Bayes rule, Occam’s Razor, and predicting threats from understanding “bad guys”

Imagine you are on a train, looking at the people around you, and you decide to do a game to pass the time. You construct imaginary pasts for the people you see. That old oriental lady there? – She was a celebrity singer in her youth back in Thailand. That heavyset man over there? He’s a Mafia enforcer on his way to do a “hit”. That middle-aged man over there? He’s wracked with internal pains from a car-accident. And so forth.

Now here is the point. The probability that you would be correct on any of these people is very, very, low. But it’s not zero. In fact, you could be correct about the entire group.

And this is because “probability” is a kind of odd concept. It’s often an expression of human ignorance, and assumptions, some of them faulty.
Its easy to understand probability when it applies to true randomness. For instance, you can never predict exactly when a radioactive atom will decay, but you can predict an average decay time for a group of atoms.
But we use probability often to predict events in our world that are unpredictable only to the extent that we lack information about their causes.

One area where people are woefully ignorant is what motivates bad people. By “bad people”, I mean people who most of us agree do bad things.
An interesting example of this was in the town of Sighet, Hungary, in World War II. Here, the Jewish villagers were warned, by an eye-witness to a Nazi massacre, that the Nazis would kill them, once the German armies reached Sighet. Instead of believing the eye-witness, the villagers decided he was crazy.

Some of the villager rationalizations were interesting. One argument was that perhaps the Nazis would hate rich Jews, but the Jews of Sighet were poor and inoffensive. Another argument was that in previous encounters with German soldiers, (in World War I), the Germans behaved fairly decently, and there was no reason to think they would be different this time.

Rev. Thomas Bayes
Rev. Thomas Bayes

Now lets examine this, but first take a note of “Bayes Rule”. Don’t be afraid of the math, there is just one equation.
P(H|E) = P(E|H) * P(H) / P(E)
E = evidence, H = Hypothesis, ‘|’ means “given”
P(H|E) = the probability of a hypothesis, given evidence
P(E|H) = the probability of the evidence being true, given the hypothesis
P(H) = the probability of the hypothesis being true, before you know about the evidence
P(E) = the probability of encountering the evidence

So if the hypothesis that you are considering is “The Nazis want to kill all the Jews”, and the new evidence (E) is the testimony of a eye-witness to a Nazi massacre of Jews, you should calculate the hypothesis probability taking into account the probability that the hypothesis is true even without you encountering the evidence, as well as the probability of a Nazi massacre happening irrespective of whether they want to kill the Jews or not.
That’s the theory.

So what happened in practice?

Well first of all, the Jews of Sighet put p(H) very low. That’s the probability, prior to hearing from Moshe (the witness) that the German soldiers would kill them. Secondly, they put p(E) very low, and its interesting to know why. They realized that P(H|E) (probability that if Moshe really saw Nazis massacring Jews in Poland that the same Nazis would then try to massacre the all Jews anywhere) was rather high. And since they simply didn’t believe P(H), they had to not believe P(E).
So how could E be invalid? Well, if Moshe was insane, then E would be invalid.

William of Ockham (occam's raxor)
William of Ockham (occam’s raxor)

And that brings up another famous rule, which unlike Bayes Rule, is just heuristic, or general principle that sometimes works.
And that is Occams razor.

According to Wikipedia Occam’s razor:

is a principle of parsimony, economy, or succinctness used in logic and problem-solving. It states that among competing hypotheses, the hypothesis with the fewest assumptions should be selected.

Now let’s think about this for the Jews of Sighet.

To believe that the Germans had changed radically from WW-I to WW-II, you would have to assume many things. It would help to know how the great monetary inflation of the Weimar government wiped out the incomes of many Germans, you might have to understand how ideology transforms people, you might have to understand what the Nazi ideology preaches, its antecedents, why it caught hold, and many other things, that even now, we can’t know.
On the other hand, assuming that Moshe was crazy just required one assumption.

Obviously making just one assumption is simpler than making many.

So does that mean that Occam’s razor is invalid, at least some of the time?

Or that Bayes theorem, while accurate, is often a waste of time, because the probability estimates that people make are based on incomplete information, and a mix of incorrect and correct assumptions and beliefs about the world that they live in? There is a saying about computers “garbage in leads to garbage out.”

I think that part of the answer is that what seems to be the simplest explanation based on your current knowledge, may not be the simplest explanation at all once you have more knowledge.

