Asymmetrical Property of the Subproportionality of Weighting Function in Prospect Theory: Is It Real and How Can It Be Achieved?

An asymmetrical property of the probability weighting function, namely, subproportionality, was derived from observations. Subproportionality can provide a reasonable explanation for accommodating the Allais paradox and, therefore, deserves replication for its high impact. The present study aimed to explore the mechanism of subproportionality by comparing the two completely opposite decision mechanisms: prospect theory and equate-to-differentiate theory. Results revealed that the underlying mechanism supports the prediction of equate-to-differentiate theory but not prospect theory in the diagnostic stimuli condition. Knowledge regarding which intra-dimensional difference between Options A and B is greater, not knowledge regarding which option’s overall prospect value is greater, indeed predicts option preference. Our findings may deepen current understanding on the mechanisms behind the simple risky choice with a single-non-zero outcome. Additionally, these findings will hopefully encourage subsequent researchers to take a fresh look at the Allais paradox.

Revisiting the primary bias: the role of innumeracy in the misperception of prevalence of common illnesses

Although people have been repeatedly found to underestimate frequencies of common illnesses and overestimate those of rare illnesses, not much is known about this consistent bias in risk perception, termed “primary bias” in the literature, as well as the origin of its variations among different subpopulations. To fill this gap, we designed and implemented a national survey to compare the perceived and actual prevalence of common illnesses, and to test the hypothesis that numeracy may play an important role in the accuracy of judgments of risk frequencies. Our data were collected through a large online survey conducted in France among a representative sample of the adult population (n = 3,245). The participants were asked to complete a 10-items numeracy scale and to estimate the prevalence of a variety of social conditions and common illnesses such as cancers or heart diseases in the French population by using a percentage scale. The analyses show that (1) participants tend to greatly overestimate the prevalence of conditions affecting small percentages of people, and underestimate those affecting a large percentage of them, (2) the Tversky and Kahneman’s probability weighting function provides an adequate model to represent the discrepancy between the perceived and actual prevalence of these illnesses, and (3) the magnitude of the primary bias varies principally as a function of the respondents’ numeracy. These results suggest that the primary bias that affects perceptions of prevalence of chronic diseases is not fundamentally different from those characterizing other types of probabilistic judgments investigated in the field of psychological and behavioral sciences. They also confirm that numeracy plays a considerable role in people’s ability to transform epidemiological observations from their social environment into more accurate estimates.

Probability weighting for losses and for gains among smallholder farmers in Uganda

Probability weighting is a marked feature of decision-making under risk. For poor people in rural areas of developing countries, how probabilities are evaluated matters for livelihoods decisions, especially the probabilities associated with losses. Previous studies of risky choice among poor people in developing countries seldom consider losses and do not offer a refined tracking of the probability-weighting function (PWF). We investigate probability weighting among smallholder farmers in Uganda, separately for losses and for gains, using a method (common consequence ladders) that allows refined tracking of the PWF for a population with low levels of literacy. For losses, we find marked probability weighting near zero, which is in line with evidence found in Western labs. For gains, the absence of probability weighting is remarkable, particularly its absence near 100%. We also find marked differences in probability weighting for traditional farmers which are in line with the observed livelihoods strategies in the study area.

A Novel TODIM with Probabilistic Hesitant Fuzzy Information and Its Application in Green Supplier Selection

TODIM is a well-known multiple-criteria decision-making (MCDM) which considers the bounded rationality of decision makers (DMs) based on prospect theory (PT). However, in the classical TODIM, the perceived probability weighting function and the difference of the risk attitudes for gains and losses are not consistent with the original idea of PT. Moreover, probabilistic hesitant fuzzy information shows its superiority in handling the situation that the DMs hesitate among several possible values with different possibilities. Hence, a novel TODIM with probabilistic hesitant fuzzy information is proposed in this paper to simulate the perceptions of the DMs in PT. To show the advantages of the proposed method, a novel TODIM is combined with hesitant fuzzy information. Finally, a case study is carried out to demonstrate the feasibility of the proposed method, and a series of comparative analyses and the sensitivity analyses are used to show the stability of the proposed method.

Towards a general class of parametric probability weighting functions

In this study, we present a novel methodology that can be used to generate parametric probability weighting functions, which play an important role in behavioral economics, by making use of the Dombi modifier operator of continuous-valued logic. Namely, we will show that the modifier operator satisfies the requirements for a probability weighting function. Next, we will demonstrate that the application of the modifier operator can be treated as a general approach to create parametric probability weighting functions including the most important ones such as the Prelec and the Ostaszewski, Green and Myerson (Lattimore, Baker and Witte) probability weighting function families. Also, we will show that the asymptotic probability weighting function induced by the inverse of the so-called epsilon function is none other than the Prelec probability weighting function. Furthermore, we will prove that, by using the modifier operator, other probability weighting functions can be generated from the dual generator functions and from transformed generator functions. Finally, we will show how the modifier operator can be used to generate strictly convex (or concave) probability weighting functions and introduce a method for fitting a generated probability weighting function to empirical data.

A NOVEL TODIM BASED ON PROSPECT THEORY TO SELECT GREEN SUPPLIER WITH Q-RUNG ORTHOPAIR FUZZY SET

Green supply chain has developed rapidly due to the advocacy of ecological civilization, and choosing a proper green supplier is a crucial issue. Considering the fuzziness of evaluation information and the psychological states of decision makers (DMs) in selecting process, a novel TODIM based on prospect theory with q-rung orthopair fuzzy set (q-ROFS) is proposed. The novel TODIM concerns both the perceived transformed probability weighting function and the differences in risk attitudes. A new distance, which concerns the herd mentality, is carried out to measure the perceived difference of the q-ROFS. Besides, a new systematic evaluation index system, named as PCEM (Product, Cooperation ability, Environment, Market), has been established. A case related to pork supplier companies is presented and fully demonstrates the effectiveness of the novel TODIM when compared with the extended one, the intuitionistic fuzzy TODIM, the Pythagorean fuzzy TODIM as well as the TOPSIS with q-ROFS. Finally, a series of comparative analyses illustrate the advantages of the proposed TODIM.