*Would you like the short version?
Here it is! *

Some
people feel very sure about their thoughts, but others might say they
are wrong. Economists used to think everyone made choices in a very
logical way. But some new thinkers, like Richard Thaler and Daniel
Kahneman, showed that people often don't follow strict logic. They
introduced the idea of "quasi-rationality," which means people can have
different ways of thinking and making choices.

Then, a new idea
called the "Choice Wave" came around that helps explain how different
people make decisions. It says that everyone can have their own way of
making choices, but they still try to make the best choice for
themselves. This means that before making a choice, there are many
possible options, and the final choice can depend on many things in a
person's mind.

Here there
are two distinct groups of people.

Each group wants to make the best choice for

themselves, but what is best is different for each group.
The Choice Wave
also shows that people can
influence each other. This is explained by the "multipoint
gravitational model," which looks at how people affect each other's
decisions based on their distance and connections.

Finally, the
"Theory of Parallel Rationality" says that different groups of people
can have their own ways of thinking, and sometimes these ways do not
match. This can lead to problems if one group's best choice harms
another group's interests. To solve this, we need something called
"bridges," which help align what different groups want.

Overall,
these ideas can help us understand people's choices better and improve
how we make decisions in business, education, police-public
interaction, and even global policies.

*Ready for the long version? Keep
reading below. *

*So,
what is this all about? *

Have you ever felt absolutely certain about your
thoughts or choices, only to be told by others that you're mistaken or
even irrational? Deep down, you know you’re not wrong or irrational,
right? For many years, economists have been constrained by the
traditional theory of classical rationality. This framework revolves
around the concept of the "economic man," who is believed to optimize
utility based on a rigid set of logical principles.

However, groundbreaking behavioral economists, including recent Nobel
Prize winners Richard Thaler and Daniel Kahneman, along with notable
figures like Matthew Rabin and Amos Tversky, emphasized the
crucial psychological dimensions of economics (Rabin,
1998). They introduced the idea of "quasi-rationality,"
which acknowledges that individuals often stray from classical
rationality, leading to results that diverge from what standard
economic models predict (Russell and Thaler, 1985;
Kahneman and Tversky, 1979). Their pioneering research
highlights an essential truth that had long been overlooked in
economics: people are inherently diverse.

But that only takes us so far. The question remains: who determines
what is rational versus quasi-rational? How do different groups of
individuals behave in distinct ways? And ultimately, how should these
variations influence the way we approach and engage with one another?

*Enter the Choice
Wave.*

# Understanding the
Choice Wave Theory

The
Choice Wave, as it came to be called, was
derived by Rutherford Johnson
in 2006 from the mathematics of quantum mechanics. Schrödinger's wave
equation was modified to apply to economics. The Choice Wave
assumes utility that is continuous, probabilistic, varies in a
non-random manner over time, always leads to temporal utility
maximization, and permits the existence of one or more individuals who
chose according to unique decision strategies (Johnson, 2012).
The first benefit of the Choice Wave is that it
conceptually permits individuals to make different choices at each
decision point and still be utility-maximizing and rational. Before the
individual makes a choice, each utility-maximizing possible choice has
a certain probability of being the one chosen. At the point of
decision, the choice is made, revealing individual preference at that
exact moment. As the various factors that comprise the decision
strategy are considered within the mind, the outcome is probabilistic
until the choice has been revealed at the decision point.

## Psychological and Mathematical
Foundations

Eqn. 1 expresses the
notion that the probability of choosing the expenditure value, *e*,
is equal to the probability that the utility of that expenditure
conditional on time, i.e., at the decision point, maximizes utility. At
the decision point, the probability that the consumer will choose the
level of expenditure becomes 1. Before the decision, all
utility-maximizing choices are possible, each with a certain
probability.

By modeling each different type of individual in a
market by a Choice Wave, which is mathematically orthogonal to every
other Choice Wave in an n-dimensional Hilbert space, a full model can
be developed in which each type of individual maximizes utility
according to their own rationality. Orthogonality means that each type
of individual has a statistically different and, in its purest form,
non-interacting decision strategy. *(See Fig. 1**. - Consumers of
different orthogonal types exist on different "planes" of choice.)*

A form of Choice Wave that satisfies the
assumptions of Choice Waves is derived from Eqn. 2. The term *H*
is given in Eqn. 3, where *U(e) *is actual utility,
and *U*_{p}(e) is potential
utility as a function of expenditure.

