4D Economics

The systemic and severe myopia of economists is something that has bugged me ever since I started learning about the topic in high school. I took some economics and finance courses in college but abandoned finance after the 2008 financial crisis woke me up to the fact that most experts in that field really have no idea what they are talking about or what they are doing.

I took some time off from college to try and figure out what I really wanted to do as a career that was not finance/econ related, and for some years I worked for a startup B2B software company in sales. I was ok at it, but the job mostly consisted of berating customers into sending us money for something they didn't really want to use but were obligated to by their business partners. In 2014 I decided to study accounting because it didn't seem too hard and most people I talked to suggested I get a "numbers based" degree for the sake of my career. I didn't really like it and to this day anything tax law related will instantly put me to sleep.

While studying accounting in early 2015 shortly after my thyroid was removed in two surgeries, I began to experience acute (severe) psychosis, of the kind where I thought I was normal and everyone else in the world was working against me somehow. There were definitely levels to the kinds of delusions I experienced, I won't detail how intense they were here because I'm trying to type about economics, but I will say they caused me to be hospitalized against my will twice in the summer of that year.

Two years later in 2017 I was slightly more stable on a weak antipsychotic that wasn't really effective for the type of psychosis I had, I was still in quite a deep level of delusion at the time I began writing my 4D Economics paper in 2017. I'm pretty sure it took me less than a month to write, part of that month was some kind of fever dream of delusion, but when my delusions weren't in control of me, I found the time to type furiously for days and nights with the goal of proving how ignorant most economists are.

This hopefully gives some context as to why what I wrote in the paper is somewhat sophomoric and parts are under-researched. It's about 16 pages long, and I just re-read the whole thing tonight after not looking at it for eight years. I haven't revisited it in so long because I didn't feel like there was a point in trying to share its insights while everyone in the world had their brains closed off to anything they deemed 'crazy'. Now that the times themselves are crazy, maybe (hopefully) people will be more open to its arguments.

In my reading of the paper tonight I was actually pretty surprised how right I was about everything I wrote. I pointed out some major flaws in accepted theory and everyone ignored it, probably because the way I wrote it was a little over-the-top and it was written by a literal 'nobody' who didn't have an economics degree from a fancy school where you're taught all the wrong things about what is important in life and the world.

Here is the paper in full, minus the footnotes:

4D Economics

A critique of modern reasoning: Re-examining the foundations of economic theories.

Abstract: This paper uses enframing (Gestell) to reconcile Rational Choice Theory with Behavioral Economics by looking at how humans make decisions under extreme or unusual circumstances. It demonstrates the inadequacies of Expected Utility Theory and Prospect Theory by pointing out that gains and losses cannot be valued independent of the circumstances in which they occur, and that most prospective gains and losses are compound prospects – gains can generate more gains in the future, and the same is true for losses. Gains, losses, and choices must be framed in the contexts in which people live. By reframing people’s decisions with regard to their goals and desires and recognizing that people are investors as well as consumers (many consumption decisions can be reframed as investment decisions), one can demonstrate the economic rationality of purchasing lottery tickets with extremely low probabilities of very high payouts. It then briefly examines the ethical and policy implications of this finding.

Making life or death decisions is a fundamental aspect of the nature of all animals, and the global population of humans is evidence that we are quite adept at making those types of decisions. Much of behavioral economics and expected utility theory focus too much on using the monetary outcomes of relatively small and insignificant wagers to explain attitudes toward risk. Modern economics tends to over-rely on shaky foundations such as:

1. The marginal utility of money, in the view of many theorists, usually decreases with each successive dollar gained.

2. Over-analyzing the statistical or mathematical outcomes of decisions with very little regard to the environments in which those decisions were made.

3. Leaving time out of (or using improper time frames in) their “utility” and “expected value” functions.

4. Analyzing the probability of some negative outcomes while ignoring the one massive negative outcome that has a 100% probability of occurring, death, as well as other negative outcomes, like the daily negative utility of continuing to live a miserable life.

