Theoretical Framework

Path dependence in risky choice was first proposed by Kahneman and Tversky (1979) when they introduced prospect theory. One distinguishing feature of the descriptive prospect theory relative to more normative expected utility theory (von Neumann & Morgenstern, 1947) is the reference-dependent valuation of

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Figure 4-1. Picture presents a coin toss game where participant can win or lose one euro. Black square and circle present the actual prospect; Grey square and circle present the prospect after the integration of a prior outcome. A, Perception of the game following a gain of one euro. If the previous gain is integrated in the prospect, the prospective loss (indicated with the black up-down arrow above ‘Losses’) ‘disappears’

while the prospective gain increases (grey down arrow vs. black up-down arrow above ‘Gains’). B, Similarly after a loss, the prospective loss increases and the gain ‘disappears’. Note also that after a loss the participant has a possibility to gain back the loss which provides a larger improvement in value than a gain of one euro.

outcomes. In general, people tend to show moderate risk-averse behavior in the gain domain and risk-seeking behavior in the loss domain (framing effect; Tversky

& Kahneman, 1981), as well as relatively strong risk aversion for mixed gambles due to a greater sensitivity to losses than to gains (loss aversion). These behavioral properties are captured in prospect theory by the shape of the value function, with diminishing sensitivity to increments in gains and losses, and also by having a steeper slope for losses than for gains of a similar size.

The increase in risk appetite after both gains and losses can be explained by insufficient adaptation of a reference point after prior outcomes (Kahneman &

Tversky, 1979; Thaler & Johnson, 1990). After a positive outcome, when the next

Path Dependence in Risky Choice Affective and Deliberative Processes in Brain and Behavior 49 prospect contains losses that are smaller than the previous gain, decision-makers may integrate the initial gains with the outcomes of the future prospect, thus decreasing the influence of loss aversion in the future choice (Figure 4-1). After a negative outcome, when only the risky gamble provides a possibility to win back the previous loss (‘break even’), decision-makers will integrate their prior losses with the current gamble, thereby promoting the risk-seeking tendency which predominates in the loss domain (Thaler & Johnson, 1990). Therefore, both the HME and the BEE can be interpreted as consequences of the nonlinearities in the value function, which account for loss aversion and domain-dependent risk attitude differences.

In the initial formulation of prospect theory the shape of the value function is assumed to reflect general psychophysical features of chance (Kahneman & Tversky, 1979) but recently the shape of the value function has been hypothesized to be more dynamic. The value function is now proposed to reflect a combined result of affective and deliberate processing systems, with the affective system driving the nonlinearities in valuation and the deliberative system valuing outcomes linearly (Hsee & Rottenstreich, 2004; Mukherjee, 2010). This new model proposes that the shape of the value function can vary depending on how strongly the two systems are involved in the processing of the decision problem. In general, converging evidence suggests that decisions are indeed influenced by an affective system, which is assumed to be fast, effortless, automatic, and associative, as well as by the deliberative system, characterized by slower and more effortful processing (Kahneman, 2003; Sloman, 1996).

The recent dual process expansion of prospect theory is supported by both behavioral and brain imaging findings. Behaviorally, affect-rich stimuli increase the curvature of the value function, which can be accounted for by assuming increasing use of a nonlinear affective processing system (Hsee & Rottenstreich, 2004). Neuroimaging research suggests that framing effects, which also relate to the nonlinear curvature of the value function, are also driven by affective neural processes whereas cognitive control mechanisms are more active when decision-makers act against the common framing biases (De Martino, et al., 2006).

Interestingly, the functioning of these brain networks relates to between-subject differences in the strength of behavioral framing effects: A recent study by Roiser et al. (2009) finds that a participant group that exhibits only weak behavioral framing effects has increased connectivity between control and affective brain

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regions, suggesting the presence of an efficient dynamic regulatory control over the emotional reactions, whereas a participant group exhibiting large behavioral effects has weaker connectivity between the brain networks. These fMRI findings imply that a risky choice situation, without an obvious emotional valence, can evoke emotional processing, which may drive nonlinearities in valuation.

Similarly, loss aversion has been related to affective mechanisms in the brain. An fMRI experiment by Tom et al. (2007) indicates that the valuation mechanisms of the brain have a higher sensitivity to loss than to gain outcomes.

Another study by Knutson et al. (2008) suggests that affective reactions in the brain (specifically in the insula) might increase the endowment effect and thus increase aversion for losses in selling situations. Further, patients who have a brain damage in another affect-related brain region (the amygdala) show a dramatically lower level of risk aversion than healthy people (De Martino, et al., 2010).

Given that path dependence in risky choice can be accounted for by nonlinearities in valuation, if we assume insufficient updating of a reference point, and given the recent research suggesting that nonlinearities in valuation might be particularly driven by affective mechanisms, we argue that the path dependence of risky choices is promoted by affective mechanisms, while deliberative mechanisms suppress path-dependent behavior. In detail, we propose that a high involvement of affective processes and a low involvement of deliberative processes in gain and loss experiences underlie path dependence in sequential risky choice²⁸.

Behavioral research on risk perception and planning provides initial support for this proposition, while also opposing findings have been reported.

Monga & Rao (2006) report that positive affect following gain outcomes mediates positive expectations towards future risks and negative affect related to loss

28 It is to some degree still an open question as to whether ‘affective process’ is a unitary system in response to both gains and losses, or whether there is a complex network of affect-related mechanisms that are different for gain and loss situations. Similarly, we consider it an open question whether the ‘deliberative process’ is truly a single mechanism, or rather an aggregate description for a network of different processes involved in

controlling behavior. Additionally, we have no a priori prediction on the timing of the affective and deliberative processes, but instead explore this as an empirical question and also test separately the processes that occur when gains and losses are revealed, and when the subsequent choices are made.

Path Dependence in Risky Choice Affective and Deliberative Processes in Brain and Behavior 51 experiences creates more negative expectations, which might lead to risk aversion after losses. Indeed, Sullivan & Kida (1995) find that decision-makers do not show increased risk-seeking attitude after prior losses that could be regained but instead they persist on risk-averse attitude. In contrast, Andrade & Iyer, (2009) provide evidence for increasing risk appetite after negative outcomes. In their experiment, the negative emotion following a loss outcome correlates with increased risk-taking behavior in respect to prior plans of the decision-maker. In detail, the results indicate that the increase in risk appetite after actual losses depends on the strength of the negative emotion experienced during the decision-making process.

However, this study does not find any differences in the risk taking behavior in respect to previous plans after gain experiences.