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Economic Fables

Ariel Rubinstein

4. Economics, Pragmatics and Seven Traps

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A visit to interdisciplinary realms

1The writing of this book is replete with doubts for me. I am discussing academic issues from a personal perspective, a very personal one. While attracted to this form of writing, I do not feel completely at ease with it. In all of my academic work, I have wrapped myself in formal models of economic theory, game theory and decision theory. Typical titles of my papers were: ”A Bargaining Model with Incomplete Information” and ”Comments on the Interpretation of Decision Problems with Imperfect Recall.” So how is it that I have stooped to using the expression ”a visit to interdisciplinary realms”? If I am not careful, the interdisciplinary realms will spill into the realms of my childhood, with its intercultural nature explaining my interest in interdisciplinary subjects. And with a little imagination, I am liable even to revisit my mythological grocer (behold – he is already here again).

2The pretense of the current visit to interdisciplinary realms is to illustrate how economic thinking can contribute to the analysis of issues that are not economic. I will embark on this visit with a critical outlook that will help me to recognize traps and perhaps even search for them. Some of the traps are unique to interdisciplinary research, while others can also be found in other contexts. I will occasionally stray from the main objective of the discussion and draw the reader’s attention to a trap, one, two, three… up to seven.

3Economics is surrounded by interdisciplinary realms. The combinations of economics with sociology, zoology, criminology, psychology, law, political science, history and brain science, adorn the names of academic journals and advanced courses. I know economists who work on such combinations and wholeheartedly believe that economics has a lot to learn from other academic fields. But, in general, it seems to me that the spread of economics to other areas derives from the view expressed by the economist Steven Levitt: ”Economics is a science with excellent tools for gaining answers, but a serious shortage of interesting questions.”

4In conversations in departmental lounges or at post-seminar dinners, economists admit that economics is an imperialist profession. The giggling of those present when someone uses the expression ”the imperialism of economics” is replaced by growing embarrassment when others begin to speak with arrogance and disdain about the natives in the colonies – that is, toward anyone who has yet to discover the treasures of economic thinking.

5I am not a ”patriot” of economics and I harbor no professional colonialist ambitions whatsoever. But I too have tried to work in interdisciplinary realms, first in economics and law and later in economics and language. I was drawn to such areas because they offer the prospect of ground-breaking innovation, originality and diversity. On days when I felt reservations about engaging in economics proper, I found an abandoned territory in the interdisciplinary realms – a refuge for economics without economics.

6Consider economics and law. The field includes areas such as corporate law, antitrust law and tax law which reflect research in economics into the structure of the firm, industrial organization and public economics. But a different meaning of economics and law is of greater interest to me, and is related to my view that economic theory aims to clarify the logic of interactions between the individuals in a society. There is no reason for economic theory to restrict itself to economic interactions only. The legal system is also designed to organize the interactions between individuals in a society. And indeed, the field of economics and law examines the legal system with the tools we use to analyze economic systems. In this sense, the field employs the method of economic thinking, not the economic content.

7Economics and language sounds a stranger combination. Language theory does not address economic problems. Here, economists assume the right to deal with topics that are supposed to be the purview of linguists and philosophers of language, based on the view that economics focuses on understanding how all social institutions function. When we use the term social institution, we are referring to the prevailing mechanisms and conventions in society that organize the interaction between individuals. What is a more fundamental social mechanism for cooperation between human beings than language? This gives rise to the urge to explain language in the same way as classical economic theory explains familiar economic mechanisms.

8Even after the previous two paragraphs, I doubt whether the reader has gained even the slightest idea of how economic thinking is relevant to other fields. Instead of continuing with abstract explanations, it would be more effective to present one interdisciplinary economic study from the field of economics and language. The study to be presented here is a project I conducted jointly with my colleague Jacob (Kobi) Glazer. The project deals with situations of argument and persuasion. I was attracted to this project because it brought to mind childhood dreams that I have not fulfilled: to become an attorney for the oppressed and to win public debates on fateful issues. One advantage in discussing this particular project is that I was involved in it, and thus I am entitled to be critical without worrying about being accused of persecuting someone on a personal basis.