5. Reluctance to analyze what it is people truly value (Why is everything a monetary gain or loss?).

4D Economics seeks to place the foundations of economics in the context of the observable world, that is, in space-time. Too many theorists evaluate decision making under risk without attaching much real risk to the situations, then draw conclusions about their risk preferences without asking what people desire. They also tend to analyze the outcome of events far too statically, ignoring the fact that all events, especially significant ones, set off event cascades. To step away from overly simple Bernoullian analysis, one must use four-dimensional situations such as this:

4D Situational Risk, Example 1:

Grace, a fast food worker, wants to quit her job and open her own business selling food from a cart on the street. She currently has $500 in her bank account, and needs a total of $1000 to buy a food cart and other business supplies. Her financial situation is precarious, rent is due soon, and she doesn’t know if she will ever be able to save up enough money to buy the cart, given that many random unexpected expenses occur throughout the year.

A university researcher meets Grace, and offers her a choice of two different gambles.

A. An 85% chance to win $1000, and 15% chance to win nothing.

B. A 100% chance to win $800.

Which would Grace pick, if she had only one chance to take this bet?

If you remove her particular circumstances from the equation, then from the perspective of mathematics and statistics option A is the better one, as it has the higher Expected Value (EV). But in Grace’s life option B dominates A, because B offers her a certain opportunity to make more money in the future. Bernoulli, Kahneman, and computers may say that Grace’s choice of option B is risk-averse, but Grace’s decision is more future oriented than their analyses suppose, and is both risk-seeking, given that she can’t know for sure whether her food cart business will be successful, and risk averse, in that she desires the assurance of avoiding the negative outcome of having to keep working at her current job. The standard definition of EV is somewhat irrelevant here, as Grace is only forgoing an extra $50 of “EV” in order to gain a considerable amount of autonomy.

Ludwig von Mises argues against the “subjective theory of value”, he was a supporter of the “classical” theory of value. The ironic thing is that he makes a magnificent case for evaluating decisions in context, which was the opposite of his intention.

von Mises: "For a long time men failed to realize that the transition from the classical theory of value to the subjective theory of value was much more than the substitution of a more satisfactory theory of market exchange for a less satisfactory one. The general theory of choice and preference goes far beyond the horizon which encompassed the scope of economic problems as circumscribed by the economists from Cantillon, Hume, and Adam Smith down to John Stuart Mill. It is much more than merely a theory of the "economic side" of human endeavors and of man's striving for commodities and an improvement in his material well-being. It is the science of every kind of human action. Choosing determines all human decisions. In making his choice man chooses not only between various material things and services. All human values are offered for option. All ends and all means, both material and ideal issues, the sublime and the base, the noble and the ignoble, are ranged in a single row and subjected to a decision which picks out one thing and sets aside another. Nothing that men aim at or want to avoid remains outside of this arrangement into a unique scale of gradation and preference."

The brief insight of the above statement is in his criticism of how these values are “ranged into a single row”, which is comparable to Kahneman and Tversky’s value function. If Grace values fulfilling the desires of her inner capitalist, or donating money to charities, where does one draw the line between subjective and objective, and why should it matter?

Unfortunately, von Mises made an error in that he declared human desires complex and difficult to describe, and then rejected any attempt at describing their desires as outside the scope of economics. (von Mises 1949)

Anyone who’s ever wanted anything that will improve their life circumstances is essentially a capitalist at heart. If money can be exchanged for capital and vice versa, then the notion that money is not in some cases equal to capital is false. For a professional poker player, money almost always equals capital, as having more of it allows them to play higher stakes games, and potentially vastly increase their income.

The term Capital is currently used so broadly that it’s difficult to know what people mean when they use it. Because what people think of as capital is essentially a subset of any object or circumstance that will positively impact the subjective value of their own well-being, and this paper seeks to greatly expand the economic frame of reference, I will define significant positive gains in objects or circumstances as C.R.E.A.M., but because periods and capital letters aren’t convenient to type, one can simply call it Cream.

Definition: Cream

Any good or service which produces an objective or subjective improvement in life circumstances over the medium or long term.

4D Choices, 4D Values, and 4D Frames

Daniel Kahneman and Amos Tversky’s 1984 paper “Choices, Values, and Frames” begins by stating “We discuss the cognitive and psychophysical determinants of choice in risky and riskless contexts.” They go on to introduce “Risky Choice”:

"Risky choices, such as whether or not to take an umbrella and whether or not to go to war, are made without advance knowledge of their consequences. Because the consequences of such actions depend on uncertain events such as the weather or the opponent’s resolve, the choice of an act may be construed as the acceptance of a gamble that can yield various outcomes with different probabilities. It is therefore natural that the study of decision making under risk has focused on choices between simple gambles with monetary outcomes and specified probabilities, in the hope that these simple problems will reveal basic attitudes toward risk and value."

