Early History of Economics- Blaise Pascal

Learning Objectives By the end of this video, you will understand the mathematical origins of economic theory. We will focus on these specific concepts. Risk, expected value, maximization, modeling decision making, and normative versus positive economic analysis. Probability Theory in the Middle Ages Well, it didn't exist. Believe it or not, all the way up until the 15th century, a rigorous mathematical treatment of the probabilistic nature of events had not been invented. Some historians believe that this is because, during the Middle Ages, it was thought that God, or gods, controlled the ultimate outcome of all events, so there really wasn't any point in inquiring about the nature of these sorts of things. Remember, this period of time is also referred to as the Dark Ages, and it marks a time when, among other things, little intellectual progress was made in many fields of study. Following the Dark Ages came a period of exploration in both the humanities and the sciences. This period is known as the Renaissance. The exploration during this time began to gather steam towards the end of this period in the 17th century, which is known as the Age of Reason. This time also marks the beginning of the formal development of probability theory. It was during this time that Blaise Pascal was working on a solution to a problem that had come up in trying to decide how to determine how winnings should be distributed in a particular game of chance. This problem is known as the problem of points. Importantly, wagering games had developed to the point where mathematics could be applied to understanding the odds of specific events occurring. Wealthy aristocrats particularly enjoyed showing off their wealth by gambling, but did not like to lose. So thinkers like Pascal were employed to determine the best strategies to guide decisions. This influence accelerated the interest in the field of probability theory. Interestingly, Pascal himself is known for inventing an early version of a roulette wheel. It is thought that he was actually trying to invent a perpetual motion machine, but it turns out he invented a very popular game found in many casinos. Let's see if we can start thinking like Pascal. The types of problems being considered are often thought of as lotteries. For example, would you buy a lottery ticket that has a 50% chance of winning $100 at a price of $45, or would you rather pass up the ticket and keep your $45? Pascal wanted to know if there is a systematic way of deciding which option to choose. At this point, I'm going to introduce the important economic concept of decision making under risk. In the context of decision making in economics, risk has a very specific meaning. It means that the decision maker knows with certainty the mathematical probabilities and outcomes of the choice alternatives. In this case, we can see that the lottery we are working with fits this description. The decision maker is told the probabilities and the potential outcomes explicitly. So, we are dealing with decision making under risk. Next, I'm going to introduce another important concept, the notion of rational decision making. In the economic world, rational behavior simply means logically consistent. We will talk about this in more detail in a later video. For now, just know that Pascal wanted to come up with a method that would produce consistent choices. To start working on this, let's rewrite the lottery that we introduced a minute ago. This will help us organize the information more clearly. Here, the two lotteries are listed in the rows, and the probability and outcome, or value, of each lottery is represented in the columns. From this figure, we can easily see that for lottery 1, there is a 50% chance of receiving $100. Furthermore, we can conceptually think of keeping our $45 and walking away from lottery 1 as a lottery with a 100% chance of us ending up with the $45. We will call this lottery 2. At the end of the day, the question is, which lottery should we choose? If we multiply probability and value, we get a new term that Pascal called expected value. Expected value is a very important concept introduced by Pascal. Please be sure that you understand it. I will explain how it is used next. Essentially, it is very easy, according to Pascal, to now make your decision. You simply choose the option with the highest expected value. In this case, Pascal would say that you should choose lottery number 1. Next, let's talk about this process as being a model of decision making. Remember that a model is an attempt to explain how some phenomenon or phenomena occurs. In this case, we know that people make decisions. We want to explain how this behavior comes about. Pascal's model suggests that people multiply probability times value to calculate expected value, and then they choose the option with the highest expected value. This is a potential explanation for observed behavior. It is a model. This is a very simple model of decision making. While it may be simple, it does have some positive features. For one, it only has two variables for guiding choice behavior. Value, which is the magnitude of the gain or loss associated with each option, and probability, which is the likelihood of actually experiencing the gain or loss. Another thing that makes this a nice simple model is that all of the parameters are observable. That is, there is no hidden information. The probabilities and value are all there for all to see. A third feature is that there is a clear method for deciding. You simply compute value times probability to get expected value, and you use the decision rule that says choose the option with the highest expected value. This