Game Theory, Morality, and Leadership

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John Von Neumann was a genius. No, I don’t mean “genius” in the way someone is called that “finishes 10 straight questions on Jeopardy” or “can tell you how much your groceries are before the checker gives the total” genius. This guy was “from another planet” genius. The kind that comes around every 750 years or so.

Born on December 28, 1903 in Hungary, he made major contributions to a vast range of fields such as set theory, functional analysis, quantum mechanics, ergodic theory, continuous geometry, economics  and game theory, computer science, numerical analysis, hydrodynamics (of explosions), and statistics.

He is generally regarded as one of the greatest mathematicians in modern history and his technical prowess was legendary. He had the ability to do advanced mathematics in his head…when he was 6 years old. His dad had hired private tutors for his lessons but they realized that he was already beyond their capabilities.

So at the age of 15. he was sent to a professor in Budapest by the name of Professor Gabor Szegő, considered the countries prominent mathematician. When Professor Szego asked John to display his knowledge of mathematics on the blackboard, just to get a sense of where he would have to begin the lessons, John proceeded to write down in chalk such an advanced mathematical progression that Professor Szego was so amazed that he started weeping.

John later went on to get his PHd in mathematics at the age of 22 while simultaneously earning a Chemical engineering degree. His accomplishments in later years were many but one of his contributions is the start of a completely new application of mathematics.

In 1944, John published a book, “The theory of  Games and Economic Behavior”, which started the development of a whole new branch of applied mathematics known as Game Theory. This is the use of mathematics to predict and advise behavior in a strategic situation when an individual’s success in making choices depends on the choices of others.

One of the rules in Game Theory that John presented was the MiniMax rule. Without going into the math of the whole thing, it states when two players are in a zero sum game, there will always be a decision that will minimize your loss while maximizing your gains. This will be the opposite for the other player. He will have a maximum loss with minimum gain.

The reason for bringing up this particular rule is that it is being applied, even today, but the people involved in the decision process do not realized as such.  Here are some facts to illustrate an example… Ford Motor Co. several years back had a car, the Ford Pinto, that had a bad design flaw. A real bad bad design flaw. The gas tank of the Pinto was mounted in such a way that if the car was ever hit from behind, the gas tank would explode and burn up the rest of the car including the occupants. It turns out that Ford knew of this design flaw, but only after production had started.

So Ford did a cost benefit analysis, essentially using the MiniMax rule, to decide that the cost of the fix, which was 11 dollars to every Pinto made, would be greater than the estimated percentages of gas tank explosions that would occur and the resultant dollars that would be paid out to lawyers and families of the burned up Pinto drivers. So they chose the latter. They minimized their losses while maximizing their gains. Unfortunately, that plan was put in a secret executive memo named the “The Ford Pinto” memo and was published by a national magazine.

Here is another example. In the health care industry, certain medical conditions produced flags for insurance companies that would initiate “Rescission” or procedures for canceling that policy holders insurance so the insurance company would not have to pay large medical payments. They have made a decision that not only will the policy holder reduce profits but may do so to an unacceptable established threshold level. They too have embraced a policy of minimizing their losses while maximizing their gains.

A question to ask about the application of this MiniMax rule is  “Why are the variables always about profits and losses of money? Couldn’t a value be placed on “doing the right thing” so that the maximized gain is the combination of  profits and “moral high ground”.  The opposite of that, the losses, would be a combination of money deficits and “immoral” decisions.

Let’s see an example where one would think that morality would enter into the picture. Who but the church would be the most likely to intercede with morality in a “MiniMax” type decision as they consider themselves to be the very gatekeepers of morality, choosing the rules and definitions of what constitutes morality, and selecting whom to be punished.

With the Catholic church and it’s apparent long history of cover-ups of documented child molestation cases, one would think that the maximized gain would be for the church to admit it’s problem, prosecute the guilty parties, and pay for their mistakes. But once again, morality is not considered part of the equation. The potential loss is money and losing power over their converted followers.

When a difficult decision is to be made, it is rare when one doesn’t know what to do. The problem is not in the best overall decision. The problem is in the difficulty of implementation of that solution.

Everybody at Ford knew that the right decision was to stop selling those Pintos, recall the ones out there, and fix the tanks. But what clouded that decision was the amount of money to do it, so that decision equation was changed.

