And now, back to our regular programming......hmm, on second thought, this is a little different than our usual farce.
Since one of my students told me that a lecture I gave right before Spring Break on making decisions in the face of uncertainty was the best he ever heard, I thought I'd share it with you. Especially after reading confirmed idiotarian Jimmy Carter's truly stupid
statement that:
President Bush and Prime Minister Blair probably knew that many of the allegations were based on uncertain intelligence
(
Note to Naval Academy: Revoke Carter's degree in nuclear engineering immdediately!)
If the following analogy isn't obvious, please commit suicide immediately as you are wasting precious oxygen.
Most people work under the false assumption that they either
know or
don't know something. The truth is that knowledge is not a dichotomous choice-->1) know or 2) don't know. Rather, when we say we "know" something, we really mean that the probability of it being true is very near 100%. Being
near 100% is not 100%, though. There is always a chance that we are wrong, even if that chance is 1/1,000,000. So knowledge is a continuum ranging from complete uncertainty to very close to certain.
Another false assumption people work under is that they must only act when they "know" something, not when they are unsure of something. But, since we can never be 100% sure of something we see that this cannot be the case. What you really mean is that you don't
want to act until your knowledge of something is close enough to 100% that you feel very confident that you aren't wrong. However, in real life decisions often cannot wait until you are sure of something. For instance, you and I are both pretty freaking pissed about gas prices. We want to pay the lowest price possible, so we shop around a bit until we find a gas station that is lower than the rest. You buy the gas. Now, was the station the lowest price? The truth is that you don't know. It
seemed to be the best price based on the information you could gather, but since the gas tank won't wait for you to do a complete canvas of all gas stations you are compelled to act. Even though we all want to act upon complete information in any situation it is simply impossible. Unless you are God,
all decisions are made on something less than 100% complete information.
Since ALL decisions are made on something less than complete information, each of us must weigh the consequences of what will happen if we make the wrong decision. Sometimes, being wrong is of little consequences, but other times the consequences can be dire. In statistics when we try to test certain hypothesis we differentiate between the consequences of being wrong as a Type I or Type II error. A Type I error occurs when a null hypothesis is rejected even though it is true. A Type II error occurs when a null hypothesis is accepted, even though it is not true.
So, in the gas tank example we come up with this hypothesis: "The Jawa gas station has the lowest prices." A Type I error would be if you rejected that hypothesis. No, you say, I don't have enough information to confirm that the Jawa gas station has the lowest prices. So, you continue to search for another station. Since you have already determined that you will only buy gas when you find the station with the lowest price you eventually run out of gas. Oops, you were wrong, the Jawa gas station had the lowest price and now its too late to go back and fill up.
A Type II error would occur if you went ahead an bought the gas, but then you go down the block only to find that the Unibrow gas station sold gas for 10 cents a gallon lower. Oops, you acted as if your hypothesis was correct but it turned out you were wrong.
In statistics we always treat the Type II error as if it was the worse one, but this is only because in science we don't want to announce a new and significant breakthrough before being pretty close to certain that we're right (remember the announcement that cold fusion had been discovered, oops). In real life we must calculate the costs of either type of error being wrong and then decide which is costlier. In our gas example, clearly the greater cost is associated with not buying gas than is the risk of finding out you hadn't paid the lowest price possible.
Humans make these error calculations on a daily basis, but most of the time we're not aware of what were doing. On some basic level we understand that all of our decisions are based on imperfect information, that there are potential hazards in making the wrong decision, and then we make decisions anyway. Can you imagine if in the gas example the person simply opted not to make any decision, but instead just kept their car in the driveway? Somehow, we manage to muddle through life and don't become paralyzed by our imperfect skills at gathering data. The following is an example that illustrates how decisions must be made on the basis of imperfect behavior, and how calculating the risk of a Type I or Type II error is important in making that decision.
In your neighborhood there has been a rash of
eggings. You know what an egging is. Thats when some punk drives around the neighborhood and throws eggs at a house. Well, this is starting to piss you and your neighbors off. "What about the children!" cries one lady at the block meeting. So, each of you decides you will try to catch the culprit. Using your children as a network of informants, you send them from house to house looking for large quantities of eggs.
Your immediate suspicion goes to the
O'Gara family *cough, cough*. They always make a lot of noise, the father wears wife-beaters, and the kids are a bunch of punk red-heads. You ask your son whether or not he has seen any eggs over at the O'Gara's trailor (yes, and they live in a trailor). No, he hadn't. Of course, he only was able to sneak a peak into their fridge on a couple of occasions and the only thing he had noticed was some Alomo beer and some Armour hot-dogs. He wasn't able to go through the whole fridge and he also reminds you that the eggs used to spoil the neighborhood were probably rotten and might not have been properly stored.
