Part 4 (1/2)

In the summary that follows, we see that option 1 has the highest probability and option 4 has the highest payoff (utility), but neither results in the highest expected value (EV). It turns out that placing a bet for team 2 or team 3 leads to the highest expected value (EV). This is because expected payoff must be tempered with probability of the outcome. The a.n.a.lysis below helps us see the optimal outcomes quickly.

SUNK COSTS.

Tip #17: Sunk costs are irrelevant to future decision making.

Suppose you bought a discounted, nonrefundable plane ticket for $500, which you had planned to use when going on vacation.

No sooner had you bought the ticket did an important meeting arise, one that you had been waiting months to arrange. It could definitely help move your career forward. You have a dilemma. How do you decide in a logical way what to do? Do you use the plane ticket you paid good money for or forfeit it and attend the important meeting?

According to economic theory, any past costs, also known as sunk costs, have no affect on future decision making. The only thing that affects future decisions are the cost and benefits of the two (or more) alternative courses of action.

This means that if the net benefits of this meeting are deemed greater than the net benefits of attending this trip, then we forget about the trip and attend the meeting. Of course, we must factor in both costs and benefits. The benefits of attending the meeting might involve securing a large account, getting promoted, or perhaps finding out about a new job opportunity. The costs involved might include travel to the meeting and/or the time and effort needed to prepare for the meeting. The benefits of going on vacation may well involve having a relaxing, rejuvenating experience. The costs will include accommodation and personal expenses incurred while on vacation. Note that the cost of the plane ticket is considered a sunk cost and has no effect on the decision to go on vacation or attend the meeting.

From a rational perspective, it makes perfect sense to ignore sunk costs. But from a emotional standpoint, it may be very difficult to do so. We may view sunk costs as awasteda costs and instinctively want to asavea them by investing more time and money in the project or undertaking. Weave all heard of the saying ato throw good money after bada and perhaps the telltale sign of the sunk cost dilemma are encapsulated by the words: aJust think how much time and money weave already spent.a Having spent time and money on a particular project or undertaking may have resulted in that project getting closer to completion, in which case the future costs to complete it and the benefits that will likely accrue from the completed project will ensure that work on the project will continue. However, the costs so far incurred are irrelevant to the future decision on whether to continue working on it or abandon it and change course.

It is especially difficult to detached ourselves emotionally from personal projects that have become alabors of love.a We must, however, at least acknowledge, that rationally, our previous time, effort, and money act as a sunk cost. In order to break our emotional attachment to sunk costs for the purpose of making an objective decision and possibly changing course, it is important to consider three things: 1) Recognize that cutting your losses does not necessarily mean youave made a mistake because your decision to pursue the original course of action may have been the smartest course of action at that time.

2) Enlist a few people you trust and ask them for their opinion. A person viewing our situation as an outsider may have a much more objective view of our situation.

3) Realize that most situations carry with them the seeds of greater benefit. Knowledge, skill, and insights gained from previous experiences can be applied to new situations moving forward.

HYPOTHESIS TESTING.

Tip #18: For the purposes of hypothesis testing, the minimum requirement for causal inference is evaluation using a atwo-waya table.

It is not uncommon to try to evaluate claims that have yet to be proven. This is the basis of hypothesis testing. Although hypothesis testing is usually a.s.sociated with hard-core research, it also has wide-ranging applicability, including everyday situations: Do vegetarians live longer? Does TV viewing lead to violence? Does a new miracle headache drug work better than aspirin? Do stockbrokers make better stock market investment decisions than regular business people? Do I have cancer?

Invariably we end up asking whether one thing leads to another, and this brings cause and effect into play. The minimum requirement for causal inference is evaluation using a atwo-waya table. This atwo-waya table is a de facto matrix, used to contrast information according to two variables, and for which information can be divided into four categories.

Consider the question of whether daughters share the same political beliefs as their mothers. Letas a.s.sume that exactly 100 females are surveyed. This cross-tabulation below, which is fict.i.tious though not implausible, suggests that the second generation of females follows the basic political beliefs of the first generation.

Political Beliefs Stockbroker Endors.e.m.e.nt aMy broker helped me achieve an above-average return on my stock investment portfolio. His predictions turned out to be correct, whether judging the stock market index or the performance of individual companies. My friend, a seasoned businessperson, tried to predict the market himself and consistently achieved a negative return. The advice is clear. Keep your hand out of the cookie jar and donat try to predict the stock market yourself. Use a broker and get the returns you deserve.a How do you go about evaluating the more general claim that brokers do in fact make better stock market investment decisions than do aregulara businesspersons?