9I have yet to say a word about economics and language and I am already talking about what attracted me to the field. It is not obvious why one would be attracted to interdisciplinary research. This seduces us to probe into the reasons that lead a person to this particular endeavor. So here, I have already stepped onto one landmine.

Trap 1: Research in interdisciplinary realms elicits personal exposure whose place in academic writing is doubtful.

Conversation and persuasion situations

10We are entering an area that lies between economics and pragmatics. We have spoken about economics. Pragmatics is a branch of linguistics that deals with the rules guiding the implications of things said in a conversation (utterances). Pragmatics seeks to decipher the mechanisms that operate in our minds when we listen to a conversation like this one:

First conversation:

A: (who is in Jerusalem, is about to travel to London and is speaking on the telephone with B, who is in London): I can’t wait to stroll around in the streets of London. Tell me, is the weather stormy there?
B: It’s not raining hard.

11B’s statement – if detached from the context in which it was spoken – does not rule out the possibility that it is not raining at all in London. Nonetheless, in the context of the conversation, the clear meaning of B’s statement is that it is raining in London, but not hard. What are the principles that lead us to understand this statement so unambiguously?

Second conversation:

C: (outside the conference room, speaking by phone to D, who is inside the conference room): Who is participating in the meeting?
D: Most of the people I see are economists.

12D did not mention participants who are not economists. In fact, he did not say that he was looking at participants in the conference room at all (and not, for example, at passersby seen from the window of the room). Nonetheless, we have no doubt that D meant to say that most of the participants at the meeting are economists, while some of the participants are not economists. How is it so clear to us that this is what D intended to say?

13Pragmatics clarifies the rules that are engraved in our minds, which make these deductions so self-evident, without our even being aware that these rules exist. The high priest of pragmatics is the philosopher Paul Grice, whose main thesis is the cooperative principle: the rules that we employ to understand statements spoken during an everyday conversation derive from the assumption that the speaker and the listener have shared interests, and the conversation they conduct is intended to promote these interests. Grice deduces from the cooperative principle that the meaning of a statement in a conversation must be consistent with the assumption that the speaker intends to convey to the listener information that is correct, relevant, and sufficiently detailed, in the simplest possible way.

14Grice’s approach reminds us of the approach used in economics to explain and understand social institutions. We imagine a super planner who has designed a social institution in order to promote a reasonable objective. We aspire to show that a familiar social institution optimally fulfills the objective of this social designer. Well, this aspiration may be a bit exaggerated. We will be satisfied if we show that the familiar social institution shares important characteristics with the social institution the social designer would have selected.

15Let’s return to the first conversation. B takes the trouble to say ”It’s not raining hard,” and does not suffice with the shorter statement, ”It’s not raining.” This indicates that he wanted to convey something more. What could he have meant? That it is raining and it is not pouring. And why didn’t he say ”It’s raining, but not hard?” Because B wanted to be relevant and knew that what was troubling A was that if it poured he would not be able to enjoy a stroll through the city. The two utterances ”It’s not raining hard” and ”It’s raining, but not hard” are not identical. But in the context of the conversation, the rules of pragmatics make them carry the same meaning.

16In the second conversation, because D is supposed to be relevant, we deduce that D is responding to C’s question and is referring to the group of people that C is interested in – that is, the group of participants in the meeting. Thus, D intends to say that most of the people in the conference room are economists. He could have stated more informatively (and just as simply): ”All of the participants in the meeting are economists.” The fact that he did not say this leads us to deduce that that statement would not have been correct and that most – but not all – of the participants in the meeting are economists.

17Grice’s rules refer to conversation situations. In this chapter, we are interested in what we call a persuasion situation. A persuasion situation, like a conversation, involves an exchange of words. What characterizes a persuasion situation is that someone (we’ll call him the petitioner) seeks to persuade someone else (we’ll call him the listener) to adopt his opinion or perform an action. Examples of persuasion situations include: a worker tries to convince an employer to hire him, a politician seeks the public’s trust, or a telephone company attempts to convince a customer to switch over from the rival company. We are interested in identifying the principles that determine what constitutes a convincing argument in a persuasion situation and how utterances aimed at persuading someone are interpreted. In other words, we are interested in developing a theory of pragmatics that applies to persuasion situations.