And what is a "type" of individual (also known as a
Consumer Type)? Each individual could theoretically have a completely
separate Choice Wave. However, individual behaviour is typically
similar statistically to the behaviour of certain individuals and
different from others. Those that are similar comprise a distinct type
of individual that may be modeled by a single Choice Wave. If, for
example, there are two distinct types of individual in the economy, A
and B, with decision strategies that satisfy the assumptions of Choice
Wave Probabilistic Demand, then they may be modeled by two orthogonal
Choice Waves, Ψ_{A}
and Ψ_{B}.
Not only does this make practical modeling of the economy in the
framework easier, it allows for both simple trends that exist naturally
among independent decision strategies of individuals and for
"group-think" scenarios, such as fads.

Rather than a sub-group of "quasi-rationals" who
deviate from economic rationality, everyone may be treated as rational,
maximizing utility according to their own strategy, for a Choice Wave
permits every possible utility-maximizing choice, each with a certain
probability, and no choices that do not maximize utility at the
decision point. A Choice Wave "collapses" to probability of 1 once the
choice has been revealed, but is indeterminate when the choice is still
in the consumer's head. Similarly, an indifference curve "floats" on
the budget constraint line until the choice is made. *(See Figs. **2 & 3.) *The key variable
of the model then becomes an expectation value.

Econometrically, this implies that data sets
containing multiple types of individuals should be split according to
those types and estimated separately (Johnson,
2016). In marketing, different
strategies can be employed for the different types. In strategic
policy, the Choice Wave can be used to model probabilistic decision
strategies between different actors and potentially separate them by
type (Johnson, 2017).

#
*Multipoint
Gra**vitational
Model.*

People do not live in a vacuum. An individual's
decision strategy may be influenced by a variety of psychological
factors, include the influence of information and other individuals.
The economic multipoint gravitational model is a mathematical method
for conceptualizing the various forms of interaction and influence
between individuals. The multipoint version of the model, based on
gravitation models in physics, permits each actor both to influence and
be influenced by each and every other actor. The degree of that
influence depends on relative strength of influence and effective
distance, where the effective distance may not be physical (Johnson, 2015).
For example, one may be influenced by affinity groups or people a great
distance away over the internet more than by one's neighbours.
Additionally, the multipoint gravitational model may be used to
incorporate the effects of history and personal experience (Johnson, 2017a).
These aspects of decision strategy can influence probabilities
associated with each utility-maximizing choice and therefore can become
a component of a given Choice Wave. A basic equation for the force of
interaction is given by Eqn. 4, where *M* is a
constant, *n*_{A} and *n*_{B}
are terms representing strength of influence for players A and B
respectively, *h*_{A} and *h*_{B}
represent historical effects, and *f(r)* is some
function of the effective distance between the players. The force
vector of A acting on B is in the vector direction, as indicated, from
B to A. There is, then, also a similar force equation for B acting on
A. In Eqn. 4, the influence terms are not only a function of historical
experience, but are expressed as a function of the influence term of
the other player to allow for possible strategic interaction or
subconscious transactions. Insofar as such interaction does not exist
in a particular case, those terms may be removed.

Eqn. 5 is the equation of the effect of A acting on
B. It may be thought of as B "accelerating" towards A or, should the
term be negative, then A towards B. The net effect of all other players
acting on a specific player then may enter into that player's utility
maximization problem, given in Eqn. 6, where *S(N)*
is a subconscious component based at least in part on the influence of
others, *k(x) *is some form of utility function, and
*Y* is income as usual.

#
*Theory
of Parallel Rationality.*

If there are multiple types of individuals in the
market, each maximizing utility based on their own decision strategies,
and, on average, those types are statistically different from each and
every other type, then they may each be represented by a Choice Wave,
which is mathematically orthogonal to each and every other Choice Wave.
Each type constitutes a non-interacting parallel "economic world," each
with its own distinct rationality.

Individuals in each parallel "world" maximize
utility according to their own rationality, as contained within their
decision strategy, and distinctly from those in other "worlds." The
classical "economic man" still exists, but there is an infinite number
of different versions of him in an infinite number of parallel
"economic worlds."

