Stephen Slade
Yale Computer Science Department
Computer Science 458/558
Fall 2016
It is trivial for a computer to make a decision. Any branching code, like an IF-THEN-ELSE statement, provides the mechanism for a computer to make a decision.
IF (abdominal pain) THEN (appendicitis)
That’s the general idea. However, this example adheres to H.L. Mencken’s aphorism:
Explanations exist; they have existed for all time; there is always a well-known solution
to every human problem — neat, plausible, and wrong.
There are many other considerations. Is the patient pregnant? How about food poisoning? Are there other symptoms? Is there a fever? Has the patient already had her appendix removed? (Does the patient have insurance?) The reader can likely provide additional exceptions or clarifications.
Mathematical logic teaches the principles of reasoning about statements which are either true or false. There is a syllogistic framework.
p implies q
p
therefore, q
All men are mortal.
Socrates was a man.
Therefore, Socrates was mortal.
Our previous example follows this paradigm.
Abdominal pain implies appendicitis.
Abdominal pain.
Therefore, appendicitis.
It is neat, plausible, and wrong - or at least not conclusive beyond doubt.
In mathematical logic, a contradiction leads to a fallacy.
p and not p
results in a dead end. No more reasoning can continue down this path.
However, humans often are faced with mixed reasons, that is, reasons for and against a given action. I want to eat the ice cream because it tastes good, but I know that it is fattening and may give me diabetes. I have “p and not p”. We want our model to be able to handle cases like this. Decision making is not a logical process. It is a psychological process. We will show that computers can handle this as well, thank you very much.
Let us look at a range of decisions. Here are some examples.
In a hand of blackjack, the dealer shows an Ace. My hand is worth 12. Should I take another card?
As an executive at Ford, I need to build a new auto plant. The options are a $40 million plant in Ohio that can produce 1000 cars a month with union labor, with an expected lifetime of 12 years and a $20 million dollar plant in South Carolina that can produce 500 cars a month with non-union labor and tax incentives and an expected lifetime of 10 years. Which is best?
My patient has a bacterial infection. What antibiotic should I use to treat her?
I am Julia Child. How do I make a strawberry souffle (for the first time)?
I am a member of Congress. How should I vote on a balanced budget bill?
According to the CDC, ``Compared to nonsmokers, men who smoke are about 23 times more likely to develop lung cancer and women who smoke are about 13 times more likely.'' If you learn that a woman has been diagnosed with lung cancer, and you know nothing else about her, what is the probability that she is a smoker?
I am a self driving car. Is it safe to turn left?
I have a retail clothing store. How many pairs of jeans should I order in each size for the fall?
I am Goldman Sachs. One of my traders has open trades totalling $250 million. Should I permit her to make more trades?
I am Netflix. You just watched Napoleon Dynamite. What movie should I recommend?
I have a program that can process 5000 cases in an hour. How can I make it process 5 million cases in a minute?
I am Google. When you run a search, before I display the results, I auction off pieces of the screen real estate to advertisers using real time bidding. How do I do that?
These examples appear to be orthogonal. They cover disparate domains. There are several unifying elements. FIrst, each is a decision or problem that can occur inside a human head. That is, each example is something that a person (albeit not everyone) can do. Second, each problem can be solved or modeled or attempted by a computer program, with little or no human intervention. That is, each problem is computationally feasible. Finally, each question corresponds to a topic discussed in each successive week of this course.
To get you in the proper frame of mind, here are some other suggestive decisions, with a more autobiographical focus.
What college should I attend?
In what should I major?
What should I do this weekend?
What do I get my brother for his birthday?
What do I do after I graduate?
Do I need a car?
Do I need to do laundry?
What am I having for dinner?
Do I want to get married?
Do I want to go to graduate school?
Should I go running this morning or sleep in?
Let me restate that major premises of this course.
Decision making is a cognitive process. People provide an existence proof. That is, it is possible for people to make all kinds of decisions.
For many classes of decisions, it is possible to create a computational model of the decision process. These process models require the explicit representation of the elements of a decision.
At this point in your computer science career, you are knowledgeable about data structures, such as lists, stacks, queues, heaps, and object oriented classes. A unifying question in this course is to define a data structure for decisions. Ideally, a single data structure, cunningly crafted, should handle all types of decisions.
