Decision-making process model in the context of individual preferences change

1 Decision-making process model in the context of individual preferences change Oksana Liashenko EMAIL: [email protected] ORCID: 0000-0001-5489-815X Universidad de Sevilla and Lesya Ukrainka Volyn National University (Ukraine) Second Workshop: Strategic and Cooperative Decisions for Sustainable Development January, 25-26 2024. Universidad Internacional de Andalucía. La Rábida, Huelva Abstract This research is focused on elucidating the intricacies associated with the application of the GibbsJames principle in scenarios involving two and three potential environmental states during the modeling of decision-making processes grounded in diverse preferences. Within this framework, decision-making scenarios are methodically formulated, considering multiple criteria, including the maximization of mathematical expectation, risk minimization, gains maximization, among others. Keywords: Decision-making process model, social preferences, strategic interactions 1. INTRODUCTION Traditional economic rationality faces a challenge from social preferences, which consider others' well-being and economic conditions, prompting a reassessment of decision-making models for strategic interaction. This fact introduces complexity into decision-making processes, prompting inquiries into the dominance of intuition versus reasoning and the influence of contextual factors. This research is focused on elucidating the intricacies associated with the application of the GibbsJames principle in scenarios involving two and three potential environmental states during the modeling of decision-making processes grounded in diverse preferences. Within this framework, decision-making scenarios were methodically formulated, considering multiple criteria, including the maximization of mathematical expectation, risk minimization, gains maximization, among others. 2 2. REVIEW OF THE LITERATURE Morselli A. (2015) delves into the intricate connection between economics and psychology in comprehending decision-making and advocates for a holistic approach incorporating psychological insights into economic decision-making theories. The revelation of social preferences introduces complexity by challenging the traditional concept of economic rationality centered on individual utility. Social preferences compel the consideration of others' well-being and economic conditions (Monroy et al., 2017; Caraballo et al., 2023; Zapata et al., 2023) leading to a cognitive duplicity where rational logic and emotions coexist. The abovementioned challenges existing decision-making models and raises questions about the prevalence of intuition, the role of reasoning, and the impact of contextual factors on decision-making, complicating the understanding of this process. Traditionally, economic decisions were exclusively tied to individual utility, neglecting the wellbeing of others. The revelation prompts radical changes in models of strategic interaction, highlighting the role of intuition and reasoning, and recognizing the decisive influence of contextual factors in the intricate and non-linear dynamics among diverse economic agents. This complexity makes developing comprehensive predictive models challenging, underscoring the impossibility of explaining economic phenomena without considering individual economic actions and their cognitive foundations. Existing papers (Liu et al., 2022; Hoff & Stiglitz, 2015) suggest that individual preferences in decision-making models are influenced by personal characteristics, social and cultural factors, social diversity (Buitrago & Caraballo, 2022) and contextual elements (including previous experiences, neighbours' preferences, and social dynamics). Researchers broaden economic discourse by incorporating insights from sociology, highlighting the importance of social contexts and cultural and mental models in shaping individual behaviour and decision-making. Some authors (Sagoff, 1988) have followed a somewhat different line of thought and have argued that it is important to distinguish between the individual's roles as a consumer and as a citizen: "As a citizen, I am concerned with the public interest, rather than my own interest; with the good of the community, rather than simply the well-being of my own family. (…) In my role as a consumer, (…) I pursue the goals I have as an individual." (Sagoff, 1988, p. 8). The individual's switch between roles in the decision-making process