In testing this hypothesis, we employ a method based on experimental design, which utilizes a matrix consisting of two primary rows and two primary columns, with nine boxes of numerical data.

Note that in this example, percentage calculations are required because the actual numbers of predictions are of unequal size (predictions by stockbrokers total 200, while predictions by regular businesspersons total 800). The percentage of correct predictions is calculated as follows: stockbrokers: 50a”200 = 25%; regular businesspersons: 100a”800 = 12.5%.

The numbers in the chart above are hypothetical. However, based on these numbers, we find that brokers are twice as likely to make correct predictions (25% vs. 12.5%), and we can conclude that there is merit in the ability of brokers, as compared with regular businesspersons, to make accurate stock market predictions. It is especially important to think not just in terms of the number of correct predictions made, but of the percentage of correct predictions made over both categories (i.e., the percentage of correct predictions made by stockbrokers versus the percentage of correct predictions made by regular businesspersons).

For a comparative problem, refer to Shark.

Hypothesis testing is about making predictions. By the word ahypothesisa we mean aa statement yet to be proven.a For example, let us say we are on our way to the doctoras office for a major checkup. In particular, we are concerned about the possibility that we might have cancer, but obviously, we know that this is a bit unlikely. So we enter our checkup with the hypothesis: aI do not have cancer.a Upon completion of tests, we will be diagnosed either as having cancer or not. In reality we may or may not have cancer, and the tests may or may not confirm this. This creates four possibilities. The hypothesis to be tested may be true or false, and we may accept or reject it. In other words, we may accept a hypothesis that is true or false, or reject a hypothesis that is true or false. The possibilities may be shown in diagram form: Generic Outline for Hypothesis Testing With respect to the chart above: TA stands for aacceptance of a true hypothesis,a TR stand for arejection of a true hypothesis,a FA stands for aacceptance of a false hypothesis,a and FR stands for arejection of a false hypothesis.a Naturally, we wish to avoid the rejection of a true hypothesis, known as a Type I error, as well as avoid the acceptance of a false hypothesis, known as a Type II error.

Hypothesis testing will always involve the possibility of Type I and Type II errors. The risk of one of these errors will always be deemed greater than the other. Letas look at the hypothesis: aI do not have cancer.a In this case, suppose the hypothesis is true and we reject it. We have committed a Type I error. Now suppose the hypothesis is incorrect and we accept it. Then we have committed a Type II error. Here, the Type II error is more serious than a Type I error. The Type II error would lead a person with cancer to go unchecked, with the cancer becoming more serious. The Type I error is not as serious but would likely prove detrimental. Not only would it be psychologically damaging to think that you have cancer, but it could also be physically damaging if you were subjected to more tests and treatments.

Now view this same example in terms of the reverse hypothesis: aI have cancer.a In this case, with reference to the following matrix, suppose the hypothesis is true and we reject it (thus committing a Type I error). Now suppose the hypothesis is incorrect and we accept it (thus committing a Type II error). This time the Type I error is more serious for the identical reason cited in the previous scenario.

In summary, all research propositions should be a.n.a.lyzed in this manner. We should ask: If the hypothesis is true, what are the consequences of rejection? If the hypothesis is false, what are the consequences of acceptance? Depending on our answer, we will risk committing one error more than the other.

Note that Type I and Type II errors are discussed with more frequency with respect to medical situations, where the impact of such errors is more serious. In other situations, as seen in the previous examples t.i.tled Political Beliefs and Stockbrokers, these two types of errors are not nearly as critical.

PRISONER'S DILEMMA.

Tip #19: The Prisoneras Dilemma provides an example of how cooperation is superior to compet.i.tion.

Once upon a time, the police caught two suspects with ample counterfeit notes in their possession. The police knew the two men were acquaintances and escorted them to separate jail cells so they couldnat connive. The police knew the men were working in collusion but couldnat find the counterfeiting machine after a thorough search of each of their premises. Without more solid evidence, the police knew the suspects would receive light sentences, as they had semi-plausible alibis.

