There are commonly accepted and objective decision rules, which are consistent with rationality, for example stochastic dominance rules. But, as can be seen in many research studies in behavioral economics, decision makers do not always act rationally. Rules based on cumulative prospect theory or almost stochastic dominance are relatively new tools which model real choices. Both approaches take into account some behavioral factors. The aim of this paper is to check the consistency of orders of the valuations of random alternatives based on these behavioral rules. The order of the alternatives is generated by a preference relation over the decision set. In this paper, we show that the methodology for creating rankings based on total orders can be used for the preference relations considered, because they enable comparison of all the elements in a set of random alternatives. For almost second degree stochastic dominance, this is possible due to its particular properties, which stochastic dominance does not possess.
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There are commonly accepted and objective decision rules, which are consistent with rationality, for example stochastic dominance rules. But, as can be seen in many research studies in behavioral economics, decision makers do not always act rationally. Rules based on cumulative prospect theory or almost stochastic dominance are relatively new tools which model real choices. Both approaches take into account some behavioral factors. The aim of this paper is to check the consistency of orders of the valuations of random alternatives based on these behavioral rules. The order of the alternatives is generated by a preference relation over the decision set. In this paper, we show that the methodology for creating rankings based on total orders can be used for the preference relations considered, because they enable comparison of all the elements in a set of random alternatives. For almost second degree stochastic dominance, this is possible due to its particular properties, which stochastic dominance does not possess.
Complex risky decision problems involve sequences of decisions and random events. The choice at a given stage depends on the decisions taken in the previous stages, as well as on the realizations of the random events that occurred earlier. In the analysis of such situations, decision trees are used, and the criterion for choosing the optimal decision is to maximize the expected monetary value. Unfortunately, this approach often does not reflect the actual choices of individual decision makers. In descriptive decision theory, the criterion of maximizing the expected monetary value is replaced by a subjective valuation that takes into account the relative outcomes and their probabilities. This paper presents a proposal to use the principles of cumulative prospect theory to analyse complex decision problems. The concept of a certainty equivalent is used to make it possible to compare risky and non-risky alternatives.
The main aim of this study is to replicate the effect shown by Traczyk et al. (2018), where individuals with higher statistical numeracy, compared to individuals with lower statistical numeracy, employed a more effortful choice strategy when outcomes were meaningful. I hypothesize that participants with higher numeracy will be more likely to make choices predicted by Cumulative Prospect Theory and Expected Value theory (CPT/EV) in high-payoff problems than in low-payoff problems. Data collection was done online by appointing 73 participants. Participants’ preference, fluid intelligence, objective and subjective numeracy were measured using thirteen high and eleven low payoff choice problems, International Cognitive Ability Resource (ICAR), Berlin Numeracy Test (BNT), and Subjective Numeracy Scale (SNS), respectively. All the measures mentioned above were presented randomly. Results showed that all participants, in high-payoff condition, on average maximized EV; however, participants with high BNT scores were more likely to make choices consistent with CPT/EV predictions than individuals with low BNT scores. Furthermore, compared to less numerate participants, highly numerate participants were less likely to make choices consistent with CPT/EV predictions in low-payoff condition. Highly numerate individuals adjusted their choice strategy by modulating their response time, indicating their discernible sensitivity towards large asymmetry in payoff. In conclusion, the effect shown by Traczyk et al. (2018) was successfully replicated.
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