Examining intuition

18Our starting point (Kobi’s and mine) was routine observation of the world. Everyday, we participate in or witness persuasion situations in the family, in the workplace, in the market and in politics. We noticed that the meaning we attribute to a statement made in a persuasion situation is often different than the meaning we would assign to the same statement if made in an ordinary, non-persuasive, conversation. When the listener interprets a statement in a persuasion situation, he is aware of the fact that the persuader is trying hard to convince him. He thinks strategically (in the sense discussed in the chapter on game theory) and takes into consideration not only what the petitioner says, but also what the petitioner chooses to say and what not to say.

19But, unlike philosophers and linguists, we economists behave as if we do not rely solely on our impressions of the world and introspection. We aspire to reinforce our impressions via experiments that usually — surprise surprise! — support our intuitions, at least in the cases that are reported. Will this also be true here?

20We asked students and lecturers in several universities around the world to relate to two stories. It cannot be said that these stories are taken from actual events though they bring to mind realistic situations. In experiments, as in models, the world is refined to the point of absurdity. We refrain from confronting the respondents with situations that are too familiar or complex. Familiar situations are not suitable because the respondents are liable to be influenced by factors specific to their own lives, but irrelevant to our study. A complex situation is liable to be incomprehensible, especially to respondents who did us a favor by participating in the experiment and have a limited attention span (you can experiment with these situations on the book’s website:​exsites/​136).

First story: Imagine that you are one of two players in the following game. There are two packs of cards in the game. Each pack contains 100 cards, numbered from 1 to 100. Two cards, one from each pack, are selected randomly and given to the other player. Only he sees the numbers on the two cards. His aim is to persuade you that the sum of the two cards in his hand is higher than 100. He can show you only one of the two cards. You have to guess whether or not the sum of the cards is higher than 100. The other player will receive a prize if he succeeds in persuading you that the sum of the numbers on the two cards is greater than 100. You will receive a prize if your guess turns out to be correct.
The other player showed you a card with the number 59. What is your guess: Is the sum of the cards in the other player’s hand higher than 100, or not?

21In this story, you are the listener and the other player is the petitioner. The story brings to mind realistic situations such as the following: a candidate for employment (the petitioner) tries to persuade an employer (the listener) to hire him. The candidate has two references from previous employers. The content of the letters can range from an enthusiastic recommendation (like the 100 card) to a scathing critique (like the 0 card). The employer does not have the time to read both of them and asks the candidate to give him just one of them (like the constraint in the story where the player can only show one card). The applicant claims that the references from his two former employers place him above the average candidate (comparable to the player claiming that the sum of the cards he holds is greater than 100). He presents a reference that is slightly better than the average (comparable to the card with the number 59). And finally, the question of whether or not the presentation of this reference supports the candidate’s chance of getting the job is comparable to the question of how to interpret the fact that the player chose to show the 59 card.

22I can think of two conflicting considerations the listener might have in mind after the 59 card is presented as evidence designed to persuade him that the sum of the two cards is greater than 100.

Naïve consideration: The listener sees the display of the 59 card as an innocent move and does not take into consideration the fact that the petitioner chose to display this card and not the other one. For the sum of the cards to be greater than 100, the number on the second card must be at least 42. The listener is aware that the second card was drawn from a pack containing 100 cards, numbered 1 to 100. He calculates the probability that the number on the second card is 42 or higher (59 %) and the probability that the second card is lower than 42 (41 %), and concludes that it is more probable that the sum of the numbers on the two cards is greater than 100.

Strategic consideration: The listener asks himself what led the petitioner to display the 59 card. He is aware of the fact that the petitioner is trying to persuade him that the sum of the numbers is higher than 100 and therefore did not show him just any card, but instead chose to show the card with the higher number of the two in his hand. Consequently, the listener deduces that the second card has a number less than 59. If so, the chance of the second card having a number between 42 and 59 (which would bring the sum above 100), i.e., 18/59, is smaller than the chance of the second card having a number between 1 and 41 (too small to make the sum of the two cards greater than 100), i.e., 41/59. Therefore, it is more probable that the sum of the numbers on the cards in his hand does not exceed 100.