4D Economic theory rejects the assumption that the findings of studies such as Pleskac & Hertwig (2014) that involve small gambles offer much insight to people’s risk preferences. Offering a college student various ways to win $10, $20, or $50 tells us nothing about how they would behave when their life or their dreams are at stake, or as one might say, no Cream is on offer. In order to gain insight into people’s true preferences, one must raise the stakes, i.e. pick a bigger weapon.

Many of Kahneman’s writings demonstrate his awareness of the problems of analyzing decisions with small stakes, but unfortunately he has not yet, to my knowledge, followed through in analyzing the consequences these problems pose for decision theory. In the same 1984 paper, Kahneman and Tversky (hereafter referred to as K&T) stated:

"It is customary in decision analysis to describe the outcomes of decisions in terms of total wealth… This representation [of small gambles] appears to be psychologically unrealistic: People do not normally think of relatively small outcomes in terms of states of wealth but rather in terms of gains, losses, and neutral outcomes (such as the maintenance of the status quo) … If the effective carriers of subjective value are changes of wealth rather than ultimate states of wealth, as we propose, the psychophysical analysis of outcomes should be applied to gains and losses rather than to total assets. This assumption plays a key role in a treatment of risky choice that we called prospect theory (Kahneman & Tversky, 1979). Introspection as well as psychophysical measurements suggest that subjective value is a concave function of the size of a gain."

The proposition that only changes in wealth and not states of wealth affect subjective value is dubious. Also, “states of wealth” are always in constant flux, so an “ultimate” state of wealth is difficult to define.

K&T’s mistake was not in their attempting to point out the flaws in expected utility theory, but that they didn’t go far enough in their analysis of just how deeply flawed it is. Why do they rely on introspection when proper analysis requires extrospection? Why do K&T spend almost their entire 1984 paper analyzing risk preferences of people via their choices on small wagers? For as many times as the paper speaks of “framing effects”, there are almost no examples framed with stakes sufficiently high enough to significantly affect people’s state of wealth or total assets.

Their 1979 paper “Prospect Theory, an Analysis of Decision Under Risk” states: “The manner in which complex options, e.g., compound prospects, are reduced to simpler ones is yet to be investigated.”

The main fault in both Expected Utility Theory and Prospect Theory is that they don’t recognize the fact that every prospect is a compound prospect. If it takes money to make money, then any significant gain in wealth could be used to generate more wealth in the future. Therefore, it is inherently impossible to accurately assess any decision independent of the person, place, and time in which the decision was made.

K&T: "Although prospect theory predicts both insurance and gambling for small probabilities, we feel that the present analysis falls far short of a fully adequate account of these complex phenomena. Indeed, there is evidence from both experimental studies, survey research, and observations of economic behavior, e.g., service and medical insurance, that the purchase of insurance often extends to the medium range of probabilities, and that small probabilities of disaster are sometimes entirely ignored. Furthermore, the evidence suggests that minor changes in the formulation of the decision problem can have marked effects on the attractiveness of insurance. A comprehensive theory of insurance behavior should consider, in addition to pure attitudes toward uncertainty and money, such factors as the value of security, social norms of prudence, the aversiveness of a large number of small payments spread over time, information and misinformation regarding probabilities and outcomes, and many others." (K&T, 1979)

K&T state that the complexity needs to be investigated, but do not sufficiently investigate the complexity. Instead of focusing solely on the “range of probabilities”, they should have examined the range of contexts and time frames in which decisions are made.

K&T state in “Advances in Prospect Theory” 1992:

"Theories of choice are at best approximate and incomplete. One reason for this pessimistic assessment is that choice is a constructive and contingent process. When faced with a complex problem, people employ a variety of heuristic procedures in order to simplify the representation and the evaluation of prospects. These procedures include computational shortcuts and editing operations, such as eliminating common components and discarding nonessential differences (Tversky, 1969). The heuristics of choice do not readily lend themselves to formal analysis because their application depends on the formulation of the problem, the method of elicitation, and the context of choice. Prospect theory departs from the tradition that assumes the rationality of economic agents; it is proposed as a descriptive, not a normative, theory. The idealized assumption of rationality in economic theory is commonly justified on two grounds: the conviction that only rational behavior can survive in a competitive environment, and the fear that any treatment that abandons rationality will be chaotic and intractable. Both arguments are questionable. First, the evidence indicates that people can spend a lifetime in a competitive environment without acquiring a general ability to avoid framing effects or to apply linear decision weights. Second, and perhaps more important, the evidence indicates that human choices are orderly, although not always rational in the traditional sense of this word."