Think of the Melanesian islanders in the years during and after World War II. (From Wikipedia:)

A small population of indigenous peoples observed, often right in front of their dwellings, the largest war ever fought. First, the Japanese arrived with a great deal of supplies and later the Allied forces did likewise…
After the war, in attempts to get cargo to fall by parachute or land in planes or ships again, islanders imitated the same practices they had seen the soldiers, sailors, and airmen use. … The islanders carved headphones from wood and wore them while sitting in fabricated control towers. They waved the landing signals while standing on the runways..In a form of sympathetic magic, many built life-size replicas of aeroplanes out of straw and cut new military-style landing strips out of the jungle, hoping to attract more aeroplanes. The cult members thought that the foreigners had some special connection to the deities and ancestors of the natives, who were the only beings powerful enough to produce such riches.

Now from the viewpoint of these peoples, who did not understand technology, and had not even met foreigners before the war, the simplest explanation for all these riches was supernatural. The hypothesis that the Gods were responsible seems reasonable, if you don’t have alternatives.

And that’s another reason people get things wrong. They can’t imagine the alternatives to a hypothesis, or they discount those alternatives.

So now lets talk about evil in a little more depth.
Recently, a famous American movie actor and producer, Robert Redford, made a fictional movie that tries to make its audience sympathetic to a sixties radical group. His main character kills a policeman and goes into hiding.

But Larry Grathwohl, who actually interviewed the real sixties American radical group, the “Weathermen”, which killed policemen and planned bombings says that “The Weatherman’s real intent was centered on a future in which the communist nations of Cuba, North Korea, China and the Soviet Union would occupy various parts of the U.S., with “re-education centers” established in the Southwest to prevent counter-revolution. These concentration camps were to be for re-educating die-hard capitalists.” The interviewer asked them what would happen to those couldn’t be re-educated, and was told they would have to be eliminated. “And when I say ‘eliminate,’ that meant ‘kill….twenty-five million people.”

My point is that a fairly ignorant, naive, but widespread view of such radicals is that they were young, passionate, and caring, and they cared so much about injustice that they resorted to violence. In fact, if I remember correctly, one of these people was treated leniently by a jury because of an argument that she was trying to stand up for oppressed black people.

So lets suppose that you read what I just wrote and dismiss it as “right-wing lies” and so forth. Your estimates of various probabilities of events will start diverging from mine. I will predict people behave in certain ways, and you will predict differently.

David Sirota
David Sirota

Take Salon contributor and syndicated columnist David Sirota, who wrote, after various people were blown to bits, or had their legs fly off their bodies in the Boston Marathon bombing, an article with the headline “Let’s Hope the Boston Marathon Bomber Is a White American.” The reason he wrote that is that he thought if it were a white person, it would be dismissed as an isolated incident, while if it were a Moslem, then

it’s easy to imagine conservatives citing Boston as a reason to block immigration reform, defense spending cuts, and the Afghan War withdrawal and to further expand surveillance and other encroachments on civil liberties.

Interestingly, the people I hang out with, who are conservatives, and very aware of Jihad, immediately assumed the bomber was a Moslem. And we turned out to be correct. It did occur to me that some anti-government extremist might blow something up, but if he did, I assumed it would be a government building, and not a marathon.

Sirota, with his talk of “white privilege,” lives in a different world of motives, and therefore probabilities of certain actions occurring  than I do. To me, Jihad is not about whites or browns, or blacks at all.   The brothers who placed bombs among spectators at the marathon were white.  Conversely, on a London street, a black convert to Islam, Michael Adebolajo hacked a British soldier to death with the help of another Moslem.  It is interesting that a convert to Islam suddenly inherits the grievances of Moslems everywhere.   If Britain attacks his Moslem brothers in Afghanistan, then he gets revenge.

One commentator thought that the motive of the Boston bombers was halfway between those of Columbine type killers and Jihadists, but one difference is that the Columbine high school massacre was perpetrated by people who felt they were bullied.  Dzhokhar, at least, was actually popular in his prestigious Cambridge high school.  Tamerlan had become a true believer in Islam, and probably despised his past episodes taking Marijuana with Americans.   In fact, it now comes out that he murdered three of those Americans, two of whom happened to be Jewish.  Whatever problems Tamerlan had in his life, I believe that without the doctrine of Jihad he and his brother would not have done what they did.

But I could be wrong.  Dzhokhar left a note claiming that the attack was revenge for American attacks on Moslem countries.  If America can kill Moslems as “collateral damage”, then the Boston victims were also “collateral damage”.  But that raises questions too.  When Osama bin Laden’s hijackers killed thousands of Americans in the space of a few hours, what was that in revenge for?  America was not fighting in Iraq or Afghanistan at the time.  In fact, American money was going to pay the Afghans not to grow crops that could be used to make drugs.

I just don’t understand how, if you have spent high school years as a popular, accepted student in the US, and if you walk among the spectators at the marathon, men, women, and children, all friendly, all happy, none of them victimizing you, that you would let loose supersonic nail and ball-bearing missiles at them.

