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 partnership, the likelihood of adivorcea is imminent. When two people both contribute substantially to a growing relationship, 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 sunshine.a Now the claim (ait sure is a nice daya) is supported by some evidence (anearly five hours of sunshinea).
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.
Evidence: The evidence includes any facts, examples, statistics, surveys, and other information or data that the author (writer or speaker) uses in support of his or her conclusion.
a.s.sumption: The a.s.sumption is the authoras unstated belief (aunstated evidencea) about why his or her claim is right. An a.s.sumption is that part of the argument that the author, writer, or speaker a.s.sumes to be correct without stating so; it is athat which the author takes for granted.a More poetically, the a.s.sumption may be said to be athe glue that holds the evidence to the conclusion.a THE ABCs OF ARGUMENT STRUCTURE Tip #20: Evidence + a.s.sumption = Conclusion. The a.s.sumption is the glue that holds the evidence to the conclusion.
The following expresses the relationship between the three elements of cla.s.sic argument structure: Conclusion = Evidence + a.s.sumption or Conclusion a" Evidence = a.s.sumption The ability to understand simple but formal argument structure is useful, if not essential, to advance critical thinking. After identifying the conclusion and evidence, we then proceed to examine the third element, called the a.s.sumption. So how do we go about identifying the first two elements, the conclusion and evidence?
Identifying the Conclusion and Evidence Confusion may arise as to what part of an argument is evidence and what part is the conclusion. Certain "guide words" always signal the use of evidence or the start of the conclusion. The chart on the next page lists the most common guide words. If, for example, you hear someone say, aBecause the economy is getting better, Iam going to buy a car,a you may presume that the phrase abecause the economy is getting bettera is evidence. The reason for this is that abecausea always signals the use of evidence. The remaining phrase aIam going to buy a cara contains the conclusion. Note that these phrases may also be reversed without affecting what is the evidence and conclusion. For example, aIam going to buy a car because the economy is getting better.a If possible, use guide words to identify the conclusion and evidence in an argument.
It is important to note that guide words will not always be present to guide you, meaning that you cannot always rely on them to locate the conclusion and the evidence in an argument.
Locating the a.s.sumption Whereas the conclusion and evidence in an argument are always explicit, the a.s.sumption is always implicit. The fact that a.s.sumptions are by definition implicit means that they will not be stated, that is, written down on paper or spoken out loud by the speaker. They exist foremost in the mind of the author or speaker. Conclusions and evidence, on the other hand, are explicit. This means that they will be stated a" physically written down on paper or spoken out loud.
EVALUATING ARGUMENTS.
Tip #21: There are effectively two ways to attack an argument: attack the evidence or the a.s.sumption(s).
In seeking to evaluate arguments, we must aggressively a.n.a.lyze each component. How strong is the evidence? How strong is the key a.s.sumption? Obviously, in order to attack the evidence and the a.s.sumption, we must be able to identify them.
Short exercises: To practice using cla.s.sic argument structure to evaluate arguments, fill in the missing pieces below a" conclusion, evidence, and a.s.sumption. Proposed solutions follow below.
1. Dorothy and her College Entrance Exam Argument: As Dorothy achieved a high score on her college entrance exam, she will surely succeed in college.
Conclusion: Evidence: a.s.sumption: 2. Finland Argument: Finland is the most technologically advanced country in the world. More people per capita own mobile phones in Finland than anywhere else on earth.
Conclusion: Evidence: a.s.sumption: 3. Taking on the World with a Smile Argument: Dear Anita: You know, I get such a great feeling when I talk to my old high school friends and find out theyare doing well. Just yesterday, I spoke with Paul and Maxine and have been in a good mood ever since. Say, I hear youare kind of down in the dumps lately. If you go home and call your high school friends, it will cheer you up and you will be ready to take on the world with a smile. Talk to you soon, Bill.
Conclusion: Evidence: a.s.sumption: 4. Quick-Stop vs. Big-Buy Grocery Stores Argument: I shop at Big-Buy grocery stores because prices are 10% less than at Quick-Stop grocery stores.
Conclusion: Evidence: a.s.sumption: 1. Dorothy and her College Entrance Exam (Solution) Argument: As Dorothy achieved a high score on her college entrance exam, she will surely succeed in college.