Health Insurance providers know that it would be wrong to cancel a policy of a cancer patient because they can say that the patient had a preexisting condition of acne, but they let the profits change the decision equation.

A true leader is one that will make the choice from all the variables and not drop something out of the equation because it causes the solution to be too difficult to implement. A true leader is the one that can carry the right solution all the way to the end, in spite of the hardships.

A true leader is a very rare thing indeed and what is sorely lacking in the world today.

But, like the mathematician Von Neuman, perhaps they only come around every 750 years or so.

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Mike
13 years ago

Ever since I was first introduced to game theory I saw the major flaw right from the start. It’s missing a possible 3rd (external) variable. The most obvious was the pinto example, the third variable (the whistle blower) was never factored and probably never would have been factored. Thus the theory failed for them.
The old two crime suspects confession game can easily be broken by both saying a 3rd suspect did the crime.

Game theory is nice for white room test groups that “consistently prove” the theory correct. But in real life there are too many possibilities

Reply to  Mike
13 years ago

Mike, I was just glancing through old posts and saw this comment.

You are absolutely right with your assessment of game theory. All of the variables were too dynamic and could never be factored in. The 2 crime suspects game you mentioned I believe is called “Prisoners Dilemma”

13 years ago

Without reading the other commentary here and going straight to my own thoughts…. what a wonderfully reflection piece of insight~! It is my own instincts, intuition and conviction that what matters most right now on this planet, at this time, is our integrity. Our personal, group, national, etc…. INTEGRITY. Your post has put some abject, empirical clarity to this conviction… in my opinion.
Gee, really well said, Krell. I mean that most sincerely. 🙂

13 years ago

Nice Herr Krell. Spoken like a true engineer. Isn’t this also a different name of a cost/benefit analysis, wherein one can do it from a purely monetary perpective, or pull in other perspectives, like good will and altruism?

Reply to  The Lawyer
13 years ago

I would think the cost/benefit analysis is similar but that usually implies just a one decision sequence with a “non-player”. Like what is the best car insurance to buy.

The examples that I gave, by having “players” on both sides, it lends itself more to a zero-sum scenario.

For example, a cancer patient (player A) submits a claim for 50k. Now the insurance company (player B) has 2 choices, to pay or not pay. If the decision is to pay then outcome is Player A gets 50k and Player B loses 50k.

If Player B doesn’t pay, then Player A has 2 choices. Accept or Fight it in review or court. But Player B has gain 50k with less than 100% percentage possibility of losing as opposed to the first scenario where it was automatic 100% chance of loss of 50k.

Now Player B can use other strategies to decrease the percentage possibility of 50k loss even further. Tactics such as delaying hearings, stalling to put pressure on Player A to settle for less, etc.

Statistical methods such as these are being used all the time today. But the message of the post was… “At what point does the bottom line become the only variable to consider?

When does the human factor get taken out? Is there a certain threshold of size for a organization or company, where they accumulate so much power or wealth, that they can no longer factor in morality?

I know a lot of small business and local groups that would go above and beyond the norm to give you satisfaction even at a loss.

Reply to  Krell
13 years ago

“The exam­ples that I gave, by hav­ing “play­ers” on both sides, it lends itself more to a zero-sum scenario.”

Got it. That makes total sense.

And yes, the issue is where does morality factor, if at all–and large corporations exist for only one reason: financial profitability and for that reason are amoral.

13 years ago

I co-sign; really enjoyed this post. Doing the right thing as a variable can be critical to our survival, an idea that’s hard for those in charge to swallow. I did a similar themed post on that today if you’re interested.

Admin
13 years ago

Fantastic post! Loved it!

13 years ago

So what is profit, if you are only couching it in terms of morality, and not money? Is it “Greatest good for the greatest number of people?” even if it means restricting the good for a few to that end?

One good example might be the whacked out religious beliefs of the guys who flew the planes into the Twin Towers. Was the buttload of virgins in heaven a good enough profit to cause the huge losses on the other side? “So Mohammad, we might be killing a few thousand people- but hey, they’re infidels, right? And we have that nice virgin tail waiting for us when we die!”