And when something like that happens, I’m going to draw some conclusions that Mr. Sirota doesn’t want me to draw.

Not what about the situation where P(E) is very low?  Unusual things do happen, they could happen to you, and in fact statistically, they are bound to happen:

Jeffrey Dahmer
Jeffrey Dahmer

I once read of an Asian victim escaping from a serial killer, (the killer was Jeff Dahmer) The victim headed down the street, naked, dazed and confused. He met two women who were inclined to help him, but then two policemen saw him, and handed him back to Dahmer who had run after him, and who told them that the Asian, who could not speak English, was his gay lover.  Dahmer took the victim home, and promptly murdered him.

The policemen, who were totally clueless, made jokes about the day’s encounter with the “gay lovers” later.

They did not realize that their routine day had been disrupted by an encounter with a serial killer of many people. After all, what is the probability of encountering a mass-murderer on any-given day? Probably very low.

Let me close with one quote, and an experience I had.
In the preface to his book “The Gathering Storm”, Winston Churchill said that World War II should have been called the “unnecessary war”. “There never was a war more easy to stop than that which has just wrecked what was left of the world from the previous struggle (World War I)”

At the end of World War I, Western armies had defeated Germany. Only twenty years later, a fully rebuilt German military nearly took over the world. Why? Basically the exhausted West made endless mistakes, including not understanding Hitler or human motivations in general.

I had an experience in some ways similar to Moshe (mentioned earlier).

I claim that I was the victim of some remarkably bad people. I will not go into the details except to say that right off the bat, there seemed to be problems with my story. First of all, one could ask, why should any bad people bother with me? Secondly, my evidence was subjective. I lacked witnesses, I had nothing on tape, or on film. Finally, if bad people wanted to victimize me, then why was I walking around the neighborhood, presumably untouched?
One policeman did say to me the following:

Nobody is going to believe your story. It’s like a movie! But I’ll give you the benefit of the doubt. You need to collect evidence. I recommend you get yourself a hidden camera.

In other words, he was saying to increase P(E), since p(H) was so low.

That raises another point though. What is “subjective experience”? On the one hand, we know it can be completely wrong.  And yet, sometimes subjective experience is all we have. Think of Moshe in the story above. Should he have been ignored just because he lacked two witnesses equipped with cameras? Or, as a second example, suppose you suddenly develop a pain in your chest. You go to the doctor. The Doctor gives you an x-ray. He is doing this based on your subjective experience (of a pain) and trying to convert it to objective evidence.

I also think that in life you do occasionally have a series of events below the surface that suddenly erupt into the open in some way, often involving a victim, and the police then have the choice of believing the victim, with the implications that there is long and involved story, and potentially serious crime-scene to uncover, or to simply believe the victim is exaggerating, or seeking attention, or delusional, or whatever.

The best way to understand the motivations of bad people is to be them, for a few minutes. We can’t do that.  In my experience, sometimes bad guys drop the mask briefly, and then you get a glimpse of malice that can really shake you up.  But in general, that doesn’t happen, because bad guys would be out of business if they advertised their personality to the public.

But the main point of this blog post is that there is a story behind everything, and often we have only bits and pieces of the story.  We may be drastically wrong about the probability of something – even experts believed the Titanic was unsinkable for instance.  Once we have enough pieces of the story, the probabilities change.  It’s not just that we have more evidence, it’s that we understand more of the underlying processes, chains of events, and causes.   Low probability obeys different rules than zero probability.  Low probability can become one hundred percent probability.

Finally we should evaluate evidence honestly, and without the wishful thinking that I think those Jews in Sighet exhibited.  Truth, no matter how painful, should be our goal.  And sometimes it takes an effort to get at the truth.  Sitting in an armchair and theorizing is not always as good getting out of the armchair and overcoming laziness and even fear to ask the right questions of the right people.


All Rivers Run to the Sea: Memoirs by Elie Wiesel (Oct 22, 1996) – (for the story on Sighet)
The Weatherman interviewer quote is at: but there is also a book: Bringing Down America: An FBI Informer with the Weathermen by Larry Grathwohl published in 2013. Amazon’s blurb says:

Time Magazine called him “the only FBI informant known to have successfully penetrated the Weather Underground.”  In 1969, Larry Grathwohl stepped out of his life and into the role of an informant for the FBI. For a year, Grathwohl ran with America’s most dangerous radicals. He planned bombings, murders, and political assassinations. He saw, up close, a gang of thugs dedicated to bringing down America.

 Note: I say at the top that “true probability” is something as simple as the decay of radioactive atoms, but the June 2013 Scientific American says that there is a new theory called QBism that finds Bayesian rules behind all “Quantum Weirdness”, and as I recall, radioactive decay is a quantum phenomenon.


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