of outcomes, and the ambiguity or risk of outcomes (e.g. Kahneman et al., 1997; Kahneman & Tversky, 1979). According to a classic distinction between ambiguity and risk derived from Knight (e.g. Chen & Epstein, 2002; Huettel et al., 2006; Knight, 1921; Krain et al., 2006), a decision situation is defined risky when the actual outcome of the decision between options is unknown, but the probability distribution for different outcomes is known. In contrast, a decision is ambiguous when the actual outcome and the probability distribution of potential outcomes are both unknown (Ellsberg, 1961; Knight, 1921). In all these cases, preferences of decision options are defined according to the chance distributions of options, i.e., according to their expected value (EV). For risk, these chances are taken to be objective, whereas for uncertainty, they are subjective. Furthermore, the size of the risk of options can be described by the spread of outcomes (Rothschild & Stiglitz, 1970), and the size of ambiguity by the lack of information (Ellsberg, 1961; Knight, 1921). The size of risk and ambiguity reduce the utility of an option. Accordingly, the goal of the present study was to vary experimentally both risk and ambiguity in order to compare them on the behavioral and on the neural level. Usually, people are even more averse to ambiguous options than to risky options supposedly also indicating a reduction in subjective utility.
During the past decades, many different studies investigated behavior of people under risk and ambiguity. Many different experimental approaches were used, which differed in paradigms and parameters, e. g. various kinds of gambles, known and risky options, or risky options only, gambles with possible gains and losses or only with gains, and special tasks like the Iowa Gambling Task (Bechara et al., 1997, 2005; Li et al., 2010), Blackjack (Hewig et al., 2010; Hewig et al., 2009; Hewig et al., 2007; Hewig et al., 2008) or the Balloon Analogue Risk Task (Lejuez et al., 2002; Mussel et al., 2015; Rao et al., 2008). Recent studies also used functional magnetic resonance imaging (fMRI) to identify blood oxygen level dependent (BOLD) responses to risky and ambiguous situations in order to reveal its neural underpinnings (e.g. Bach et al., 2009; Hsu et al., 2005; Smith et al., 2002; Tobler et al., 2007). Some of these studies found activations of brain areas associated with EV, like the ventral striatum (Breiter et al., 2001; Knutson et al., 2001; Knutson et al., 2005; Tobler et al., 2007; Yacubian et al., 2006) or the anterior cingulate cortex (Brown & Braver, 2005, 2007, 2008; Kuhnen & Knutson, 2005). Others compared ambiguous and risky decision-making and showed that ambiguous decision-making is related to increased neural activity in the dorsolateral prefrontal cortex (DLPFC), amygdala, posterior inferior frontal cortex, and posterior parietal cortex (e.g. Bach et al., 2009; Hsu et al., 2005), whereas risky decision-making is related to activity in OFC, ACC, and parietal cortex (e.g. Krain et al., 2006; Platt & Huettel, 2008; Tobler et al., 2007). These differences may indicate that ambiguity imposes not merely more intense uncertainty but might even represent a different kind of uncertainty, which is based on a different neural processing by different neural sources. To differentiate between risky and ambiguous decisions, the magnitude, the probability, and the EV of decision options have to be defined as independent experimental variables and the functional neural structures have to be described that account for their differential phenomenological cognitive and behavioral functions.
To master such challenges, Tom, Fox, Trepel, and Poldrack (2007) investigated risky gambles using a parametric experimental design to assess BOLD responses related to risk and loss aversion. The network functional relevant for gains included regions in dorsal and ventral striatum, ventromedial prefrontal cortex (VMPFC), ventrolateral prefrontal cortex (VLPFC), ACC, OFC, and other dopaminergic structures whereas structures relevant for losses included the striatum, the VMPFC, ventral ACC, and the medial OFC. In relation to loss aversion, they showed activity in bilateral ventral striatum, bilateral lateral and superior PFC (pre-supplementary motor area), and right inferior parietal cortex. The authors termed this pattern a neural system of loss aversion.
In a subsequent study also using parametric analyses, Canessa et al. (2013) replicated activations in regions in the left ventral striatum and in the posterior frontomedial cortex in response to gains and losses. In addition, they found an interesting differential pattern of activation between losses and gains of the right posterior insula and the parietal operculum. These areas showed greater activation to increasing losses than deactivation to gains. An opposite pattern was found in the left ventral striatum and the frontomedial cortex, which showed larger loss-related deactivation than gain-related activation. Furthermore, they identified a loss-related network involving the right amygdala, putamen, and portions of the right posterior insula, indicating that the neural system of loss aversion involves the amygdala, thalamus, striatum, and posterior insula.