Are the O'Gara's the eggers? No, or at least you won't accuse them simply because they are white trash. If your wrong, and it turns out they are the eggers you or someone in the neighborhood might get egged tonight. If your right, and they aren't the eggers, then no big loss.
That night you're up late when you noticed that your neighbor's house is getting egged! Who is doing it? Why, its the O'Gara kids. Oops, your initial suspicion has been confirmed. Apparently, the reason stereotypes have such lasting power is that they are usually true. You've committed a Type I error and your neighbor is suffering the consequences.
That does it, you won't make that mistake again. You and your neighbors confront Mr. O'Gara with the new evidence. He's appalled! He'll stop the kids from egging in the future and by the sounds of the kids getting beat that night, you assume he will stop the behavior. Unfortunately, the eggings continue. They are more sporadic now, but the smell of rotting eggs still tortures the block.
As block captain you go to Mr. O'Gara and confront him. He claims its not his kids, it can't be his kids, he hasn't bought eggs since the day his brats were caught and he sent them to County General. Can you come in and see the fridge, just to be certain? Nope. Mr O'Gara claims the house is a mess and anyhow it wasn't his kids. What should you do?
Well, now you are confronted with a choice. You must act. If you accuse the O'Gara kids to the cops and it turns out they were innocent, you are afraid Mr. O'Gara might go ape on you. If you accuse the O'Gara kids and they are guilty, then everyone is happy. But, if you don't accuse them-even though you believe they are
probably guilty-and it turns out to be the same Irish brats causing havoc, then you are at risk of getting egged.
You choose to not accuse the kids. Better to get egged than get punched in the face. Then it happens. You had no idea the kind of damage eggs can cause to paint until it happens to your house that night. It literally ruins all the paint it touches. Its not just the house, its the car. Your car's paint is ruined! It will cost you thousands of dollars! Maybe getting punched in the face would not have been as bad as getting egged? At least your face will heal pretty fast, but the car and the house will take quite awhile to repair.
That's it. You go to the cops and accuse the kids. The cops call on a "mediator" to resolve the dispute. The mediator works out a deal. The O'Garas will let you enter their house and check to see if there is anything in the refridgerator if you promise not to have their kids put in juvie. Ok, you agree.
The first day you walk in and see this in the fridge:
What the freak! They still have eggs in the fridge. Yes, but the eggs are only for home consumption claims Mr. O'Gara. They won't be used on you.
Nope, not good enough, you want them gone. Ok, he agrees to get rid of the eggs. For the next few weeks you go over to his house and don't find any eggs. After awhile he gets miffed at you coming around and starts complaining around the neighborhood. "Really," he says, "this man is quite obsessive. He keeps coming in to my house and searching for eggs disturbing my family. Its even effecting my pest-control business and I'm losing money. It has to stop!" Some of your neighbors are sympathetic. Of course, these neighbors were the ones who never got egged and so don't really know what a hassle it is.
The decision must be made. Should you trust that he has no eggs and let him continue life as if nothing had ever happened or should you continue to bother his family and intrude on his privacy? Either way you run the risk of being wrong. If you stop the inspections, he could begin to buy eggs and thus the egging *
may* begin again. If you continue the inspections, though, you could eventually ruin his business and force him into poverty, even though he *
may* never buy eggs again or if he does his kids *
may* never take up their egging hobby again.
Well, as long as your block captain you are in charge, dangit. You continue searching his house for eggs. Just as the neighborhood is about to turn on you and force you to resign your position out of sympathy you discover something of great importance:
When confronted at the next block meeting, though, Mr. O'Gara denies it. He admits he has a carton, but he uses that for his rock collection. As proof he brings this to the meeting:
Well, you didn't actually
look in the egg carton did you? No. So it could be that you simply saw the rock collection, right? Yes. But given the family history you want to play it on the safe side. You insist on continuing the inspections. You go back to the house and search some more. Days go by. The neighborhood is getting antsy, they want you to stop. You don't, though, convinced that he still has eggs and that if your inspections stop his kids will begin to use them again.