It is true that choice is a “constructive and contingent problem.” The failure of decision theories is that to date, few people have taken the time to examine all the contingencies. Every complex problem is a “compound prospect”, but because people don’t always seem to make decisions that maximize “(mathematical) expected value”, scientists assume that people are over-simplifying the prospects by taking mental shortcuts. However, if these complex problems are more thoroughly evaluated in four dimensions, it can be shown that in many cases people are making rational decisions even though those decisions appear from a narrow mathematical point of view to have negative expected value.

Prospect Theory refers to compound prospects (or events) as sequences of prospects, one following the other. The argument 4D Economics makes is that a (significant) single event is not, in time, a single event. If you gave a 21-year-old fast food worker an 80-story office building in Manhattan, you’re giving them a lifetime of multi-million dollar checks in the bank. The subjective value to them of that outcome is almost incalculable, and certainly much higher than the list price of the building. The idea that significant events are compounding is not new, it is the idea behind compound interest. One must examine the event cascades people are aware of to better understand human decision making.

Leonard Savage, in his 1954 book “The Foundations of Statistics”, defined an event as “a set of states.” Savage discusses the difficulty of enumerating the states of the entire world, and the problems this poses for decision theory. On page 92 he discusses Daniel Bernoulli’s paper:

"Bernoulli begins by reminding his readers that the principle of mathematical expectation, though but weakly supported, had theretofore dominated the theory of behavior in the face of uncertainty. He says that, though many arguments had been given for the principle, they were all based on the irrelevant idea of equity among players."

The idea of players having unequal starting points grounded much of the empirical evidence for the theory of diminishing marginal utility. Savage continues on page 94:

"[Bernoulli] admitted that the possibility of examples in which the law of diminishing marginal utility, as it has come to be called in the literature of economics, might fail. For example, a relatively small sum might be precious to a wealthy prisoner who required it to complete his ransom. But Bernoulli insisted that such examples are unusual and that as a general rule the law may be assumed."

In 4D economics, examples where utility does not diminish on the margin are not rare, due to event cascades, or what is commonly known as “the butterfly effect”. The common economistic observation that utility diminishes “on average” is only true in some frames, “rare” events occur very often. The problem with thinking too much in terms of statistics was well identified by Nassim Taleb in his book “Black Swan”. These rare events happen often enough in the macro-economy, but they occur far more frequently in each person’s micro-economy. The knowledge that today “on average” you won’t die in a car crash isn’t very helpful if you do, hence we have seatbelts, airbags, and hundreds of other vehicle safety laws. The average value of the SIN(X) is zero, but the average doesn’t tell you much useful information about the nature of a sine function. The average day on earth sees fewer than one 100-kilometers in diameter asteroids smashing into it, therefore we should all eat, drink and be merry.

Savage briefly discussed this on page 97 in terms of statistical variance but seemed to dismiss its implications:

"Why should not the range, the variance, and the skewness, not to mention the countless other features, of the distribution of some function join with the expected value in determining preference? The question was answered by the construction of Ramsey and again by that of von Neumann and Morgenstern, which has been slightly extended in sections 2-4; it is simply a mathematical fact that, almost any theory of probability having been adopted and the sure-thing principle having been suitably extended, the existence of a function whose expected value controls choices can be deduced. That does not mean that as a theory of actual economic behavior the theory of utility is absolutely established and cannot be overthrown. Quite the contrary, it is a theory that makes factual predictions many of which can easily be observed to be false, but the theory may have some value in making economic predictions in certain contexts where the departures from it happen not to be devastating."

4D economics seeks to overthrow utility theory as understood since Bernoulli, by observing that too many of its predictions are observably false, that it is only useful in very narrow contexts, and that the departures from it are utterly devastating. Because much of prospect theory is based on expected utility theory, many of K&T’s findings must also be re-examined in various contexts.