Indeed, a confession was needed. The police decided to offer immunity to the first suspect who confessed and also offered up the location of the counterfeiting machine. This person would go free, and the other suspect would get a 10-year prison sentence. If they remained silent, they could each expect a three-year prison sentence for possession of multiple counterfeit bills. Each suspect was also told, out of judicial fairness, that if they both confessed they would each receive a seven-year prison sentence.

Each suspect faced four possible outcomes: If you were one these suspects, what would you do?

First you might consider what your partner will do. Letas say the you both decide to keep quiet. If you keep quiet too, you get three years; if you confess, you go free. Thus, itas better for you to confess when your partner keeps quiet a” you go free.

But what if he confesses? Now if you keep quiet, you get ten years; if you confess, you get seven years. Thus, if he confesses, itas also better for you to confess (results in three fewer years). Regardless of what he does, you avoid three years in jail by confessing.

It sounds like you should confess. The hitch a” a big hitch a” is that if he figures things out the same way, heas going to confess a” just like you a” and you will both get seven years, even though you both could have kept quiet and only received three years each.

This situation is called the Prisoneras Dilemma. The story was first told by economist A.W. Tucker in 1950. The police have probably known this game for a long time. So have criminals. It is just one version of a simple but compelling bargaining game.

The Prisoneras Dilemma is an example of a mixed-motive game: Both parties can do well if they work together by cooperating or they can try to gain an advantage over each other by competing. The fact that elements of both cooperation and compet.i.tion are simultaneously present makes for mixed motives and contributes to the inherent complexity in these and similar games.

The Prisoneras Dilemma game is also an example of an individual versus group game. Here we can choose to work for the group or for ourselves. When everyone in a group contributes (i.e., acts cooperatively), everyone benefits. If some people act individually, however, they keep what they might have contributed to the group, and they also share in what everyone else has contributed. It is the cla.s.sic distinction between givers and takers. It is the basis for the conclusion that anice people finish last.a Dilemmas that fit the requirements for a Prisoneras Dilemma often can be summarized as follows. The first word in each pair denotes the outcome of the first person; the second word in each pair denotes the outcome of the second person: If both parties cooperate, they are rewarded; if they both defect, they are punished. If one cooperates, but the other defects, the cooperator is the loser (or sucker or saint, depending on your point of view) and the non-cooperator is a winner (but traitor). In true Prisoneras Dilemma games, the winneras payoff always exceeds the loseras payoff (measured here in terms of fewer years served).

As highlighted, the aggregate benefit of cooperation exceeds the aggregate benefit of non-cooperation. For example, if both counterfeiters cooperate, they will serve an aggregate of 6 years of prison time (i.e., 3 + 3 = 6 years). If both counterfeiters fail to cooperate, they will serve a total of 14 years of prison time (i.e., 7 + 7 = 14 years). A middle ground arises when one person cooperates and the other doesnat because this leads to an aggregate of 10 years of prison time (either 10 + 0 = 10 years or 0 + 10 = 14 years).

Not surprisingly, expectations play a big role in how people respond to these dilemmas. In other human endeavors, if one person defects when the other cooperates, the pair faces a major crossroads. If one of two business partners, for instance, doesnat contribute as much as the other thought he or she would, they may have to work out a whole new arrangement. If two people pursue individual and mutually contradictory goals within a single partners.h.i.+p, the likelihood of adivorcea is imminent. When two people both contribute substantially to a growing relations.h.i.+p, aromancea can flourish.

Chapter 4.

a.n.a.lyzing Arguments.

I can stand brute force, but brute reason is quite unbearable.

There is something unfair about its use.

It is. .h.i.tting below the intellect.

a” Oscar Wilde.

OVERVIEW.

Arguments What is an argument? An argument is not a heated exchange like the ones you might have had with a good friend, family member, or significant other. An argument, as referred to in logic, is aa claim or statement made which is supported by some evidence.a A claim is part of a larger concept called aargument.a aOh, it sure is a nice day today.a This statement is certainly a claim, but it is not an argument because it contains no support for what is said. To turn it into an argument we could say, aOh, it sure is a nice day today. We have had nearly five hours of suns.h.i.+ne.a Now the claim (ait sure is a nice daya) is supported by some evidence (anearly five hours of suns.h.i.+nea).

Letas get some definitions out of the way.

Definitions Conclusion: The conclusion is the claim or main point that the author, writer, or speaker is making.