Conclusion: Dorothy will surely succeed in college.
Evidence: She achieved a high score on her college entrance exam.
a.s.sumption: Success on a college entrance exam leads to success in college or, stated another way, success in college requires the same set of skills as is required to perform well on a college entrance exam.
Letas evaluate the argument.
Attack the evidence Did Dorothy really score high on her college entrance exam? How high is high? In other words, we need to find out what score she actually got and then verify that it was indeed a ahigha score.
Attack the a.s.sumption This argument a.s.sumes that a high test score is not only enough to get accepted to college in the first place, but also that itas a good predictor of success in college. First, the college admissions process also considers other factors, including a candidateas written application essays, extracurricular activities, personal/academic references, and even an interview. Second, other factors that are likely required for success in college are not related to taking a test. Succeeding on a test requires no interaction with anyone except oneself. What about other factors, such as personal motivation, independence, or emotional stability? Some courses may require group projects. In short, Dorothy may not have the personal qualities to succeed in college, even though sheas mighty fine at taking an entrance exam!
2. Finland (Solution) Argument: Finland is the most technologically advanced country in the world. More people per capita own mobile phones in Finland than anywhere else on earth.
Conclusion: Finland is the most technologically advanced country in the world.
Evidence: More people per capita own mobile phones in Finland than anywhere else on earth.
a.s.sumption: Ownership of mobile phones is the best criterion for determining whether a country (or its people) is technologically advanced.
Letas evaluate this argument.
Attack the evidence Even though people own phones, do they actually use them? Do they know how to use the vast majority of all the phone functions? Also, are mobile phones as technologically sophisticated in Finland as they are in other countries?
Attack the a.s.sumption Perhaps ownership of mobile phones (per capita) is not the best criterion for determining technological advancement. Perhaps a better, more accurate criterion is ownership of computers or the ability to use computer software. Or perhaps the best criterion for determining technological advancement is the ability to manufacture technologically advanced equipment.
3. Taking on the World with a Smile (Solution) Argument: Dear Anita: You know, I get such a great feeling when I talk to my old high school friends and find out theyare doing well. Just yesterday, I spoke with Paul and Maxine and have been in a good mood ever since. Say, I hear youare kind of down in the dumps lately. If you go home and call your high school friends, it will cheer you up and you will be ready to take on the world with a smile. Talk to you soon, Bill.
Conclusion: If you go home and call your high school friends, it will cheer you up and you will be ready to take on the world with a smile.
Evidence: You know, I get such a great feeling when I talk to my old high school friends and find out theyare doing well. Just yesterday, I spoke with Paul and Maxine and have been in a good mood ever since. Say, I hear youare kind of down in the dumps lately.
a.s.sumption: In the same way that calling his high school friends aworksa for Bill, it will also aworka for Anita.
Again, there are two ways to attack this argument: Attack the evidence Is Anita really feeling down? Are Billas buddies actually doing well? Are Paul and Maxine actually the high school cla.s.smates of Bill?
Attack the a.s.sumption Does Anita have high school friends? Are they also doing well? Upon hearing that Anitaas high school friends are doing well, will she react as favorably as Bill did (hopefully Anitaas not the jealous type)?
4. Quick-Stop vs. Big-Buy Grocery Stores (Solution) Argument: I shop at Big-Buy grocery stores because prices are 10% less than at Quick-Stop grocery stores.
Conclusion: I shop at Big-Buy grocery stores.
Evidence: Prices are 10% less.
a.s.sumption: Price is the decisive factor in determining where I shop for groceries. Or stated more simply, when choosing between Big-Buy and Quick-Stop, I choose based on price.
Letas attack the argument: Attack the evidence Are prices really 10% less at Big-Buy grocery stores? Are prices even cheaper at all? We need proof. Perhaps itas time to check grocery receipts to verify claims of lower prices. Donat just take for granted that all evidence is really agooda evidence. Moreover, is quality constant? If the quality of two items is different, better quality might warrant paying higher prices.
Attack the a.s.sumption For example, we may want to attack the a.s.sumption by saying that price should not be the motivating factor as to where we shop. Perhaps location or proximity is a better criterion, or perhaps customer service should be the key factor influencing where we shop; perhaps store appearance and cleanliness should be the determining factor; perhaps prestige is the driving factor.