From a 4D perspective, K&T’s assumption that people evaluate monetary gains mostly in terms of changes of states of wealth and not in ultimate states of wealth or assets is, again, extremely problematic. More importantly, why would any person seek to acquire “the general ability to avoid framing effects” when their ability to frame decisions is essential for their survival? In reality, people are hyper-aware of the frames in which their decisions are made. A key problem with K&T’s theory is that they assume the frames in which K&T state the problem are the only frames which the subjects of their experiments are paying attention to.

A somewhat more accurate version of K&T’s value function:

The function is non-continuous at the points where increased or decreased access to Cream is obtained or lost. The marginal value of monetary gains in each continuous segment has a decreasing slope (concave), but the marginal value of each successive access to Cream is an approximate exponential function of the gain (convex). I do not claim that this graphical representation is accurate in any place or time frame, it is meant only to illustrate complexity and show how to begin to deconstruct K&T’s S shaped value function. A better value function would be an animated visualization of a balance sheet and chart of accounts, with sub-accounts for everything a person values, such as their children’s education, family and partner’s happiness, etc.

Social scientists would do well to further investigate why human choices are orderly, and stop assuming that their decisions do not exhibit consistent risk preferences because they don’t maximize expected value where time equals one day or one year. If we neglect to expand time horizons and leave people’s perceived negative utility of the status quo out of our utility functions, we will never accurately model human decision making.

Indeed, it’s possible that Kahneman may agree with the preceding assertion, as he paraphrased Gary Becker in his book Thinking Fast and Slow:

"[Gary Becker] was making a valuable point: when we observe people acting in ways that seem odd, we should first examine the possibility that they have a good reason to do what they do. Psychological interpretations should only be invoked when the reasons become implausible… (Kahneman, 2011, p. 412)"

Edward McCaffery touched on the inherent complexity of the interpretation of prospects in “Why People Play Lotteries and Why It Matters” 1994:

"Except for the occasional Silas Marner or King Midas, who enjoys the look, feel, and smell of money itself, most people do not want money per se. They want the things that money can buy."

Carl Menger wrote essentially the same thing in his book, Principles of Economics, 1871:

"It is true, as we have seen, that the importance of goods to us with respect to a direct employment and with respect to an indirect employment for the satisfaction of our needs are only different forms of a single general phenomenon of value. But their importance to us may simultaneously be very different in degree in the two forms. A gold cup will undoubtedly have a high exchange value to a poor man who has won it in a lottery. By means of the cup he will be in a position (in an indirect manner, through exchange) to satisfy many needs that would not otherwise be provided for. But the use value of the cup to him will scarcely be worth mentioning at all."

4D Economics extends this basic idea by emphasizing the importance not only of the time value of money, but the time value of everything. If money can, over time, be employed to generate more money, and debt over time will generate more debt, then any decision theory which ignores these facts and attempts to collapse the time in which outcomes obtain their value as close to zero as possible will fail to accurately describe the way in which the majority of complex decisions are made.

McCaffery, again (1994):

"Perhaps the strongest message to come out of our inquiry is simply this: the consumer is a complex being. Fitting all of her actions into a single continuous graphic representation, or assuming that she is persistently risk averse, may be an improper and even dangerous theoretical conceit. Writing off major aspects of her activity to stupidity or craziness may be even worse. We ought to begin to unite the various intellectual disciplines in pursuit of a deeper theory of the consumer, one that presumes her rationality in the first instance, and that rests more on respectful observation than on a priori theory."

The intention of this paper is to begin to lay the foundation of 4D Economics. McCaffery’s 1994 paper should be considered the cornerstone. It examines previous theories of why people play lotteries in much more depth than is covered here. McCaffery had the correct intuitions and conclusions, but he, as did all the writers on the subject (that I am aware of), did not discuss the consumer/investor duality of people’s nature. He did however call for a deeper theory of the “consumer”, and that is what 4D Economics seeks to provide.

Kahneman, in Thinking Fast and Slow, gets to the crux of the issue by emphasizing the importance of time:

"The rules that govern the evaluation of the past are poor guides for decision making, because time does matter. The central fact of our existence is that time is the ultimate finite resource, but the remembering self ignores that reality. The neglect of duration combined with the peak-end rule causes a bias that favors a short period of intense joy over a long period of moderate happiness" (Kahneman, 2011, p. 409)

It’s unclear to me what evidence or studies which Kahneman is basing the claim that “the remembering self ignores [the fact that time is the ultimate finite resource]” on. This is a quite surprising claim because so much human action throughout the course of history contradicts it. If people are always so focused on short periods of intense joy, why do so many of them read (sometimes very boring) books in order to better educate themselves?

