The Choice Wave and the Theory of Economic Parallel Rationality were devised and developed by Pp. Rutherford Johnson, PhD, ALM, FRGS as a means to conceptualise behavioural influences on economic decisions and strategic behaviour. He holds a Master of Liberal Arts degree in Sustainability and Graduate Certificates in Business Communications, Social Justice, and Corporate Sustainability and Innovation from Harvard University Extension School, a PhD in Agricultural Economics from the University of Kentucky, a Master's degree from the School of Economics at Georgia Tech, and a Bachelor's degree with honor in Applied Physics, also from Georgia Tech. He was named a Fellow of the Royal Geographical Society in London in 2018. In addition to being a clergyman and career academic, he was President and CEO of ARRCC, Inc. from 2008-2019, an international charitable and humanitarian non-profit foundation in consultative status with the United Nations Economic and Social Council. He still serves on the Board of Directors. His primary languages are English, Italian, Spanish, and French. A qualified mariner, he enjoys sailing and travel (particularly by sea), and is a former high-altitude mountaineer.

What are the Choice Wave & Parallel Rationality?

Have you ever been confident in your ideas or preferences, but been told by others that you're wrong or crazy? You don't feel wrong...or crazy, do you? Economists for generations have been saddled by the theory of classical rationality. Models are based on "economics man," who maximises utility according to a set of clearly-defined rational principles. Then behavioural economists such as recent Nobel laureates Richard Thaler and David Kahneman, as well as Matthew Rabin, Amos Tversky, and others, noted that there is a psychological aspect to economics (Rabin, 1998). The concept of "quasi-rationality" was developed in which individuals may deviate from classical rationality, causing outcomes that differ from those predicted by standard economic models (Russell and Thaler, 1985; Kahneman and Tversky, 1979). That work suggested the common-sense piece that had been missing from economics - that people are indeed different. Yet, who is to decide what constitutes rationality vs. quasi-rationality? And how to those different groups of people behave differently? How should they be treated? A different perspective is needed to improve understanding of our economy and the people in it as we seek a sustainable future. Parallel rationality helps to do just that and can be applied not only to economics, but decision strategy, international diplomacy, environmental policy, social justice, and more.

Enter the Choice Wave.

The Choice Wave, as it came to be called, was derived by Rutherford Johnson 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. 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, maximises 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 maximises 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 Up(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, ψA and ψB. 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 maximise 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).

(See articles and suggested reading at the bottom of this page.)


Multipoint Gravitational 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, nA and nB are terms representing strength of influence for players A and B respectively, hA and hB 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" maximise 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.

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.

Article in Qrius (formerly the Indian Economist)

Article in the Newsletter of the Royal Economics Society

(See more articles and suggested reading at the bottom of this page.)


Parallel Rationality and the Economics of the Overview Effect

Pp. Rutherford Johnson and
Frank White, AB, MPhil, developer of the Overview Effect
at the Harvard Faculty Club.
A concept that has proven quite compatible with parallel rationality is the Overview Effect. Developed in the 1980s by Frank White, AB, MPhil, the Overview Effect is a cognitive shift experienced by astronauts after being in space and seeing the earth from a broad overview perspective. The cognitive shift then results in modifications to decision strategy and behaviour on earth. For example, those who have experienced the Overview Effect often report seeing the earth less in terms of borders and more in terms of interconnected humans. There are also "overview analogue" experiences that can lead to similar outcomes without going into space. The Overview Effect has become a key philosophical component of sustainability and can be useful in the investigation of economic situations that cross national and cultural lines. It may not only help provide interesting insight into situations, but also may be useful in providing suggested solutions.

Article on Space Philosophy site,

Article in Qrius (formerly the Indian Economist)

Article in Psychology

Article in the Journal of WEI Business & Economics

Article in the Journal of Religion and Business Ethics

(See more articles and suggested reading at the bottom of this page.)


Sustainability Economics

Growth and sustainable development are not necessarily the same thing. They can be at odds with each other, or they can be two sides of the same coin. Sustainability is the ability to be successful today without damaging the ability of oneself or others to be successful in the future. Growth can take place in a sustainable fashion, or it can work in a way that is counterproductive to sustainable development.

One type of growth facing the world now that may easily impact sustainable development in a negative way is population growth. The population of nations and of the world is clearly on the rise. Yet, whether that is sustainable in the long run or not depends on a number of factors. For example, the resources of the world are scarce (a basic tenet of economics) and unevenly distributed. Furthermore, the population itself is not evenly distributed. Urban areas, with their concentrations of opportunities, etc., have been major population centres particularly since the shift from agrarian society to urban life in the Industrial Revolution. Although that often brought opportunities for those who moved to town, and industrial advances in agriculture resulted in lower labour requirements, it also created additional problems. One such problem was that over time more and more people began to use the scarce resources in geographically small areas, while the resources in less populated areas were used less - at least in terms of basic living, not counting use of resources in remote areas for the benefit of those and populous areas. If the carrying capacity of an area, whether urban or rural, is exceeded, then it is not a sustainable situation in the long-run.

