The Choice Wave | Behavioral Science and Decision Theory

The Choice Wave is a behavioral-science theory and analytical technique developed by Radislav Romanovich Johnson for modelling a decision as probabilistic before it is made and observable at the moment of choice.

Its subject is human choice broadly understood: conscious aims, subconscious strategies, social influence, learned responses, and interactions among people whose conduct may be internally coherent but governed by different rationalities. Economics supplied the framework’s first empirical applications since people often reveal their subconscious beliefs through monetary choices, but it is one field of application rather than the boundary of the theory.

Scope of the analogy. The model uses wave-function mathematics as a formal language for probability and choice. It does not require the claim that human decisions are themselves physical quantum events.

Choice WaveRepresents the probabilities associated with the utility-maximizing choices available before a decision is observed.

Parallel RationalityAllows statistically distinct groups to maximize utility according to different decision strategies.

Multipoint InfluenceModels how history, affinity, information, and effective distance can alter the probabilities attached to choice.

Conceptual Background

Classical economic models commonly begin with a consistent decision-maker who maximizes utility according to a defined set of preferences and constraints. Behavioral economics demonstrated that observed choices often differ systematically from the predictions of that model. Work by Daniel Kahneman, Amos Tversky, Richard Thaler, Matthew Rabin, and others placed psychology more firmly within economic analysis and developed concepts such as bounded or quasi-rational behavior.

The Choice Wave begins from a related but different question: what if statistically distinct groups are not merely departing from one central rationality, but are following different internally coherent decision strategies? Under this interpretation, diverse groups may each maximize utility while assigning different probabilities, meanings, or weights to the available choices.

Behavioral Science and Subconscious Strategy

The framework distinguishes an observed act from the full decision process that produced it. A person may pursue an overt practical objective while also responding to habit, identity, historical experience, social expectations, or a subconscious psychological payoff. These influences are not treated as noise by definition; when they produce stable, testable patterns in revealed preference, they may form part of the person’s decision strategy.

Transactional Analysis provides one way to describe this layered conduct. An interaction may contain both an overt social transaction and a covert psychological transaction. In a recurring game such as Eric Berne’s “Now I’ve Got You,” an apparent dispute over a material issue can also yield the psychological payoff of obtaining moral or emotional advantage over another person. The Choice Wave adds a probabilistic structure: a potential game player may or may not play when an opportunity appears, and another participant may or may not provide the trigger or expected response.

Layered motivationObservable choices may reflect practical objectives together with subconscious scripts, learned responses, identity, and anticipated psychological rewards.

Conditional interactionBefore an encounter, each actor faces uncertainty about the other’s type, trigger, and response. At the decision point, those possibilities resolve into observed conduct.

Resultant strategyWhen distinct Choice Types interact, the encounter may become a joint decision system with a resultant wave shaped by both participants rather than by either actor alone.

A participant’s Choice Wave can therefore be represented as a combination of an ordinary decision wave, a game-specific wave, and the conditional influence of the other participant’s likely trigger or response. This permits subconscious behavior to be framed as probabilistic and testable without assuming that the actor can articulate every motive. It also explains why changing a constraint—through a rule, penalty, training programme, or institutional bridge—may change an immediate outcome without necessarily changing the underlying behavioral strategy. Repeated experience and sustained institutional design may, over time, alter the strategy itself.

This psychological interpretation broadens the framework beyond consumer demand. It can be used to formulate hypotheses about organizational conduct, conflict, policing, education, diplomacy, religion, sustainability, and other settings in which human beings respond simultaneously to material conditions, social meaning, and subconscious incentives.

Probabilistic Choice at the Decision Point

Before a choice is made, several utility-maximizing outcomes may remain possible, each with an associated probability. At the decision point, the selected outcome becomes observable and its probability becomes one. The model therefore distinguishes the probabilistic structure of a decision before choice from the revealed preference observed afterward.

{ψ (e)}_{t} = {\begin{cases} P (U_{e} (e | t) = Max U^{*}), & at the decision point; \\ P (U_{e} (e, t) = Max U), & otherwise. \end{cases}

Equation 1. Probability of choosing expenditure e at the decision point.

The practical emphasis is on the distribution of possible choices, not only the final outcome. The expectation value of that distribution becomes central to estimation and comparison.

Consumer Types and Orthogonality

Although every individual could theoretically have a distinct Choice Wave, empirical work normally groups decision-makers whose observed behavior is statistically similar. Each group, or consumer type, may then be represented by its own wave. In the formal model, different types are represented as orthogonal Choice Waves in an n-dimensional Hilbert space.

In the empirical classification procedure used in the published demand application, a proposed partition is accepted only when all three conditions hold:

The representative, per-capita-weighted mean of each proposed Choice Type is statistically different from the representative mean of every other type.
Each member is not statistically different from the representative mean of its own type.
Each member is statistically different from the representative mean of every other type.

These tests make the grouping a result of revealed preferences rather than an impression imposed after viewing demographic, political, racial, or geographic labels. Candidate partitions can be evaluated computationally—and modern artificial intelligence may make that search substantially more efficient—but the statistical conditions, declared significance threshold, robustness checks, and out-of-sample validation remain the governing evidence.

Diagram of consumers represented on different orthogonal planes of choice — Figure 1. Statistically distinct consumer types represented on orthogonal planes of choice.

Orthogonality expresses statistical distinction between types. It permits multiple rationalities to be modelled together without requiring one group to be defined simply as an irrational deviation from another.

- U (e) \frac{d^{2} ψ (e)}{d e^{2}} = H ψ (e)

Equation 2. A form of the Choice Wave.