Given that money can be used to obtain sexual partners, children, happiness, longevity, higher degrees of freedom, and businesses that generate more money, it is apparent that economists and statisticians have for years been making fallacious arguments that the expected value of low probability gambles such as lotteries is negative. If a well invested $10 million after-tax lottery win has an objective value of $40 million over the next 50 years, it could easily have a subjective value to the winner of greater than $500 million. (The fact that lottery winnings are not always so well invested has been well covered by others, and is not within the scope of this paper.)

J.S. Flemming’s 1969 paper “The Utility of Wealth and the Utility of Windfalls” began to look at these types of decisions in a broader context, but his, Menger’s, K&T’s and Expected Utility Theory analysis suffers from the flaw of treating people as consumerbots, seeking only to maximize their own utility over discrete periods of time. In reality, almost all people are both consumers and investors. If we do not assess the motivations and impacts of their investment decisions and opportunities, we will not be able to fully understand the choices they make.

Decision Making With Knowledge of Certain Death

Kahneman, in Thinking Fast and Slow wrote: “But life is more complex for behavioral economists than for true believers in human rationality.” (Kahneman, 2011, p. 412)

It’s true that life is very complex, the question is why so few behavioral economists have delved deep enough into its complexities. To illustrate where previous decision theories falter in their analysis of complexity, it helps to look at extreme scenarios.

4D Situational Risk Example 2: Mega-lottery

In the simplest case, almost no math is needed to show why a person might play the lottery. Consider this scenario:

A ship sailing through the Pacific Ocean encounters a rough storm. A pianist on the ship, Lang Lang Crusoe John (LLCJ for short) is thrown from the deck into the sea, floats onto an island where there are trees to catch some shade, plenty of fresh water, but the only food source is fish. LLCJ needs an average of five fish per day to survive, it takes about 15 minutes to catch one fish, and it has never taken him more than half an hour to catch one fish.

An omnipotent actor, let's call her Alanis, appears before LLCJ and offers a wager: Robinson can risk one fish for a 2 in 1000 chance to win 2000 fish. A computer with infinite fish might take this gamble knowing that it has a positive expected return, but few people can afford to take that bet enough times for it to pay off once, and even if they do, they don't need 2000 fish, assuming they don’t have a way to keep them from rotting two days after getting them.

But a mega-lottery is a wager so different in magnitude that it differs in kind. For what Alanis is offering with a mega-lottery wager is not a 1 in 300 million chance to win 100 million fish, the wager is a 1 in 300 million chance to be teleported to a new house in Pacific Heights, San Francisco, be given another house in Lake Tahoe, a nice yacht near each house, several nice cars, an attractive partner, as many kids as he wants, the opportunity to send his kids to any school he wishes, for his children, their children, their children's children, to have the opportunity to pursue rewarding careers of their own, the ability to help people he knows and loves make it through tough financial situations, the ability to start a company of his choice, the ability to be remembered long after he dies for being a good person, and the opportunity to once again inspire people by playing the piano for them.

Alanis told LLCJ that because she is omnipotent, there is zero chance that he will escape the island via any method other than the wager she offered. LLCJ not only knows that every day on the island carries a much greater risk of death than an equivalent day spent in the city of his choice, but also that he will almost certainly die before winning Alanis’ mega-lottery.

Given this situation, one might expect that LLCJ would wager as many fish as possible, until he was no longer physically able to fish. An economist might counter that if LLCJ values his leisure time at all, he should spend more time enjoying the island, after all, he’s got the sun in the morning and the moon at night, so he shouldn’t take Alanis’ wager to try to escape his condition.

Stated logically: If a person has a goal that requires a large amount of money in order to achieve and the only way to obtain that amount of money is to play the lottery, then there is a strong chance that they will play the lottery.

Lloyd Cohen came to the same conclusion in a 2001 paper titled “The Lure of the Lottery”: "Those people who have fewer plausible dreams and paths to fulfilling those dreams will, ceteris paribus, play the lottery more frequently."

