From Cognitive to Computational Modeling: T ext-based Risky Decision-Making Guided by Fuzzy Trace Theory (2022)

Abstract: Understanding, modelling and predicting human risky decision-making is challenging due to intrinsic individual differences and irrationality. Fuzzy trace theory (FTT) is a powerful paradigm that explains human decision-making by incorporating gists, i.e., fuzzy representations of information which capture only its quintessential meaning. Inspired by Broniatowski and Reyna’s FTT cognitive model, we propose a computational framework which combines the effects of the underlying semantics and sentiments on text-based decision-making. In particular, we introduce Category-2-Vector to learn categorical gists and categorical sentiments, and demonstrate how our computational model can be optimised to predict risky decision-making in groups and individuals.

## introduction imagine that your town is preparing for a viral outbreak which is projected to kill 600 people. two alternative programs to combat the virus have been proposed. assume that the exact scientific estimates of the consequences of the programs are program a: "200 people will be saved"; and program b: "1/3 probability that all 600 lives will be saved; 2/3 probability that no lives will be saved". given these choices, which program would you choose? alternatively, if choices were presented as follows, which program would you choose? program c: "400 people will die"; and program d: "1/3 probability that no one will die and a 2/3 probability that all 600 will die". this problem is a modified version of the asian disease problem (adp) (tversky and @xcite , a well-studied risky decision-making problem (rdmp) in psychology where decisions are made under risk or include probabilistic outcomes @xcite . in this rdmp, programs a and b form the gain frame where choices are worded in a positive and optimistic manner, whereas programs c and d form the loss frame where choices are written in a negative and pessimistic manner. studies have validated that in the gain frame, humans overwhelmingly prefer the safe choice a (72%), whereas in the loss frame, they overwhelmingly prefer the risky choice d (78%) even though the choices and outcomes in both frames are equivalent @xcite . this phenomenon, known as the allais paradox, implies that observed human choices are inconsistent with predictions based on expected utility alone, thereby confirming the influence of language, wording of choices, and sentiments on human decision-making. being able to understand, model and predict human decision-making leads to many real-world applications, from predicting election results @xcite , to improving user experience in recommender systems @xcite . however, allais paradox means that understanding the integral but complex cognitive process of decision-making, particularly in humans, is extremely challenging due to our diverse characteristics, beliefs and experiences. furthermore, human decision-making is often fraught with irrationality even in the presence of overwhelming evidence against some choice or beliefs @xcite . this brings into question how human decisionmaking can be modelled with these complexities and nuances involved. this is an especially important task when considering current approaches to decision-making, such as utility theory which typically lacks any behavioural basis and ignore human sentiments during human decision-making @xcite . our goal is to develop a model of automated human decision-making that bridges current decisionmaking techniques with fuzzy trace theory (ftt), an established cognitive theory to predict group and individual decision making outlined in sections 2.2. originally proposed by brainerd and reyna in the 1990s, ftt aims to explain cognitive phenomena in memory and reasoning (brainerd and @xcite . in a nutshell, ftt posits that humans form two types of mental representations, known as verbatim which are detailed representations and gist which are fuzzy representations that only capture the most quintessential meanings, and people prefer to make decisions based on gist rather than verbatim representations. in contrast with alternative cognitive and decision-making theories such as expected utility theory @xcite and prospect theory @xcite , we adopt ftt for two reasons. firstly, ftt is the most holistic cognitive model which encompasses theories of how information is stored in memory and how memory plays an important role in our decisionmaking rather than treating decision-making as an isolated process. because of this, ftt provides us with an extensive set of tools to explain and evaluate decision-making. secondly, is ftts suitability for computational modelling as conceptual parallels can be drawn between representation learning, particularly in neural-based language modelling, and the process of creating gist representations by distilling the quintessential information. for example, popular embedding methods for words, sentences and documents in nlp aim to create fuzzy semantic representations through dimensionality reduction of language to semantic vectors which can be viewed as gist representations of the original language @xcite . contributions: we investigate two levels of textbased risky decision prediction tasks, group and individual-level prediction from a computational standpoint and incorporating state-of-the-art methods in nlp, we further investigate: ## ftt-guided risky decision-making the br model. broniatowski and reyna laid out four main ftt principles in developing a cognitive model, i.e., the br model, for the gl-rdm task @xcite . these principles are: (c1) decision choices are encoded in different levels of gist representations, e.g., categorical-and interval-levels based on the psychological notion of levels of measurement @xcite . (c2) categorical gist representations of choices are distinguished based on binary (positive/negative) sentiments and decisionmakers will prefer options with positive associations. in the br model, sentiments of categories are drawn upon social and moral principles which are stored in long-term memory, e.g., saving lives is fundamentally good. (c3) when comparisons of categorical gist representations do not arrive at a conclusive result, the decision-maker will revert to more precise gist representations. in the br model, gist representations compete and combine such that the simplest gist representation is chosen. (c4) categorical gist is encoded based on the decision-maker's prior experiences and individual differences, i.e., need for cognition (nfc), numeracy (num), and risk sensitivity (rs). human experiments have provided evidence that the br model is capable of explaining gl-rdm. however, being a box-arrow model, the br model is comprised of hypothesized concepts or processes that lack precise definitions. hence applying the model requires human interpretations and judgements on, e.g., notions such as gist lattices of each rdmp, the acquisition of sentiments, and individual differences. this informal nature, along with the inflexibility of the model being unable to be easily adapted to il-rdm prevents the model from being used as an automated predictive tool. our model. towards a fully automated tool for the rdmp tasks, we propose a computational model of risky decision-making that takes the input text descriptions of an rdmp and solves the gl-rdm and il-rdm tasks automatically. the model is depicted in figure 1 . the key features of our model include: (1) all model components are automated, i.e., gist representations are extracted through nlp as categorical embeddings. (2) categorical and interval representations are formally defined as hierarchical with the interval level encapsulating the properties and information of the categorical-level @xcite . (3) individualistic differences, nfc, num and rs (see below) directly affect decision-making at a representational level and errors in judgement can propagate through the model adding more expressive. ## computing gist representations the first challenge we tackle is the computational encoding of gist representations and how individual differences encode error, a mechanism to model variations in human decision-making at a representation level to perform gl-rdm and il-rdm. ## learning individual differences the last challenge we explore is how optimal individual-level parameters, nfc, num and rs can be inferred in gl-rdm and il-rdm by optimising the following objective functions. gl-rdm objective. is given by equation 4 where @xmath0, nfc, rs) are individual-level parameters which represent the characteristics of the entire group and @xmath1, e 2 , . . . , e i } is the set of results based on human psychological experiments where each e is a 5-tuple described in the task formulation in section 2.2. il-rdm objective. is given by equation 6 where ivd @xmath2, nfc, rs) is the parameters which characterises individual i, rdp is a set of nrdmps and p c is the mapping function of individuals to their preferred choices defined in the task formulation in section 2.2. thus, the goal is to learn optimal individual parameters for each individual which maximises the expectation that cdm chooses their true preferred choice over all rdps.