Source-linked AI summary
Dynamic probabilistic decision networks
V. I. Yukalov, E. P. Yukalova
TL;DR
The paper addresses the limited treatment of probabilistic, affective, and dynamically interacting agents in decision models. It develops and analyzes a classical dynamic probabilistic decision network, illustrating it with the Allais paradox; under moderate or weak imitation, emotional influence diminishes over time, while strong imitation can produce oscillations.
Problem
Existing decision models are limited by deterministic utility maximization, while affective decision modeling must represent stochastic choices and time-varying emotions during information exchange.
Method
The paper develops a classical dynamic probabilistic network whose heterogeneous intelligent agents combine utility, emotions, information exchange, imitation, and different memory properties.
Results
Under moderate or weak imitation, emotional influence in collective decision making diminishes over time; strong imitation with short-term-memory agents can produce oscillatory hesitation.
Takeaways & Limitations
The model provides a framework for analyzing collective decisions involving probabilistic choice, affective influences, repeated decisions, information exchange, and memory.
Takeaways & Limitations
Applications to particular cases and analysis of concrete predictions are left for future research.
Abstract
from arXiv · showhide
A new type of decision networks is suggested and its operation is analyzed. The network nodes are represented by intelligent agents who can denote either some biological beings, like humans, or neurons of the brain, or the nodes of artificial intelligence. The specifics of the network are in the following: It is probabilistic in the sense that the choice, accomplished by each agent, is characterized by the related probability. It is dynamic, with the probabilities varying in time due to the exchange of information between the agents. It is affective, because the agents choose between alternatives by taking account of utility as well as of biases and emotions. In general, it is heterogeneous, being composed of the groups of agents with different properties, for instance having long-term memory and short-term memory. The network dynamics, caused by the information exchange, results in decision error decrease. The network operation is illustrated by the example starting with the Allais paradox, its resolution, and the decision error diminution in the process of decision dynamics with information exchange. Resorting to machine-learning techniques it is possible to regulate the behavior of the network agents forcing them to choose particular alternatives.
1 Introduction
The paper motivates a classical decision-network model that combines probabilistic individual choices, affective influences, and collective dynamics from information exchange. It addresses limitations of deterministic utility-based models and distinguishes its multi-agent repeated-decision setting from machine learning.
- Motivation: Decision-making models should account for both utility evaluation and biases or emotions, while also representing information exchange among agents.The paper treats individual affective choice and collective dynamic effects as complementary requirements.
- Motivation: Affective decision modeling remains difficult because emotional influence must be measured and emotions change through multi-agent information exchange.The paper presents this challenge as motivating a model with temporal evolution of affective decisions.
- Motivation: Expected-utility extensions are limited by fitted parameters and by their deterministic assumption that decision makers maximize a constructed value functional.The paper characterizes these models as primarily descriptive with relatively low predictive power.
- Motivation: Real decision makers choose probabilistically because preferences vary across repeated decisions and neural decision processes involve noise.The paper attributes this variability to fundamental stochasticity and instability in neural networks.
- Proposed approach: The proposed network uses classical terms to model probabilistic choices whose probabilities change over time through information exchange, while combining utility with emotional attractiveness.Its nodes are intelligent agents, and the framework is intended to represent biological, neuronal, and other agentic networks.
- Distinction from machine learning: Unlike machine learning, the framework studies societies of agents making repeated decisions under unchanged utility factors while accounting for emotions and imitation.Machine learning is described as fitting parameters from large datasets for a single decision under fixed data.
2 Decisions at initial stage
The initial decision stage models each agent’s choice probabilistically by combining rational utility with emotional attraction. Applied to lottery decisions, the framework explains observed deviations from expected utility theory and agrees with aggregate experimental data.
- Initial probabilistic choice: Each agent independently chooses among alternatives using a behavioral probability that combines a utility factor with an attraction factor.The utility factor measures rational usefulness, while the attraction factor represents emotional influence.