Obviously, most people do not live in a Crusoe economy, but many people's lives share some similarities. If one examines the mathematical implications of the data gathered in Michael S. Barr's "No Slack" on low and middle income people’s net assets over time, it is clear they are intensely aware of the stochasticity of their income and expenses, as well as the probabilities of future shocks to their budget. Among the Low-Middle Income (LMI) households Barr studied, he found that:

"Nearly 30 percent of the sample respondents have monthly expenses that exceed their income during most of the year… The median debt burden among LMI households, excluding home and automobile, is $500, and the mean debt outstanding is more than ten times that amount. Looking forward, a significant portion of households (37 percent) anticipates a major expense over the next five to ten years for which they are unable to save."

Why save $2 per week, or $104 per year, if you know that there is a very high probability of you owing someone $2000 that you do not have at some point within the next two years? Because their savings are so likely to be necessarily liquidated in order to pay for a likely major expense, the utility of saving small amounts of money is greatly reduced, and buying small amounts of lottery tickets that have nonzero potential to make a large material impact on their life is in some cases a rational choice. The case for buying lottery tickets is even stronger in light of the fact that the best way for them to save is through Social Security, because creditors do not have the ability to place an immediate claim on their SSI funds.

If a person makes enough money to feed themselves but doesn’t qualify for Medicaid, then every day they (and everyone else, but some people face worse odds) are essentially playing the death lottery, so they might as well also play the money lottery, which gives them a small chance of being able to afford medical care to prevent their early death. For this person, what is the marginal utility of two extra dollars in their bank account? Why spend it on chips or soda? What’s the point of saving $2 per week when what they need is $800,000? Certainly this is more rational than spending money on alcohol or Chanel handbags.

Kahneman might say that buying lottery tickets is a result of people overweighting small probabilities (K&T 1984, 1992), but a closer look at observed empirical data (Barr 2012) shows that people have well developed models of their own microeconomies in their minds. From a 4D perspective, people are not necessarily overweighting the small probability of winning the lottery, instead it is social scientists who are underweighting the value of winning the lottery.

In mathematical terms, if the marginal value of $2 per week approaches zero, and the value a person attaches to improving the circumstances of their life approaches positive infinity, then the purchase of a $2 lottery ticket once per week has positive expected value. The utility of $100 million dollars is so different from $2 that it’s misleading to even call both amounts dollars. $100 million is not equal to 100 million or less utility units (utils). From most people’s point of view, $100 million equals living a happier life and leaving a legacy that you consider important.

Buying lottery tickets, like many decisions people make, is very future-oriented. It is only irrational (in the sense that it has negative expected-value) or risk-seeking if you collapse time or assume the marginal value of money always has a decreasing slope. Humans are intensely time-oriented; we all know with certainty that we will die, which very few if any scientists put into their utility functions, and many of us make well thought out strategic long term plans.

There is probably a very good reason the Carnegie Endowment is named as such, as well as why the Chan Zuckerberg Initiative and Bill and Melinda Gates Foundation aren't named the "Save the World Initiative/Foundation", even though that is a better descriptor of their aims.

Why do we assume that poor and middle-class people don't also want to leave lasting legacies? Instead, we tell them to save $2 per week because then they could have $1040 after ten years, or $1500 if they invest it well. Twisting Keynes here, people are very aware that in the short run they have a higher risk of dying if they don't have $100k in the bank, or if they live in economically disadvantaged neighborhoods.

It is also important to note, as many researchers of the subject have (McCaffery 1994), that lottery play is not limited to people living in objectively dire circumstances. This is because a sizable lottery win can also help a middle-income person realize their dreams and desires. If there is a couple in their 60s who raised their daughter in Kent, Ohio, and their daughter had to move to Silicon Valley because the best job she could find was in Menlo Park, the couple might want to move closer to their daughter to help raise their grandchildren. Their problem is that few people who earned anything near the median income during their careers can afford to move to Silicon Valley in 2017. Winning the lottery might be the lowest risk way they have of being able to afford a house near Menlo Park. The fact that they know they almost certainly won’t win doesn’t matter too much to them, as it’s the only conceivable way for them to reach their goal. If they value helping to raise their grandchildren at something approaching positive infinity, then a lottery ticket has positive expected value.