One day, while looking under a stack of High Society you find this:
Aha! Proof that he was lying all along. But O'Gara refuses to let you open the carton. Its the rock collection and nobody is going to look at them! But, its too light to be rocks, you say. Ok, its not rocks, O'Gara retorts, but it contains *ahem*
precious bodily fluids so he doesn't want you to see *ahem*
it. Your first reaction is *
sick*, but you also realize you want to see because he could be lying. You insist on opening the box. He refuses. You call in the mediator and the cops. Finally, he is forced to open the carton. Here is what you see:
You were vindicated! But he claims that he forgot about these eggs. He had been wondering where the smell was coming from, thanks for finding them. He puts them in the garbage disposal as the whole neighborhood watches. He swears that is the last of them. Will you please, he urges, stop showing up to his trailor. His business is just about in ruins and then he will be forced, along with his innocent wife and daughters, to move out of the neighborhood and go on "the welfare". A few on the block think he has turned over a new leaf, but most of the others say the inspections should continue in light of the fact that he had lied before. As far as the majority of the block is concerned, he has always had eggs.
In spite of a concerted effort on his part to show the suffering of his family, you continue to show up at his house. Everyone agrees that he still has eggs, but many think the inspections are a little over the top. Maybe, they say, the risk of his kids throwing the eggs at a house has been diminished. So what if he has eggs, they certainly wouldn't use them after all the suffering they have gone through. For weeks there is no evidence that he has eggs, until one day this shows up:
Mr. O'Gara, again, claims that it is his rock collection. In fact, he's done with you dropping by the house. He refuses to let you in. Now, you've seen the box but are not allowed to look inside. What is in the box? Is it eggs? Is it his rock collection?
You are at a decision point. You do not know for 100% certainty what is in the box. O'Gara will not let you look inside, but you must make a decision based on incomplete information. You can either assume that he has the eggs or that he doesn't, but in each case you can't know if you are correct. Either way, there are certain consequences if you make an assumption and it turns out you are wrong. Its also possible you make an assumption and your assumption turns out to be correct.
1) Assume he has the eggs. You press charges. The police come and find the carton is full of eggs. The kids go to juvie and life in the neighborhood gets back to normal. O'Gara goes out of business and moves.
2) Assume he has no eggs. You don't press charges. The inspections stop and life in the neighborhood gets back to normal. O'Gara gives you stern looks every day.
3) Assume he has the eggs. You press charges. The police come and find the carton has rocks in it. You look like a jack-ass. No-one blames O'Gara for punching you in the nose. You heal.
4) Assume he has no eggs. You don't press charges. The inspections stop and life in the neighborhood gets back to normal. You get egged. O'Gara winks at you as he passes by in his U-HAUL. He is moving.
What do you do? There is a chance that O'Gara has no eggs in the carton, but given past experience it seems like a fairly low probability that this is the case. It is much more likely that there are eggs in the carton, you believe. If you are wrong, and it turns out that there were no eggs in the basket, then the worst that could happen is that you get punched in the face. Which is worse, getting punched in the face once or getting egged? It is your call, you must decide.
You press charges. The cops come and find the egg crate. Here it is:
Oh, snap. No eggs! Even though in most people's estimation he still had eggs, there always existed the slim chance that he was actually (finally) telling the truth. Because there was
no way of knowing for sure, you had to act in the face of some amount of uncertainty.
Did you do the right thing? The answer to this of course is purely subjective. It always depends on what the risk is of making a Type I or Type II error. Which is worse, getting punched in the face or having your house egged? Some may fear a bruise on the face, but others will fear the egging.
Of course, in real life the consequences of making an error can be either more or less severe. The consequences of being wrong about the lowest gas prices are pretty minor. However, when designing the O rings for the Space Shuttle, it was once thought that 1/10,000 chance of failure was acceptable risk. Then Challenger happend. D'OH! Are we sure that O rings will never fail again? NO! Today's O rings
still have a risk of failure but the chances are more like 1/1,000,000. We design them better because the consequences of being wrong about their safety, it turns out, are too dire in our estimation.
It is the
consequences of being wrong that determine our willingness to act. Imagine, if you will, that the eggs were bombs. Suddenly, our calculations of risk change. Getting punched in the face seems even less severe when compared to anhialation.
You cannot
know which of your assumptions will turn out to be correct in the future. Fortunately, most of the time we get it right. But since, even when our assumptions turn out to be right, we are still acting without complete information you must weigh the consequences of being wrong in every situation.
After reading that, think about the upcoming Presidential election.
What kind of person do you want making decisions that affect national security under conditions of uncertainty? Do you want someone that will take out terrorist states, even when it turns out we are wrong about their having weapons of mass destruction? Such a decision is costly. Remember, people die in war.
Or do you want someone that will hope for the best, and if it later turns out they were wrong, what then? Oops, sorry Los Angeles.
I guess it turns out that those guys actually had a nuclear weapon!