Based on these studies using fMRI we expected risk-related activity in dorsal and ventral striatum, ventromedial prefrontal cortex (VMPFC), ventrolateral prefrontal cortex (VLPFC), dACC (mainly BA 32), OFC, parahippocampus, inferior frontal gyrus IFG (BA 47), SMA (BA 6), frontomedial cortex, and insular cortex in mixed-risk trials for the parameter “wins”. In contrast, for the parameter ”losses” we expected activity in insula, parietal operculum, amygdala, thalamus, striatum (in particular ventral), VMPFC, ventral ACC, the medial OFC, bilateral lateral and superior PFC (pre-supplementary motor area), and right inferior parietal cortex. We further expected ambiguity-related activity in dorsolateral prefrontal cortex (DLPFC), amygdala, posterior inferior frontal cortex, and posterior parietal cortex. Since our experimental design eliminated the confounding influence of average risk levels between our experimental conditions, the remaining regions are considered to relate specifically to the risk difference in mixed gambles.
In the gambling paradigm used here, the probability of outcomes was known to the subjects to elicit decisions under risk in one part of the experiment, and in the other part of the experiment the probability of outcomes was unknown in order to induce decisions under ambiguity. We completely avoided fully known outcomes, because risk and ambiguity may appear to be more similar in their presence because they both entail some uncertainty as compared to known outcomes. Instead, we varied both risk and ambiguity systematically to contrast and compare them to each other. The degree of risk was varied experimentally by using three different combinations of high- and low-risk options in each trial of a two-choice decision-making task. High-risk gambles comprised two high-risk options, low-risk gambles comprised two low-risk options and mixed-risk gambles comprised a high- and a low-risk option. EV was always the same in each gamble. This enabled us to experimentally separate influences of the difference in risk from the overall level of risk or EV and from the overall level or magnitude of gains and losses. Previous studies used known outcomes versus risky gambles, or known outcomes versus ambiguous gambles. Thus, for each decision between two gambles the average risk level of both alternatives (high/low) is confounded with the risk difference between the two alternatives. For example, many studies use a known outcome option and a risky option. The risky option can vary in its variance of outcomes. Thus, the average risk of both alternatives and the average magnitude of the outcomes are confounded with the difference in risk between the two alternatives. A trial with a known option and a low-risk option has lower overall risk, lower difference in risk between the options, and lower outcome magnitudes. Whereas a trial with a known option and a high-risk option has higher overall risk, higher difference in risk, and higher outcome magnitudes. Accordingly, a difference in brain activation in the comparison of these two kinds of trials may be due to any of these three differences between trials. For this reason, we combined 2 kinds of options: high-risk options (larger variance in outcomes) and low-risk options (smaller variance in outcomes). Thus, we created a high-risk condition with two high-risk alternatives, a low-risk condition with two low-risk alternatives and a mixed risk condition with a low and a high-risk option. If we now compare brain activity between the mixed condition and the average of the two other conditions, we may disentangle risk level and risk difference.
We expected that minimizing the risk is primarily triggered by the difference of outcome variance between the two options, which should lead to the strongest risk aversive effects in mixed gambles. We further varied the degree of ambiguity experimentally in another block of trials by using one condition without any information about the probability (high ambiguity) as compared to another condition where we provided a range of probabilities for each outcome (low ambiguity). In a narrow sense of decision-making under risk, where all information is available, the latter trials with high ambiguity are not decision-making under risk. However, according to the definition of the degree of risk with the spread or variance of outcomes these trials can still be recognized in terms of higher or lower risk, since the magnitude of the difference between the potential wins and losses (variance of outcomes) is a function of risk level even in the absence of probability information. This allows a systematic comparison of decision-making under risk with decision-making under ambiguity across experimental blocks keeping all other aspects of the task comparable.
In the present study, we aimed to clarify and extend previous findings by using mixed-risk trials with and without ambiguity and compared them to high- and low-risk trials. Furthermore, we aimed to compare risk and ambiguity directly with each other. Thus, the target condition is as similar as possible to the control conditions. We focused on the moment of decision-making in our analyses. Following previous research (Canessa et al., 2013; Tom et al., 2007), we also used a parametric fMRI design to separate effects that are due to potential gains from those of potential losses. Importantly, previous research focused on the idea of neural loss aversion, which is related to the different degree of brain activity in response to gains and losses, and supposedly drives cautious decision-making under risk. In addition, Vorhold and colleagues (2007) showed that subjective ratings of risk are moderating decision-making. We therefore also assessed ratings of riskiness and reports about reasons of individual decision-making.