also depends on the state of the environment, which shapes the context of decision-making and influences changes in individual preferences. Researchers (Bröder & Schiffer, 2003) have reported that the Bayesian method effectively assesses cognitive strategies in multi-attribute decision-making, enabling inferences from behavioural data to cognitive theories. The Bayesian approach allows for taking into account changes in individual preferences depending on the state of the environment and, therefore, for switching the decision-making agents’ roles. This line of research draws on game theory, mathematical statistics, and decision theory, taking into account the varying degrees of uncertainty, with the Bayesian approach being a vital tool in addressing such problems. Within decision science, the Bayesian approach embodies the principle of maximising the information used throughout the decision-making process, involving continuous review and information reassessment at each stage. Methods rooted in the Bayesian approach operate on the premise 3 that practically any assertion or event carries a prior probability of being true, no matter how small. If a hypothesis is deemed probable, there must be a set of conditions supporting it. The absence of such conditions would halt the assessment, leaving the prior probability unchanged. However, in the presence of messages related to the problem, the prior probability can be adjusted to derive the posterior probability of the same hypothesis, considering the new information. In essence, the Bayesian approach facilitates the computation of the validity of competing hypotheses by accounting for the influence and presence of accompanying evidence. 3. METHODOLOGY Based on the above mentioned literature, the decision-making situation is described by set - {𝑋,𝜃,𝐹}, where: 𝑋={𝑥1,𝑥2,..,𝑥𝑚} - set of possible decisions, 𝜃={𝜃1,𝜃2,..,𝜃𝑚} ⎯ set of environment states, 𝐹={𝑓𝑘𝑗}− assessment matrix, as defined on Casterian product  Х, 𝑓𝑘𝑗 = 𝑓(𝑥𝑘,𝜃𝑗), 𝑘=1,𝑚, 𝑗=1,𝑛. In the expanded form, the decision-making situation is represented as a matrix, the components of which are real numbers 𝑓𝑘𝑗 - quantitative assessments of possible decision 𝑥𝑘∈𝑋, given that the environment is in a particular state - 𝜃𝑗∈𝜃: 𝑓= ( 𝜃1... 𝜃𝑗... 𝜃𝑛 𝑥1𝑓11 ... 𝑓1𝑗 ... 𝑓1𝑛 ... ... ... 𝑥𝑘𝑓𝑘1 ... 𝑓𝑘𝑗 ... 𝑓𝑘𝑛 ... ... ... 𝑥𝑚𝑓𝑚1 ... 𝑓𝑚𝑗 ... 𝑓𝑚𝑛 ) . (1) Values 𝑓𝑘𝑗 , typically, are denominated in monetary units, and they signify either potential losses or gains. For optimal decision-making probabilities of the particular environmental states are necessary to know 𝑃(𝜃1)=𝑝1,𝑃(𝜃2)=𝑝2,...,𝑃(𝜃𝑛)=𝑝𝑛, at the same time 𝑝1+𝑝2+...+𝑝𝑛=1. In case when 𝑓𝑘𝑗 are gains the better decision is maximum value of ∑𝑓𝑘𝑗𝑝𝑗 𝑛 𝑗=1 , 𝑘=1,𝑚: 𝐵+(𝑥𝑘0,𝑝)=𝑚𝑎𝑥 𝑘=1,𝑚∑(𝑝𝑗𝑓𝑘𝑗 +), 𝑛 𝑗=1 (2) This type of decisions is acceptable without probabilities expertise. However, if such an assessment is conducted to make a more weighted decision, its results should be taken into account according to the following scheme. Let 𝜉1, 𝜉2, ... , 𝜉𝑁 denote possible outcomes of the experiment. Then, according to the rules of probability theory, it is necessary to calculate the conditional probabilities 𝑃(𝜉𝜈 𝜃𝑗),(𝜈=1,𝑁, 𝑗= 1,𝑚) of obtaining the result 𝜉𝜈 given the economic state 𝜃𝑗. Subsequently, having a specific result 4 of the experiment 𝜉𝜈0, Bayesian formulas are used to calculate the posterior probabilities of the states: 𝑃(𝜃𝑗/𝜉𝜈0)= 𝑃(𝜉𝜈0/𝜃𝑗)𝑃(𝜃𝑗) ∑𝑃(𝜉𝜈/𝜃𝑗)𝑃(𝜃𝑗) 𝑛 𝑗=1 . The obtained probabilities are then used to find the minimum or maximum of the functional ∑𝑓𝑘𝑗𝑃(𝜃𝑗 𝜉𝜈0 𝑛 𝑗=1 ). If this result significantly differs from that based on prior probabilities, it is advisable to conduct additional scrutiny in this case. When the probabilities 𝑝𝑗(𝑗=1,𝑛) are unknown, the Bernoulli-Laplace criterion or the principle of maximum entropy (Gibbs-James principle) is employed to select the optimal decision solution. According to Bernoulli's principle, probabilities ),1( njpj= should be considered equal if there is no information to consider any state θ from the set 𝜃={𝜃1,𝜃2,..,𝜃𝑛} more probable than any other. Therefore, based on the Bernoulli-Laplace criterion, a decision is considered optimal if 𝐵+(𝑥𝑘0,𝑝)=𝑚𝑎𝑥1 𝑛∑𝑓𝑘𝑗+ 𝑛 𝑗=1 . (3) While recommendations based on probabilistic methods may sometimes lead to suboptimal decisions, with frequent repetitions of similar decision-making situations, they generally yield better results than intuitive decision-making. 4. 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