John von Neumann Was a Big Fat Idiot

Since I know that almost nobody reads my articles, I feel quite comfortable in insulting geniuses. I am also comfortable that one of my heroes will never know that I totally poached his title.  Thank you, Al Franken! Keep up the good work in congress!  IF there happen to be any economists out there reading this, you know that John von Neumann is the economics analog to Albert Einstein.  For those of you who have never heard his name before, you should know that John von Neumann discovered the Mutual Assured Destruction equilibrium strategy for InterContinental Ballistic Nuclear weaponry, designed implosion lenses for the Manhattan Project, founded the field of study known as continuous geometry (developed from the algebra he invented), introduced stochastic computing and artificial intelligence to the world, and originated the concept of self-replicating spacecraft that could mine resources from an entire other planet.  In other words, we can credit him with much of the preservation and success of the free world.

He may yet turn out to be the savior (or ultimate destroyer) of all mankind. Seriously.  So, of course, he dabbled in economics a bit and, according to Wikipedia, “Von Neumann's functional-analytic techniques—the use of duality pairings of real vector spaces to represent prices and quantities, the use of supporting and separating hyperplanes and convex sets, and fixed-point theory—have been the primary tools of mathematical economics ever since.”  By many people’s accounts, John von Neumann was the smartest person who has ever lived.  So here’s why I think he was a big fat idiot.

In economics, one of his many major accomplishments is the definition of the “rational actor”.  Yes, John von Neumann was so incredibly brilliant he even designed the ultimate human being.  This uber-individual is the omniscient and omnipotent consumer, able to know all prices of every good everywhere and also know the exact amount of utility (the economics version of pleasure and/or well-being) each good would provide her. She knows exactly how much income she must make to purchase that set of goods, exactly how to go about making that much money, and exactly how to value her time on this planet in order to maximize her own utility, and then maintain that level of utility by optimizing her trade-offs among the options available in each moment of her life.  And this infallible automaton, the “Econ”, is engineered by integrating a set of five axioms, which John von Neumann defined.  Each rational actor, including you, dear reader, can, without error, determine their preferences with ordinal certainty through:

1. Completeness - People have well-defined preferences, and so you always know which thing or set of things you’d prefer when compared to another thing or set of things.  A critical feature of the way von Neumann defines “things”, however, is that these things might be of uncertain outcome.  In other words the “things” are probabilistic and so are most often referred to as lotteries.  But Econs can discern exactly what the odds are for any lottery and so can determine exactly which risks they’d like to take.  In math-speak: for any 2 gambles g and g' in G, either g is preferred to or is equivalent to g' or g' is preferred to or is equivalent to g.  Now we add that for any gamble in G, there exists some probability such that the decision-maker is indifferent between the "best" and the "worst" outcome. This may seem irrational if the best outcome was, say, $1,000, and the worst outcome was being run over by a car.  However, think of it this way - most rational people might be willing to travel across town to collect a $1,000 prize, and this might involve some probability, however tiny, of being run over by a car.  So the probability of collecting the prize plus the probability of dying, together, would create a “thing” in von Neumann’s world.  And an Econ can easily determine if collecting $1,000 is 99.999% probable and dying in car wreck on the way is 0.001% probable, or if collecting and dying in a wreck are each 50/50% probable (presumably based upon the Econ’s texting habits), and they can therefore easily determine what lotteries they prefer to others.  No problem, right?  Let’s move on to the next axiom now, shall we?

2. Transitivity - Preferences are consistent so that if you prefer one thing to a second thing and prefer a third to the second, then you prefer the third thing to the first thing.  This holds for sets of things as well.

3. Continuity - Some negligibly small change in the thing or set of things will not make you change your mind about your preferences. In math language this assumption states that the upper and lower contour sets of a preference relation over lotteries are closed.

4. Independence or Substitution - Irrelevant events or outcomes do not change your preferences. This means that if a decision-maker is indifferent between two possible outcomes, then they will be indifferent between two lotteries which offer those outcomes with equal probabilities, if the lotteries are identical in every other way; i.e., the outcomes can be substituted. So if the agent (actor/decision-maker) is indifferent between outcomes x and y, then they are indifferent between a lottery giving x with probability p, and z with probability (1-p), and a lottery giving y with probability p, and z with probability (1-p). NOTE THAT the outcome “z with probability (1-p)” is the same in BOTH lotteries and is, therefore, irrelevant!!  Similarly, if x is preferred to y, then a lottery giving x with probability p, and z with probability (1-p), is preferred to a lottery giving y with probability p, and z with probability (1-p).  Got it?  OK, then.

5. Monotonicity - This big ugly word simply means that a gamble which assigns a higher probability to a preferred outcome will be preferred to one which assigns a lower probability to a preferred outcome, as long as the other outcomes in the gambles remain unchanged. In this case, we're referring to a strict preference over outcomes, and don't consider the case where the decision-maker is indifferent between possible outcomes.  This has been described as the “more is always more” axiom.

Thanks to http://www.econport.org/content/handbook/decisions-uncertainty/basic/von.html for easy access to a good description of JvM utlity axioms.