THE FIVE COMMON REASONING FLAWS.
Tip #22: The five most common critical reasoning errors include: comparing aapples with oranges,a over-generalizing on the basis of small samples, ignoring relevant evidence, confusing cause and effect, and failing to antic.i.p.ate bottlenecks when plans are put into action.
When we speak of critical reasoning errors, we are referring largely to errors relating to the a.s.sumptions we make. Of the five common types of a.s.sumptions, the first category falls under comparison and a.n.a.logy a.s.sumptions and requires that we compare two things which, although different, are logically equivalent. In general, we want to compare apples with apples and oranges with oranges, without mixing the two. The second category falls under representativeness a.s.sumptions. This reasoning error involves overgeneralizing on the basis of small samples or limited experience. In making the a.s.sumption that a sample is representative of the larger whole, we strengthen an argument. In making the a.s.sumption that the sample is not representative of the larger whole, the overall argument is weakened. The third category falls under agood evidencea a.s.sumptions. This reasoning error occurs when we take for granted that the evidence chosen is valid. The a.s.sumption that evidence chosen is objective, typical, and truthful serves to strengthen any argument; the idea that evidence chosen is subjective, atypical, or spurious serves to weaken any argument. The fourth category falls within the topic of cause-and-effect a.s.sumptions. This reasoning error occurs if we mistakenly match cause with effect, or a.s.sume, without adequate evidence, that one event is the cause of another. The fifth category falls under implementation a.s.sumptions. This reasoning error arises from not antic.i.p.ating bottlenecks when plans are put into action, and occurs whenever we a.s.sume outright that plans can be turned into action without significant impediments.
Comparison and a.n.a.logy a.s.sumptions We make comparisons based on people, places, things, or situations. Often it is done through a.n.a.logy. What is an a.n.a.logy? An a.n.a.logy is a comparison of two (or more) items made on the basis that because they share one or more similarities, we can therefore a.s.sume they are alike in one or more other respects. An a.n.a.logy is created every time a researcher delves into the realm of biological experimentation and compares the results done on animals, usually mice, to human beings. Sometimes, the comparison involves personal characteristics. We may see certain traits or characteristics in a father and son or mother and daughter and believe it is the basis for their sharing other similar characteristics. Other times, the comparison involves comparing two situations or events over different time periods. Many corporate decisions are still based on the idea that what has worked in the past will work in the future. International law is also, in large part, based on the principle of historical precedent.
The general strategy for attack is as follows: In terms of evaluating or attacking comparisons, when two things are deemed similar, our goal will be to find dissimilarities in order to show that the two things are not alike. Consider the following example: aMartha did such a great job selling cutlery that weare going to promote her and put her in charge of condominium sales.a What is being a.s.sumed is that sales ability is the key ingredient in making sales, and the type of product being sold is of secondary concern. How could we attack this argument? One way is to indicate that there could be a big difference between selling cutlery, a commodity product, and selling a condominium, a luxury good. A person effective at selling one type of product may be ineffective when selling another type. In the entrepreneurial context, a person successful in one industry may not be successful when switching to another industry.
In terms of evaluating or attacking comparisons, when two things are deemed dissimilar, our goal will be to find similarities in order to show that the two things are alike. For example, two male sports enthusiasts are having a beer, when one says to the other: aThere is no comparison between athletes today and athletes of yesteryear. Mark Spitz won seven gold medals in swimming in the 1967 Mexico City Olympics, but his winning times are not good enough today to qualify for any of the menas Olympic swim events.a To damage this argument, the second sports enthusiast might want to choose an example to show how athletes today are in some ways comparable to the athletes of yesteryear. For example, Jack Nicklausa final round score of 271 in 1965 to win the Masteras Golf Tournament in Augusta, Georgia, could be compared to Tiger Woodsas final round score of 272 in 2002 to win the Masteras Golf tournament on the exact same course. In this respect, by comparing two athletes in this manner, things do not look so dissimilar after all.
When comparing two things, particularly those across different time frames, we must be careful not to a.s.sume that information gathering techniques and, therefore, the quality of the data obtained are comparable. For example, any report comparing the findings of worker satisfaction levels in the 1940s to worker satisfaction levels today would be suspect, for no other reason than the difficulty of comparing the results of information gained under differing circ.u.mstances.