Humanity seems to have both a capacity for growing without concern to long-term sustainability and a remarkable but unsurprising ability to seek solutions out of a sense of self-preservation. Unlike actual sustainable development, that ability is almost instinctual and typically very focused individually or on a small scale. For example, a booming population on the island of Manhattan left the New York boroughs with nowhere else to put people. Technological advances that accompanied the Industrial Revolution (which is, along with the immigration wave taking place around the same time, arguably one of the biggest reasons for the population increases as people moving to the city for jobs) allowed for the city to build upward when it could not build outward. The latter half of the 20th century saw growing dissatisfaction with the city "rat race," leading to those who were able to move to the suburbs or smaller cities doing so. Neither approach fully addresses the concerns of sustainable development. For example, moves to suburbs often further accentuate economic disparity among allocation of resources, though not exclusively so. Suburbs themselves likewise are not often considered to be efficient and sustainable.

It seems clear that sustainable development is a process not likely to happen if people are simply left to their own devices. The invisible hand of Adam Smith might work in markets (though that is also up for debate), but it does not seem to be very likely to succeed in long-term sustainable development, particularly as the world population and population density increase. Coordination rather than individual efforts are needed for effectiveness. Yet, what should be the driving force and the main concern? Who should make the decisions?

In the growing world population, there are many stakeholders. A simple Keynesian-esque economic approach in which government dictates population behaviour seems an overly-simple solution to a highly complex problem and one that is very likely to fail. Furthermore, the problem is global rather than national. On the macro level, nations could easily seek their own benefit at the expense of other nations, which only exacerbates the problem. On the micro level, states/provinces or even communities in companies could seek their own benefit at the expense of others. That is what history shows, though it is not necessarily an indictment of human nature. It is not surprising or unreasonable that, in the absence of an impetus towards cooperation, even civic minded and compassionate nations, companies, and individuals will seek to help themselves and "their own" first. Game theory also suggests that the possibility for the other side of the transaction to renege on an agreement makes actors less likely to cooperate in a manner that will yield the best outcome for all parties concerned. That same game theory which applies to military and diplomatic interaction between nations is surprisingly useful for sustainability negotiations and decisions. Thus, something is needed that balances the various concerns of the diverse groups of stakeholders.

And who are these stakeholders? In the abstract, of course, every individual is a stakeholder. Given the vast world population, that is an impossibly finally parsed set of stakeholders. Something more manageable is clearly needed.

One manner of defining stakeholders is to look in the abstract at the various aspects of sustainable development. For example, atmospheric environment, the oceans, land environment, sustainable food sources, land/real estate sustainability, and the population itself. Another matter defining stakeholders is to consider different subdivisions of the population, segmented by region, degree of sustainability problems, political system, available natural resources, and economic situation. Combining those two systems could allow for a robust description of interacting influences and competing interests. From there it becomes a constrained optimisation problem towards an efficient and equitable outcome. The problem is one that requires significant mutual cooperation to have a hope of being successful. That cooperation needs joint top-level guidance and oversight since individual uncoordinated efforts are unlikely to have much impact on the system overall. Without coordination, cooperation is likely to deteriorate due to strategic games.

When seeking to optimise an efficient and equitable system of sustainable development, one approach is to determine groups of actors behaving in parallel rationality. That is, certain sets of stakeholders may exist that have similar goals, needs, beliefs, etc. within their own set, but are very highly distinct from other groups of stakeholders. If such divergence exists, then the decision strategy of any given set of stakeholders is non-interacting with the decision strategies of all other distinct sets of stakeholders. In that case, strategic games leading to sub-optimal outcomes are more likely, and governance of sustainable development would do well to consider the distinct strategic processes of the sets of stakeholders when attempting to find common ground, develop policy, and implement action. Strategic policy at the governance level should seek "bridges" that attempts to reconcile divergent points of view and differing strategic goals among actors.

Ultimately, in seeking coordination to avoid game-related sub-optimal outcomes, the goal of such bridges could be to move towards an "overview" approach to sustainable development. That approach, derived from the Overview Effect, involves seeing the world as a whole metaphorically from the outside rather than thinking only of our individual position on the globe. In such a framework, national boundaries still serve a purpose on the micro level, but on the macro level they essentially disappear as people from all nations and cultures come together to work towards a common long-term sustainable development goal. That is easier said than done, of course, since a true overview experience can only be obtained by going into space and looking back at the earth, and thus one must be an astronaut. Yet, it is possible to learn from others who have experienced the overview effect and apply what it teaches to government and corporate policy. Whether people will listen and inwardly digest is another matter. Likewise, whether governments will adopt cooperative policies in accordance with the overview effect is entirely unclear.

At least in the short term, governance of sustainable development will likely need to take into account the strategic processes in the transactions between various actors. In order to be successful, treaty-based international cooperation and oversight is needed. The voices of stakeholders need to be heard, and those voices include the diverse perspectives not only of populations, companies, and governments, but of NGOs that focus on the various areas of concern in sustainable development. If the process working towards a sustainable future is based only on a few select opinions and agendas, then a sustainable outcome is much less likely if even possible at all. Ultimately it is an effort that is both coordinated and universal that is needed in order to ensure that growth does not hinder sustainable development, but rather is in harmony with it. Rather than restricting freedoms, if done correctly, this should maintain or even increase freedom through reducing the strain on scarce resources. It is perhaps an idealistic outcome, but it nevertheless worth pursuing, for even a partial success would be a step in the right direction.

Article in the Grand Forks Herald

Article in Modern Economy

Article in the Journal of Applied Business Research

References & Suggested Reading

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

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

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

Rutherford Card. 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 Card. 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 Card. Johnson. "A Spatial Application of Choice Waves: Decline in Church Giving in the United States during the Recession." Journal of behavioural 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.

Rutherford Card. Johnson. "The Psychology of the Overview Effect and Global Economic Ethics." Psychology. Vol. 9. No. 7. July 2018.

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