H = U (e) + U_{p} (e)

Equation 3. The relationship between actual and potential utility.

Choice Wave probability distribution before a decision — Figure 2. A probabilistic distribution before the choice is observed.

Choice Wave and revealed choice at the decision point — Figure 3. The distribution resolves at the decision point.

Econometrically, the framework suggests that a dataset containing materially different decision types may be more informative when those types are identified and estimated separately. Published applications have examined consumer demand, strategic interaction, sustainability, education, and police–public conflict.

The Multipoint Gravitational Model

Choice does not occur in isolation. Information, institutions, affinity groups, personal history, and other people may affect the probabilities within an individual’s decision strategy. The Multipoint Gravitational Model represents these influences using an analogy with gravitational interaction.

Each actor may influence, and be influenced by, every other actor. The degree of influence depends upon relative strength and effective distance. Effective distance need not be geographical: a distant online community, historical experience, or shared identity may exert more influence than a physically nearby person.

\vec{F_{A B t}} = \frac{M n_{A t} (h_{A}, n_{B t}) n_{B t} (h_{B}, n_{A t})}{f (r)} \vec{r_{B A}}

Equation 4. A general force-of-interaction term.

\vec{e_{B A t}} = \frac{q (\vec{F_{A B t}})}{p (n_{B t})} \vec{r_{B A}}

Equation 5. The effect of actor A upon actor B.

Max U (x, S (N)) = k (x) s.t. d (Y, \frac{{}_{B}{\bar{F}}^{net}}{n_{B t}})

Equation 6. Social and subconscious influence within a utility-maximization problem.

The model can accommodate strategic interaction, subconscious transactions, and historical effects. Where a particular form of interaction is not relevant, its corresponding term may be omitted.

The Theory of Parallel Rationality

When several statistically distinct types maximize utility according to their own decision strategies, each can be represented as a parallel economic state with its own rationality. The classical “economic man” remains one possible type, but not the sole standard against which every other type must be judged.

Diagram illustrating parallel rationalities and a bridge between them — Parallel decision systems may remain distinct even when a bridge temporarily aligns their incentives.

Parallel rationalities become especially important when different types are stakeholders in the same decision. If each group’s preferred outcome conflicts with the interests of another, misaligned incentives and inefficient outcomes may result. A bridge—an institution, rule, transaction mechanism, or naturally occurring overlap—can help align those incentives.

A Pigouvian tax provides one conventional example of an artificial bridge: it changes the producer’s constraint so that environmental costs borne by others enter the producer’s decision. A natural bridge occurs when otherwise distinct actors happen to prefer compatible outcomes at a particular decision point.

P (B) = \sum_{a, b} (\int_{a}^{b} ψ_{A} (e) d e + \int_{a}^{b} ψ_{B} (e) d e)

Equation 7. General probability of a natural bridge between two actors.

Applications

Business and marketsConsumer types can be estimated separately for segmentation, demand analysis, and strategy.

Public policyStakeholder groups can be examined according to their own incentives, constraints, and expectations.

Diplomacy and conflictThe model can represent strategic misalignment and the institutions needed to make cooperation beneficial.

SustainabilityBridges can incorporate costs or benefits that otherwise fall outside an actor’s decision process.

EducationBehavioral groupings can inform analysis of different learning expectations and choices.

Institutional designEffective-distance and influence terms can help describe networks, trust, history, and group interaction.

The framework does not assume that cooperation is always the immediate optimum for every actor. Instead, it helps identify when incentives diverge and what kind of bridge would be required to make a more broadly beneficial outcome compatible with the rationality of each participant.

References and Selected Applications

Rutherford Johnson. “The Choice Wave: An Alternative Description of Consumer Behavior.” Research in Business and Economics Journal, vol. 5, February 2012.
Rutherford Johnson. “A Spatial Application of Choice Waves: Decline in Church Giving in the United States during the Recession.” Journal of Behavioral Studies in Business, vol. 8, 2015.
Rutherford Johnson. “A Probabilistic Demand Application in the American Cracker Market.” International Journal of Food and Agricultural Economics, vol. 4, no. 3, 2016.
Rutherford Johnson. “Choice Waves and Strategic Interaction.” Journal of Technology Research, vol. 7, March 2017.
Rutherford Johnson. “The Inclusion of Geo-Cultural, Historical, and Legal Considerations in the Analysis of Anglican and Roman Ecclesiastical Division.” Interdisciplinary Journal of Research on Religion, vol. 13, 2017.
Rutherford Johnson and Eddie Walker II. “A Probabilistic Shortage of Private Land Opened to Hunters in Northwest Minnesota.” Modern Economy, vol. 9, no. 1, January 2018.
Rutherford Johnson. “Improving Police-Public Conflict Resolution to Improve Sustainability Decision Strategy.” Journal of Human Resource and Sustainability Studies, vol. 9, no. 4, 2021.
Rachel Lundbohm and Rutherford Johnson. “Implications of Hybrid Courses on Perceived Learning of Undergraduate Students and their Anticipated Benefits in a Post-Pandemic Environment.” Transnational Journal of Business, vol. 7, 2022.
Daniel Kahneman and Amos Tversky. “Prospect Theory: An Analysis of Decision under Risk.” Econometrica, vol. 47, no. 2, 1979.
Matthew Rabin. “Psychology and Economics.” Journal of Economic Literature, 1998.
Thomas Russell and Richard Thaler. “The Relevance of Quasi Rationality in Competitive Markets.” American Economic Review, 1985.