And to Osori: It might be one thing for the health care company to deny a $250k procedure with the rationale that the money would be better spent on several thousand immunizations for children. But I doubt that is what they do. Instead they save all that money and award themselves huge bonuses. Sometimes I wish there was an afterlife so that the virgin-expecting terrorists could sit elbow to elbow with the health insurance actuaries as they wait their turn for a lava enema.

osori
Reply to  Mother Hen
13 years ago

Yes, I agree. For the greater good, one can rationalize it. Hard to do cause most of us don’t want anyone to suffer, but your immunization for children example makes the point very well.
But to do it for profit-I can’t comprehend the type of mind that works that way.

osori
Reply to  Mother Hen
13 years ago

I might also point out,that 72 virgin thing is a myth. The 9/11 guys may or may not have been religious but if they were religious and thought they were carrying out an attack in defense of their religion and thought they were being martyrs they would expect to die painlessly and go straight to heaven. But not to be rewarded with 72 virgins.

Reply to  osori
13 years ago

I believe that Muslim men in general get multiple sex partners/ concubines in the afterlife, not just the “martyrs”; their heaven is described in graphic detail, and expounded upon by later clerics. Not all name a specific number, until the Islamic Traditions where we find the 72 virgins in heaven specified: in a Hadith (Islamic Tradition) collected by Al-Tirmidhi (died 892 CE) in the Book of Sunan (vol IV, chapters on The Features of Paradise as described by the Messenger of Allah [Prophet Muhammad], chap 21, About the Smallest Reward for the People of Paradise, (Hadith 2687).
The same hadith is also quoted by Ibn Kathir (died 1373 CE ) in his Koranic commentary (Tafsir) of Surah Al-Rahman (55), verse 72: “The Prophet Muhammad was heard saying: ‘The smallest reward for the people of paradise is an abode where there are 80,000 servants and 72 wives, over which stands a dome decorated with pearls, aquamarine, and ruby, Here is an interesting link for reference: http://www.guardian.co.uk/books/2002/jan/12/books.guardianreview5

Reply to  Mother Hen
13 years ago

This is certainly the accepted common belief — the hadîth is the second most authoritative source in Islam after the Koran itself.

Ibn Warrâq (author at your link) is a great writer; he was raised Muslim but left the religion and can write about it as an ex-insider as very few Westerners can. I highly recommend his book Why I Am Not a Muslim if you’re interested in the subject.

The “raisin” interpretation of hûr, though, is not accepted by most scholars, and certainly wouldn’t represent such an incentive.

Then also there are the ghilmân of Paradise, those “immortal, pearl-like ephebes or youths” which gentlemen of, er, different tastes throughout Islamic history have interpreted as a promise that they, too, would be provided for — but maybe I’d better not get into that.

13 years ago

Thanks OSORI, they do make that cost/benefit analysis but the bottom line is that it is with peoples live. How can they live with themselves?
Another example like that which comes to mind is the history of the “Radium Girls”, the ones that used to paint the radium dials on watches. Tragic story!

osori
Reply to  Krell
13 years ago

I just read up on the Radium Girls. Damn. I didn’t know of that, and it’s almost with despair I write that I’m not surprised by it at all.

To anyone following along this thread, US Radium corporation hired hundreds of women to paint radium on watch dials.and encouraged them to lick or form the brushes with their lips when they began to lose shape (so as not to have to purchase so many new brushes) plus the ladies would paint their nails with the stuff, to have them glow in the dark.

The plant chemists and owners and scientists only went near the radium with tongs and lead screens and protective gear, so they knew the effects but didn’t let on to the poor women, who began to suffer the effects of radiation poisoning years later.

The US Radium encouraged the rumor that the women had contracted syphilis rather than radiation poisoning.

Five women sued, and the company settled out of court (1928) for 10K plus 600 a year and paid medical expenses.

Reply to  osori
13 years ago

The defense lawyers strategy for the Radium Company against the women was to stall and delay until the women all died.
Clearly the morality of the issue was not in the equation.

osori
13 years ago

Krell,
GREAT post man.Like the old baseball maxim that a guy who makes a great play in the field almost always seems to be first at bat next inning (wonder if Mr Von Neumann ever studied that?) you made a great play with your info then followed with a home run by tying it into morality.

it brings to mind another health insurance gambit. I believe the max state fine for improperly denying a needed procedure is 100.00 per day? So if the procedure costs say 250,000.00 it would be a minimize/maximize situation where the HI would figure in how long the poor patient would stay alive X 100.00 and stack it up against 250K.

