Análisis de los resultados de la barra de la pierna

Intertemporal choice modelling started with economic rationality (Fisher, 1930). Later on, it is the behavioural regularities that have motivated the development of the theories and models of intertemporal choice. In this section, I will briefly outline the history of the theory and model development in the study of intertemporal choice, with the implications from the present thesis.

5.2.1 Static models

In the early stage of model development, intertemporal choice models were often built upon specific empirical findings. For example, to accommodate decreasing impatience (or hyperbolic discounting), a class of hyperbolic discounting models were proposed (e.g., Herrnstein, 1981; Mazur, 1987; Laibson, 1997; Loewenstein & Prelec, 1992). To accommodate both decreasing impatience and increasing impatience, more sophisticated discount models have been proposed (Bleichrodt, Rohde, & Wakker, 2009; Ebert & Prelec, 2007; Sayman & Öncüler, 2009). To accommodate the absolute magnitude effect, value functions with increasing elasticity have been proposed (e.g., Chapman, 1996b; Loewenstein & Prelec, 1992; Scholten et al., 2014).

Violations of transitivity in intertemporal choice gave rise to the class of attribute-based models (Leland 2002, Roelofsma & Read, 2000; Rubinstein 2003; Scholten & Read, 2010). Chapter 2 further suggests that the descriptive accuracy of attribute-based models is beyond intransitivity because attribute-based models that cannot accommodate intransitivity in terms of weak stochastic transitivity still exhibit much stronger descriptive accuracy than alternative-based ones.24 _{This suggests that} the attribute-based evaluation rule is probably more psychologically plausible than other evaluation rules (Vlaev, Chater, Stewart, & Brown, 2011). This idea is compatible with a recent eye-tracking study by Arieli et al. (2011). Their process-level eye-tracking data suggest that eye movements during decision making are made more often within attributes than within alternatives in intertemporal choice. This cognitive process strongly suggests that decision makers make attribute-based evaluation more often than alternative-based evaluation in intertemporal choice.

24 _{Note that, as shown in Chapter 2, in combination with the Luce specification most attribute-based}

models can accommodate relative-nonadditivity (an intransitive choice pattern) in terms of the violation of the product rule. However, no model, except for the full tradeoff model (TM), predicts intransitivity in terms of the violation of the weak stochastic transitivity.

CHAPTER 5 GENERAL DISCUSSION

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5.2.2 Dynamic models

Recently, dynamic diffusion models have been introduced to account for the stochastic components in value-based decision making including intertemporal choice (e.g., Busemeyer & Townsend, 1993; Usher & McClelland, 2004). For example, Dai and Busemeyer (2014) applied dynamic diffusion models to capture the stochastic variation in the choice process, which is viewed as a preference accumulation process. Correspondingly, a choice is made when the accumulated preference for an option reaches a threshold.

Some other researchers extended dynamic diffusion models with the involvement of the process-level data, though outside of intertemporal choice (e.g., Krajbich et al., 2010; Krajbich & Rangel, 2011; Towal, Mormann, & Koch, 2013). Particularly, Krajbich and colleagues made a crucial assumption that the speed of preference accumulation of an option depends on visual attention. Preference accumulation for an option will be accelerated when it is focused attention on. This approach has embraced great popularity and has accumulated evidence in many studies (Armel et al., 2008; Franco-Watkins et al., 2016; Krajbich et al., 2010; Krajbich & Rangel, 2011; Shimojo et al., 2003; Stewart et al., 2016 Störmer & Alvarez, 2016). Implicitly, these studies held an option-wise attention effect. Following this line of accounts, the study in Chapter 3 further suggests that not only does the attention effect operate in an option-wise way, it also operate in attribute-wise and component-wise ways.

In addition, the study in Chapter 3 reveals background contrast effects on intertemporal choice, symbolising a violation of sequential independence. The order effect found in Experiment 2 of Chapter 4 further suggests a violation of sequential independence. Recently, Lempert, Glimcher and Phelps (2015) and Stewart et al. (2015) also provided evidence on how the revealed discount function, as well as the revealed utility function, for intertemporal choice varies according to the distributions of attribute values (either outcomes or delays) used in the experiment. A few models have offer accounts to the violations of sequential independence. For example, the Decision-by-Sampling model (Stewart, Chater, & Brown, 2006; Stewart et al., 2015; DbS) assumes that the valuation of a quantity is relative but not absolute, which has its deep roots in psychophysics (Laming, 1997; Stewart, Brown, & Chater, 2005). Models such as Decision-by-Sampling is also compatible with a constructive view of preference (Payne, Bettman, & Johnson, 1992).

5.2.3 A theory gap

Models such as Decision-by-Sampling (Stewart et al., 2006) offer theoretical accounts for the constructive features of intertemporal choice or preference. Although they do not dictate that preferences are purely constructed, the inherent stability of preferences is rarely an integral part of these models. By contrast, static intertemporal choice models assume stable intertemporal preference but are unsurprisingly silent on the dynamic features that arise from the elicitation of intertemporal preference. There is a lack of theoretical linkage between the two voices.

A possible solution to filling this gap is the Bayesian approach to human learning (Gopnik &. Tenenbaum, 2007; Oaksford & Chater, 2007; Tenenbaum, Griffiths, & Kemp, 2006). Within the Bayesian approach, time preference can be viewed as a mental construct with uncertainty and can be learnt or updated from repeated choices (Amir & Levav, 2008), interactions with the environment (Rieskamp, Busemeyer, & Mellers, 2006), arbitrary anchoring (Ariely, Loewenstein, & Prelec, 2003) and peer influence (Narayan, Rao, & Saunders, 2011). Accordingly, the decision maker has a prior probabilistic distribution of his own time preference. Exposure to a tradeoff between the delays the outcome magnitude is regarded as a signal, or a piece of evidence, that decision makers takes into consideration when learning their own preference. With the piece of evidence, the prior distribution can be updated to a posterior distribution. This approach may also make a sensible link between the “trait” voice, which focuses on the prior or posterior distributions of the probabilistic time preference, and the “constructive” voice, which focuses on the evidence for preference updating.