- Initial probabilistic choice: The additive structure is motivated by treating rational reasoning and emotional processes as complementary contributions, while recovering classical decision theory when emotion effects vanish.The model selects addition rather than multiplication because the multiplicative form fails the limiting condition.
- Initial probabilistic choice: The alternative with the largest behavioral probability is defined as preferable, even when the alternatives maximizing utility and attraction differ.This distinguishes the most useful, most attractive, and optimal alternatives.
- Allais paradox: For the Allais-type lotteries, expected utility favors L1 whereas most participants choose L2, a pattern the model explains through lottery quality and attraction.The model’s prediction for L2 is reported as agreeing with experimental data within experimental accuracy.
- Empirical justification: Across 18 Kahneman–Tversky lotteries, qexp = 0.27 agrees with the quarter-law value 0.25 within the stated experimental accuracy of 0.1%.The paper presents this as an aggregate prediction without fitting parameters.
3 Operation of decision network
The decision network evolves as agents exchange information, imitate one another, and update emotion-related attraction through memory. It supports heterogeneous agents and represents collective decisions by combining group-level behavioral probabilities.
- Network dynamics: Agents first form primary opinions, then exchange information and may imitate one another, causing their behavioral probabilities and opinions to change over time.The network dynamics are built around communication and imitation after the initial choices.
- Network representation: Each agent’s behavioral probability is indexed by alternative and time, and an agent may represent either an individual or a group fraction choosing that alternative.The model uses pj(An, t) for agent-level or representative group-level choice probabilities.
- Heterogeneous agents: The network accommodates humans, animals, neurons, and artificial-intelligence nodes because the same mathematical representation is used for agents with intrinsic noise.The interaction structure can nevertheless depend on whether agents are mobile societies, mechanistic nodes, or neural units.
- Memory and updating: Attraction factors evolve through agent memory, which accumulates information gains weighted by interaction influence; utility factors may remain constant over periods short relative to discounting time.The information gain can be expressed using a Kullback–Leibler form.
- Memory and updating: Long-term memory uses time-independent interactions, whereas short-term memory retains only recent information, allowing heterogeneous memory properties across agents.The paper distinguishes long-term and short-term memory as limiting cases of memory duration.
- Collective decisions: The collective probability for an alternative is the weighted sum of group probabilities, with weights determined by group population fractions that may change over time.The fractions remain fixed without transitions between groups and vary when group membership changes.
4 Allais paradox and its resolution
The paper resolves the Allais paradox by combining utility with probabilistic attraction factors representing affective influences. This framework can reproduce preferences that contradict standard expected utility theory without producing a paradox.
- The Allais paradox contrasts observed lottery choices with the predictions of standard expected utility theory.
- The standard theory yields contradictory utility inequalities for the observed preferences over L1, L2, L3, and L4.
- The probabilistic approach combines utility factors with attraction factors linked to affective decision making.
- The probabilistic theory therefore explains the observed Allais choices without the contradiction generated by standard expected utility theory.
- L1 is preferred to L2 because its behavioral probability exceeds that of L2, despite L2 having the larger utility factor.
- L3 is both more useful and more attractive than L4, so the probabilistic model predicts preference for L3.
5 Dynamics of Allais paradox
The model extends individual Allais choices into a dynamic network of heterogeneous agents that exchange information and may imitate one another. Depending on emotions, memory, and imitation, probabilities can oscillate, converge, or lose emotional influence over time.
- The network contains long-term- and short-term-memory groups whose behavioral probabilities are updated through information exchange and imitation.
- If ε1 + ε2 = 1, the two groups’ choice probabilities become equal for all t ≥1, even when initially different.
- With weak imitation and negative short-term-memory emotions, probabilities approach limiting values, while near-zero initial probability can produce early oscillations.