In some cases, these parallel rationalities simply
represent different types of consumer in a market. In some cases,
however, two or more parallel rationalities (represented by
mathematically orthogonal Choice Waves) may both represent stakeholders
in a particular economic scenario. If the decision strategy of each
parallel state of rationality chooses an outcome significantly
different from the other stakeholders, then there is a misalignment of
incentives, and an inefficient allocation of resources and sub-optimal
outcomes may result. A "bridge," in the form of an institution or
mechanism, is necessary to span the two economic worlds and align their
incentives to create a more efficient allocation of resources and a
more optimal outcome.

In the case of externalities, for example, a
producer that does not bear the cost of environmental damage may make
decisions without taking into account sustainability issues. Consumers,
on the other hand, feel the cost of that environmental damage.
Producers and consumer have different decision strategies and comprise
different economic worlds (each represented by a distinct Choice Wave),
the the preferred outcome of producers does not align with the
preferred outcome of consumers. A Pigouvian tax is one form of bridge
that can span those two worlds, aligning incentives and hence aligning
decision strategies to yield a more optimal outcome. Both producers and
consumers remain separate economic worlds, however, since their
strategies only align in the presence of a bridge.

Bridges, akin to a wormhole in quantum theory, may
be naturally-occurring or artificial. A Pigouvian tax, as in the
previous example, is a form of artificial bridge. An institution that
helps to facilitate transactions by eliminating friction could also be
an artificial bridge. Mathematically, artificial bridges are typically
included within a constraint term within the Choice Wave. The
probabilistic decision strategy is the same, yet faces different
constraints in the presence and absence of the artificial bridge.

A natural bridge, on the other hand, occurs when
there are overlaps between consumer types. Although the "worlds" of
consumer types are non-interacting and statistically different in
expectation, there exists a probability that a particular choice of one
individual may be, at a specific decision point, statistically with the
choice of another individual. That constitutes a natural bridge and
only exists as long as those choices happen to align. Should those two
individuals both be opposite parties to a transaction, such as a
supplier and a buyer, such bridges can result in alignment of
incentives and more optimal outcomes, however fleeting it may be. Eqn.
7 gives the general form of the probability of a natural bridge, *B*,
existing between two actors, A and B. The integrals in Eqn. 7 are taken
over the boundaries *a* and *b* of
every possible range of overlap of choices.

## How the Choice Wave Can Influence
Decision-Making

In strategic policy in general, actors may easily
find themselves in situations in which the optimal outcome for one side
does not align with the optimal outcome of another side. In more
extreme cases, the optimal solution for one side may not only misalign
with that of the other side, but may actually be harmful to the other
side. In global diplomacy, this model demonstrates diplomatic rivalry
and, when misalignment increases sufficiently, the origins of a war.
The potential misalignment of incentives predicted by the Theory of
Parallel Rationality implies that situations may exist in which the
best decision of countries is not to cooperate or seek a peaceful
solution, for to do so would benefit the opposing side at one's own
expense. Depending on the circumstances, that can result in an extreme
form of a "prisoner's dilemma" game. Furthermore, such scenarios may
impose negative externalities on other countries, yielding a
sub-optimal societal outcome. The only solution is a bridge that helps
to align the incentives of the interacting countries to yield a more
optimal outcome for each interacting country and a more optimal
societal outcome for the world at large.

__References ____&
Suggested____
Reading__

Rutherford Johnson.
"The Choice Wave: An Alternative Description of Consumer
Behavior. *Research in Business and Economics Journal.*
Vol. 5. February 2012.

Rutherford Johnson. "Improving Police-Public Conflict Resolution
to Improve Sustainability Decision Strategy." Journal of Human Resource and
Sustainability Studies. Vol. 9. No. 4. 2021.

Rutherford Johnson.
"A Probabilistic Demand Application in the American Cracker
Market." *International Journal of Food and Agricultural
Economics*. Vol. 4. No. 3. 2016.

Rachel
Lundbohm & 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.

Rutherford Johnson.
"Choice Waves and Strategic Interaction." *Journal of
Technology Research.* Vol. 7. March 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.
" 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. 2017a.

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.

Kahneman, Daniel; and Amos Tversky. (1979)
"Prospect Theory: An Analysis of Decision under Risk." *Econometrica*.
Vol. 47, No. 2.

Rabin, Matthew. "Psychology and Economics." *Journal
of Economic Literature*. 1998.

Russell, Thomas, and Richard Thaler. "The
Relevance of Quasi Rationality in Competitive Markets." *American
Economic Review*. 1985.