Like the Church and its coverups-how can they live with themselves?

13 years ago

Maths was never made exciting for me at school, so I still look at it like it’s very hard work.

Read your post with interest all the same and it reminded me of the movie “A Beautiful Mind” the story about John Nash, the Nobelist who developed a similar economic theory.

Reply to  Holte Ender
13 years ago

Actually, Nash took Von Neumann’s initial work, greatly expanded it to create something called the Nash Equilibrium theorem, and won the Nobel Prize in Economics for it. But in between I believe he went bat shit crazy? Never saw the movie so don’t know how it went.

Reply to  Krell
13 years ago

The story of the movie tells of how Nash suffered mentally but the great power of his mind reasoned with the illness and the breakthrough he made in recognizing his disillusion. A fine movie.

Bee
Reply to  Holte Ender
13 years ago

I saw the movie, read the book, saw a couple of PBS shows about Nash. He was paranoid schizophrenic – very, very much so. After years of decline, he finally decided to solve the problem. He used his mind, his logical skills, and determined that his hallucinations were not real, and that he should proceed to ignore them since the meds in the 50’s made him a virtual zombie. He’s still alive, btw. His son also developed the same condition – I saw a documentary where Nash was trying to teach his son his technique for living with paranoid schizophrenia. Quite a story, his.

Interesting post, Krell – I wouldn’t have thought to tie the catholic churches self-imposed problems in with minimax.

Reply to  Bee
13 years ago

Bee..I thought about my remark “bat shit crazy” and now regret commenting with that statement. Mental illness affects a lot of people and to be so flippant with that offhand remark was ignorance on my part. I apologize to anyone that may have been offended.

Getting back to the post, for the Minimax decision rule to be applied to decisions for examples I gave in my post, I am not so sure it can be applied in a conventional mathematical sense. Game Theory is valid for some applications such as economics but for other applications it can get a little vague. Too much has to be assumed for the decisions the other player will make.

Back in the 50’s this branch of mathematics really captured some interest because it was thought it could be applied to nuclear defense issues and MAD. The Rand Corporation lead the way in this school of thought and one of the major proponents was a person by the name of Herman Kahn. Quite the controversial figure, his book “On Thermonuclear War” is a book that cannot be described in words, after getting the book and reading it myself, I wished I hadn’t. Weird, I always felt that book took a small piece of my…for lack of a better word….hope.

One of the major flaws of applying Game Theory in “games” such as war is that it applies logic to things that may not be logical. People cannot always be expect to act rational or make decisions in their best interests, so the “if I do A then player will do B” scenarios do not always follow.

Reply to  Krell
13 years ago

Krell, you said, “One of the major flaws of apply­ing Game The­ory in “games” such as war is that it applies logic to things that may not be log­i­cal. Peo­ple can­not always be expect to act ratio­nal or make deci­sions in their best inter­ests, so the “if I do A then player will do B” sce­nar­ios do not always follow.”

I’ll bet there’s a way to factor that in. First you’d have to start with who is designing a particular war game. They are products of their culture, sub-culture, life experience, personal information/education, class, age and sex. When they wage war against a different group, they are looking at that group through the always distorted lens of who they themselves are. What looks “illogical” to them, may be part of another group’s values and lifestyle.

The US thought that powerful bombs would defeat the Vietnamese and the Iraqis. They underestimated the will of those groups to not be defeated by shock n’ awe. They thought it would be cakewalk and said so. They were wrong. The reason may be that they assume that Americans would surrender if shocked and awed under constant carpet bombing. We just might, because we’re so dang fat and used to comfort that we freak out over someone at the next table lighting a cigarette.

When the designers of war really know their enemies (or victims, depending on the war), they have a better chance of success. This includes knowing if the enemy uses a “crazy like a fox” strategy to bluff and appear nuts (like the guy running North Korea), but in reality has a method to his madness.

Reply to  Kit (Keep It Trill)
13 years ago

You bring up some good points, Kit. It can be tough to quantify tenacity and will. Probably a good reason not to apply logic to the human condition.

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