Example 3: Underweighting Grace’s True Ambition

Thanks to the kind university researcher, Grace’s food cart business is doing decent business, but she can only save about $2000 per year. Now that she has more free time, she has been spending it reading about mathematics and applied logic. The year is 1945, and she thinks that she can vastly improve the way humans communicate with computers, but needs a university education to be able to make her contributions. She only needs $60,000 to live comfortably while attaining her degrees.

Omnipotent Alanis politely introduces herself and offers Grace a choice:

A: 100% chance to get $60,000

B. 98% chance to get $10,000,000 and 2% chance to get nothing

Grace is strongly tempted to choose option B, but she knows that almost all her goals in life can be met by choosing A. Some of those goals include letting others employ her contributions to computer science to end the Cold War years earlier than it otherwise would have, free millions of people from totalitarianism, and reduce the chance of worldwide nuclear Armageddon.

If Grace thinks there is even a 0.001% chance that her work could prevent mutually assured destruction, then she is not overweighting the risk of choosing option B, getting $0, and being unable to revolutionize computer science. As Kahneman wisely observed in Thinking Fast and Slow: "A moment can also gain importance by altering the experience of subsequent moments."

Policy Implications

If the rationality of purchasing lottery tickets becomes accepted as conventional wisdom, then many people might feel encouraged to spend more money on wagers they have almost no chance of winning. If people feel “rationally” compelled to purchase lottery tickets, as many people's observed behavior currently implies, then from an ethical perspective, it may be argued that we should limit jackpot size to $10 or $20 million. Lower jackpot sizes would probably have the effect of reducing some lottery play by people in the middle and upper middle-income ranges.

We should also consider setting lower limits on prize sizes to discourage people from thinking "even if I don't win the jackpot, I might win $2000", because $2000 (or $20) won't really help them achieve their main goal, which is to greatly improve their life circumstances. People who run lotteries are well aware that offering small and relatively useless prizes is a way to condition people to expect more wins in the future, and generate more lottery ticket sales.

One area of improvement might be to separate lottery games by non-overlapping prize sizes, so scratcher "A" might have prize sizes of $20 to $1000, "B" $1250 to $5000, etc. This might induce people to make "better" decisions by helping them to more carefully and clearly evaluate which game to play based on what their financial hope is. This could have the effect of driving more people to casinos where the odds could be worse, then less money would go to taxes, so those consequences would also need to be examined.

What the above three suggestions have in common is that they would reduce small prizes and roll those rewards into more frequent larger (than current) prizes. Assuming most people play the lottery with the hope of winning the larger prizes and not the smaller ones, this would give them more of what they want, without the unpleasant side effect of using small prizes that do not improve their life circumstances to train them to buy more lottery tickets.

Also, ban all lottery advertising.

A major initiative should be undertaken to increase people’s access to low or zero fee ERISA protected saving accounts are exempt from creditor claims. HSA and 401k accounts should be available to anyone, not just through employer managed plans. Just because one person’s job is better or different than another’s should not determine their eligibility to save money in an account (tax-free, in the case of HSA’s) that creditors will not have a claim on. This may not decrease lottery spending by more than a few percent, but I am unable to imagine many valid arguments against it, and surely it is a step in the right direction.

Conclusions

J. Doyne Farmer has argued that our understanding of technological evolution is pre-Linnaean. It is my opinion that our understanding of economics is pre-Copernican. Using an analogy where the only thing of value in our environment comes from water – fish – Adam Smith pointed out that groups of people can work together to more efficiently get fish out of streams. Henry George pointed out that when streams aggregate into larger rivers (towns and cities) they are even more useful, as they hold more fish and are navigable. John Maynard Keynes showed that we can put dams on rivers to better manage their flow and create our own lakes full of fish. Paul Krugman’s observation of how specialized industries tend to form agglomerations near each other was akin to pointing out that due to gravity, water flows into oceans. This was quite novel in 1991 because prior to the invention of advanced shipping and other technologies, few people knew what an ocean of commerce looked like. Current macroeconomic policy attempts to make fish farming more efficient in the hope that doing so will cause just the right amount of rainfall.

The field of economics needs to be re-thought in terms of who people are, what their goals are, and how they interact with their environment. Human behavior must be evaluated in time frames beyond what economists currently consider. Economic theory must cease focusing on people’s consumption preferences, and acknowledge the consumer/investor duality of all our natures. Economists have become the victims of their own focusing illusions, not realizing that many of the illusions they use to elucidate human behavior are illusion illusions.