In case you aren’t familiar with the term “axiom”, an axiom is defined as a self-evident truth or a universally accepted principle or rule.  Now…  I ask you…  Is it self-evident that you are able to know whether you prefer rocky mountain oysters to hagis if you have never experienced either?  According to these axioms, John von Neumann says it is because you can.  Clearly, this individual known as the “Econ” is equally as fictitious a creature as the rainbow-farting unicorn.

Now, I know that John von Neumann knew that he was acting as the equivalent of Dr. Frankenstein when he created the axiomatic automaton that is the “Econ” of today’s staunch economics modelers. He knew that only he, himself - the guy who predicted that if France didn’t re-militarize after WWI that WWII would ensue - only he could really be held to such omniscient and omnipotent standards.  But other economists and politicians use the concept of the “rational actor” as though there are 7 billion of them walking the earth.  The fact is that we are all really just a bunch of bumbling fools who buy cheese flavored chips with no actual cheese in them and work for less than we are worth simply because we don’t know what other people who do the same job are making.

Like any other social scientists, Economists can only observe choices, and economists have presumed that people’s choices are the manifestation of a rational train of thought, specifically the train of the onerously rational axioms above, and that people, therefore, make choices by connecting rational decisions to all the possible actions they can take according to their logical, probabilistic consequences (the outcomes), and then perform the action (make the observable choice) that is connected to the outcome with the highest utility.  If all those things happen, then we say that the actor is behaving rationally.  But long ago psychologists discovered the impulse - behavior where action is taken without substantial conscious deliberation being involved.  Some behavior is even instinctual or habitual where almost no conscious behavior occurs prior to the action or set of actions.  One estimate states that 80% of all human activity is completed without conscious intervention (Freud thought 90%).  And this isn’t just breathing and walking! We’re talking driving, eating, speaking, interpersonal interactions, posture, mannerisms, moods and emotions, anything that is considered “routine” or “habit”, cognitive habits and biases...

The fact is that we Humans do most of the things that we do without any conscious cognitive intervention whatsoever. And that means that we Humans make mistakes. And not just once in awhile, but all the time.  I know that I, for one, make utility-destroying choices every day. Just today I went to a grocery store for eggs and milk and came back with several other items including, not one, but, two bags of Australian licorice, which I regret buying because I have already gained 5 pounds since starting my PhD program due to eating such things and sitting for longer periods of time while studying. I am currently sitting at a computer at nearly 11 pm and I have promised myself to go running in the morning to try to shed these pounds, so I regret being up late.  Let’s see... what else...  I disappointed my son by choosing to go to a different event than his water polo match, I blew off making dinner (to go to the grocery store) and so we ate out which meant that we spent more money than we would have if I had waited until after dinnertime to go to the grocery store, and I wore horribly uncomfortable shoes to the event I went to earlier and I now have a blister on my pinkie toe.

And that’s not even a personal record for regrets in one day.  When I think back to the number of choices I made, versus the number of decisions I made, there is a large discrepancy.  Many of the things I did I did out of automaticity.  When something is missing from the cupboards you go to the grocery store.  ‘Cause that’s what you do.  In other cases, I was making active choices without really thinking about all of the consequences (go to grocery now did not equal spending money to get take-out for dinner when I left for the grocery store).  Sometimes I knew what the consequence might be, but made up an excuse to go ahead and do what I wanted to anyway (wear the cute shoes, you’ll be sitting most of the time anyway).  And sometimes I had to do what I had to do in spite of the fact that it would have a negative impact on some other aspect of my utility at some other point in time (go to networking event because you are restarting a career – feel bad about missing son’s thing later).  We could consider the last choice here as rational, right?  I knew that I would be destroying utility in one part of my life by gaining utility in another.  I knew what the trade off would be.  But here’s the kicker.  I should not regret missing my son’s water polo game if I was aware of the trade off.  If someone could please tell my amygdala that, I’d appreciate it. These are just a few of the ways in which we do things without thought and/or with thought but without a full understanding of the consequences.  I often think back to my college years and think that I would have chosen different courses and studied more “if only I knew then what I know now.”  Stuff it, John von Neumann.  I’m not going to feel bad about not becoming a brain surgeon.

Okay, okay... I am done using old John as my whipping boy, but let me wrap this up by making my true point.  We Humans are fallible; subject to beliefs, emotions, habits and impulse.  It should be clear that having a rationale is not the same as acting rationally or no one would ever eat an artificially flavored snack chip or drink a third martini. Decisions and choices are not the same thing, and, moreover, often our choices in one aspect of our lives have an impact on another at a different point in time and our non-Econ brains simply can’t make the connection.  But philosophers and economists alike have, for centuries, extolled the rationale as the means to an end for a rational act and I find this patently illogical.  Rationales and rationality are not the same thing and they need to be extracted from one another once and for all.  In recent books and papers economists have taken to distinguishing the difference between “Humans” and “Econs” and I, for one, appreciate it.  In fact, let us economists begin to allow for the vagaries of the Human mind as a HUGE driver of economic activity.  ‘Cause, let’s face it!  If we all were able to know exactly how to maximize our potential from the moment of birth the world wouldn’t need lawyers or yoga teachers and then where would the world be, I ask you?