is known as maximizing expected value, taking the highest expected value, which is another important concept you need to be familiar with. Finally, an observer could say whether the chooser chose correctly or not. In other words, there is a way to determine if a person's behavior is consistent with the model, and therefore rational behavior. Could this method of decision making help people live better lives? Pascal certainly thought so. Imagine someone who is deathly afraid of being struck by lightning. So much so, they suffer terrible anxiety whenever there is a storm. In contrast, the same person is not at all worried about the possibility of dying from cancer. The idea simply does not lead to any anxiety. How can Pascal's method help reduce this person's anxiety? First, Pascal would draw the person's attention to the fact that the odds of dying from lightning are about 1 in 161,856. That's an extremely low probability. Then, Pascal would explain to the person that the odds of dying from cancer are 1 in 7. That's a 12.5% probability, much greater odds than dying from lightning. In this example, the odds are essentially the expected value of the two outcomes. In this case, since we are talking about the probability of dying, the lower the probability, the better. So, if an individual has no anxiety with a 12.5% chance of death from some cause, they should be consistent and be content with dying from any cause that has lesser odds. Pascal would point out that this person's behavior is irrational, and they should not be anxious about the lightning. Pascal believed that just by explaining this rationale to people, they should be willing to change their behavior. If the person does not change their behavior, there is nothing wrong with his method, there is something wrong with the person. More on this in a minute. Now we will turn our attention to a famous thought experiment proposed by Pascal, known as Pascal's Wager. Pascal was a devout Christian and very much interested in convincing people to believe in the Christian God. He therefore set about constructing a logical argument built on his model of decision making. Here is the thought experiment. There are two possibilities. One, God exists, and two, God doesn't exist. Pascal accepts that no mortal can ever know for certain which of these outcomes is true. However, even though mere mortals can't know the exact probabilities, there are only two options. So we can say, God exists with some probability p, and God doesn't exist with probability 1-p. What a person can choose is what to believe. The options are one, believe in God, or two, do not believe in God. What can we say about the value of the outcomes associated with a person's decision to believe or not? Well, if God exists and you believe in God, the value is thought to be infinite happiness. In contrast, if God exists and you do not believe in God, then it is thought this would lead to infinite sadness. Since we know the value and the probabilities, we can calculate the expected value of the decisions. If God exists and we believe in God, we multiply p times infinite happiness and get an expected value of infinite happiness. If God exists and we do not believe in God, then we multiply p times infinite sadness and get an expected value of infinite sadness. Remember, anything multiplied by infinity is infinity. What if God doesn't exist? In this case, we multiply 1-p times zero. Since God doesn't exist, there is no value to this outcome, so the expected value overall equals zero. This is regardless of whether or not the person believes in God. This figure illustrates the current situation. As you can see, if you add up the expected value for each of the potential outcomes for a specific choice, you get the total expected value for that choice. So, in this case, the choice to believe in God leads to an expected value of infinity, whereas the choice to not believe in God leads to an expected value of negative infinity. Of course, this only holds true if p is greater than zero. If p equals zero, then the expected value is also equal to zero. Pascal argues that clearly if there is even the remotest chance that p is greater than zero, then we should maximize expected value by choosing to believe in God. Additionally, because we can never know if p equals zero, we should err on the side of caution and believe in God. I think Calvin and Hobbes captures this idea quite nicely. A while back, I mentioned that I would return to the idea that Pascal believes that if a person does not abide by his model of maximizing expected value, then they can be said to have made a mistake. It is the person that is wrong, and they should change their behavior to conform to the model. For Pascal, this was a judgment call, or an opinion. He makes no attempt to systematically test his claim. This is an example of a normative analysis of behavior. Please watch the accompanying Khan Academy video that nicely summarizes the difference between the normative and positive approach. We will talk about the positive approach in a later video. At this point, you have hopefully achieved the learning objectives and now understand the concepts of risk, expected value, maximization, modeling decision making, and normative versus positive economics. Again, we'll focus more on the positive economics in a future video. To solidify all this a bit, create two lotteries with different probabilities and outcomes, explain which lottery a person should choose and explain your reasoning using the concepts you have learned, and finally write a short critique of Pascal's model. Just a few sentences. Can his model really explain people's decisions? Why or why not? Upload this assignment to Blackboard.