- For weak positive emotions, both groups converge to a common limit above the utility factor f, reaching 0.668 when q2 = 0.25.
- Strong imitation produces regimes broadly similar to weak imitation but can add a regime because the groups’ memory dynamics are asymmetric.
- Information exchange reduces emotional influence, with |q*_i| ≤ |q_i|; long-term-memory agents usually lose emotional influence, but groups generally need not reach consensus.
6 Regulated decision making
The paper uses machine-learning regulation of utility to steer agents toward prescribed decision probabilities. Simulations show convergence to a shared target despite differing initial emotional states.
- Machine-learning techniques can regulate alternative utilities so that agents’ decision probabilities converge toward prescribed values.
- The regulation uses a gradient-descent equation with a learning rate chosen to guarantee procedural stability.
- Agents with different initial emotions converge to p*_i = 0.418, matching the Allais utility factor f_i = 0.418.
- When the prescribed final probability is p*_i = 1, all agents are forced to choose the first alternative with probability one.
7 Discussion
The paper develops a heterogeneous dynamic probabilistic decision network in which agents combine utility, emotions, memory, information exchange, and imitation. The Allais example shows that moderate or weak imitation diminishes emotional influence, while machine learning can regulate final choices.
- The proposed network represents intelligent agents making probabilistic choices from rational utility evaluations and emotional attractiveness.
- The network is heterogeneous, including agents with long-term and short-term memory, and can represent social, biological, or neural systems.
- In the Allais example, strong imitation can produce oscillatory hesitation, whereas moderate or weak imitation reduces emotional influence over time.
- Machine-learning techniques can regulate final probabilities and force agents toward required alternatives.
- The paper presents the model as an introduction, leaving applications to particular cases and analysis of concrete predictions for future research.
Declaration of competing interests
The authors report no declarations in the competing-interests section.
- The authors report nothing to declare.
- The declaration section contains no reported interests.
- No competing-interest declaration is provided.
Funding
The research received no specific grant from public, commercial, or not-for-profit funding agencies.
- The research received no specific grant from funding agencies.
- The funding statement covers public, commercial, and not-for-profit sectors.
- No specific external-sector funding is reported.
Competing Interests
The authors state that they have no conflicts to disclose.
- The authors have no conflicts to disclose.
- The competing-interests statement reports no conflicts.
- No author conflicts are disclosed.
Authors’ contribution
V.I.Y. and E.P.Y. jointly conceived, designed, prepared, collected, and analyzed the study materials, while V.I.Y. drafted the manuscript and E.P.Y. completed numerical calculations. All authors reviewed, commented on, and approved the final manuscript.
- Study conception and design: V.I.Y. and E.P.Y. conceived and designed the study.
- Material preparation, data collection, and analysis: V.I.Y. and E.P.Y. prepared materials, collected data, and performed the analysis.
- Manuscript preparation: V.I.Y. wrote the first manuscript draft, and all authors commented on previous versions.
- Numerical calculations: E.P.Y. completed the numerical calculations.
- Final approval: All authors read and approved the final manuscript.
Figure Captions
The figures show how decision probabilities evolve over time under absent or strong imitation, varying attraction parameters and α. Some settings produce convergence to fixed probabilities, equalization, or persistent oscillations.
- Figures 1–2: Without imitation, changing q2 alters the limiting probabilities p1(t) and p2(t), including p1(t) → p∗1 = f = 0.418 and p2(t) → p∗2 = 0.1607 or 0.320.For q2 = 0, p2(t) remains equal to its initial value f.
- Figures 3–4: Under strong imitation, p2(t) tends to f = 0.418 while p1(t) reaches values such as 0.1664, 0.518, or 0.6505 as q2 varies.When q2 = q1 = 0.25, both probabilities remain equal to 0.668 for t ≥0.
- Figure 10: The three-group, three-temporal-slice network is represented as a distinct network class.The caption identifies the network structure without reporting a probability trajectory.