Here are some additional questions to consider when modelling decisions.
Who is affected by this decision, positively or negatively?
How much will it cost to put this decision into action? (Allocating resources such as time and money)
How do I feel about this decision?
What are the moral implications of this decision?
How do I explain this decision?
How can I persuade someone else to make a decision? That is, persuasion can be viewed as decision making once removed.
Does the outcome define the quality of the decision? For example, if I am a doctor and the patient under my care dies, did I make a bad decision?
That last question may seem odd. A good decision is one that results in a positive outcome. If I buy a stock and it goes up, then the decision was good. Otherwise, it was bad. If I decide to attend Yale and I graduate and have a happy life, it was a good decision.
Conventional wisdom is to judge the quality of the decision by its outcome. A leading researcher who questioned this position is Ronald Howard, a professor at the Stanford Business School and the founder of the field of Decision Analysis in the 1960’s. (see reference) Howard has illuminated many aspects of decision making, including the sometimes misleading focus on outcomes.
We note that there is a recursive dimension to decision making. That is, making a decision, like what kind of car to buy, requires a prior decision, namely, to buy a car, and more subtlely, to think about car buying at all. Decisions often involve resource allocation, such as how much money to spend. All decisions require allocation of cognitive resources, or attention. If we assume that the brain has something like an operating system which schedules what you think about and when and for how long, this mental scheduler is making decisions about how to focus your attention. The scheduler is operating more or less non-stop. Presumably it is even deciding what happens when you sleep, and whether you need to wake up when you hear a loud noise in the night. The point is that decision making is constant, at some level. It is useful to be able to view and analyze individual decisions in isolation. In physics, the laws of motion are formulated for isolated points in space without friction. At some point, friction needs to be introduced. Similarly, a realistic model of decision making must account for attention. What domains may require such a robust model?
The process of thought is often labeled reasoning. More specifically, decision making often entails the generation of reasons: the justification for a given choice. If the decision involves another party, an explanation is often required. The psychologist Ellen Langer performed an experiment in which someone was interrupted at the copy machine in an office and told one of the following three statements by the experimenter.
Excuse me, may I use the Xerox machine?
Excuse me, may I use the Xerox machine because I want to make copies?
Excuse me, may I use the Xerox machine because I am in a rush?
Note that cases 2 and 3 provide reasons, though the reason in case 2 really does not add any information. Langer found that compliance was greater in cases 2 and 3, than in case 1. There was little difference in the compliance rate for cases 2 and 3. The conclusion is that the subject was responding merely to the existence of a reason, not the substance.
We have a higher standard for a decision making model. It is compelling to review decisions, both public and private, and determine to what degree the reasons or explanations are in fact reasonable.
It seems axiomatic that good decisions are based on good reasons. Particularly if we want to evaluate the quality of a decision by factors other than the outcome, we should insist that the reasons support a decision are sound.
This is not as easy as it may seem. Let me give you a personal example. Some decades ago, I had a relative who needed major cancer surgery during the Christmas holidays. The patient had older friends who advised her not to have the surgery. They reasoned that the doctors were merely trying to generate work for themselves during the slow holiday period. They suspected that the doctors’ true intentions were to make money for themselves during a slack time, rather than the dire need for medical intervention. The patient ignored this advice and went ahead and had the surgery (and is still alive today). At that time, I was appalled at questioning the doctors' motives. I felt that this advice was not only misguided, it also needlessly added to the trauma and suffering of the patient by introducing additional worry and doubt.
Recently, I was reminded of this episode when I learned of studies that showed that doctors regularly recommend Caesarian sections for childbirth when natural childbirth is clinically indicated. The studies conclude that doctors benefit from the Caesarian procedures both in terms of fees (they can charge more for an operation than for natural childbirth), and convenience (operations can be scheduled during normal work hours instead of occurring whenever the baby decides to arrive). In addition, Caesarian birth can pose greater risks for the mother. The clear conclusion is that the motives of the doctor are not always benign.
Howard, Ronald. The Foundations of Decision Analysis Revisited
http://www.usc.edu/dept/create/assets/001/50843.pdf
http://opinionator.blogs.nytimes.com/2014/05/07/in-delivery-rooms-reducing-births-of-convenience/
hw: introduction to Python and R
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Slade, Automated Decision Systems |
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