23So, do people interpret the display of the 59 card as evidence that supports the petitioner or as evidence against his argument? Our sample included more than 1,500 respondents. Some 43 % of them apparently exercised the naïve consideration and deduced that the sum of the cards was greater than 100. Most of the respondents, 57 %, exercised the strategic consideration and deduced that the sum of the two cards did not exceed 100.

24What would happen if the statement ”one of the cards is the 59 card” is uttered during a conversation between two people and not in a persuasion situation? Imagine, for example, that two people are talking on the phone. One of them holds the two cards in his hand. The two people have a shared interest in determining whether the sum of the cards is greater than 100. The person holding the cards says to the other one: ”The number on one card is 59 and the number on…” and at that moment, before the speaker has a chance to mention the number on the second card, the conversation is cut off. The listener is left to guess whether or not the sum of the cards is higher than 100. Unlike in the persuasion situation, the great majority of those asked to interpret the statement (”The number on one card is 59”) guess that the sum of the cards is greater than 100. It seems that in a conversation, the listener believes that the speaker decided randomly which of the two cards to take first and not necessarily the higher card.

Second story: You are speaking with someone about the change in the level of education in major cities in the world. You are very eager to persuade him that the level of education has risen during the past decade in most cities in the world. You tell him that you have reports about the trends in the level of education in Brussels, Cairo, Manila and Mexico City. He says that he saw a reliable report indicating that the level of education in Bangkok declined during the past decade. All of your four reports support your contention, but you only have time to show him information on just one of these four cities. Presenting information on which of the four would strengthen your position most?

25The story describes a persuasion situation. You are the petitioner. Now that Bangkok has been presented as a counter-argument to your contention, you are expected to respond with an argument that is ”proximate” to the argument made about Bangkok. In this context, most people think about proximity in the geographic sense and the listener expects to hear from you about the level of education in a city near Bangkok – in our case that would be Manila. So if you present the report on Mexico City, the listener will deduce that the report on Manila does not support your contention. He will know that one case (Mexico City), supports your position, while two other cases (Bangkok and Manila) do not. If you present the details of the report on Manila, the listener will not draw any conclusion about the level of education in any of the other cities. He will then have data that supports your position in one case (Manila) and does not support your position in another case (Bangkok). Therefore, your situation will be better if you present the report on Manila.

26The findings support our intuition: in a survey conducted among about 600 students, 51 % of the respondents said that Manila was the most persuasive argument, compared to 23 % who selected Mexico City and 13 % who chose Cairo and Brussels. And this is despite the fact that Manila is not the most prominent of the four cities. When we replaced Bangkok with Amsterdam, 71 % of the respondents selected Brussels as the best argument, with the rest of the votes split evenly between the three other cities.

27A different interpretation would be attributed to this conversation if it were simply conducted between two inquisitive people rather than in the context of a persuasion situation. Let’s say that at the beginning of the discussion it becomes apparent that the level of education in Bangkok had declined (and incidentally we conducted the experiment before I visited Bangkok, when I learned that the level of education had actually risen there in the last few years). Let’s assume that one of the interlocutors is knowledgeable about the level of education in the four cities (Brussels, Cairo, Manila and Mexico City) and he mentions that the level of education in Mexico City has risen. I doubt that this statement would be taken in any way other than literally. No one would deduce anything about the level of education in the other cities based on the fact that the speaker chose to cite Mexico City as an example.

28It seems that most of the respondents, in regard to both stories, took into consideration the fact that the petitioner chose what to say and what not to say, and that his choice was made with the goal of persuading the listener.

29In the first story, the petitioner presents evidence – the card with the number 59. Ostensibly all he said was ”I have a card with the number 59,” but most of the respondents say to themselves that the speaker is rational and was doing his best to persuade the listener. If the speaker held a more convincing card, he would have shown it. Consequently, the respondents deduce that the speaker was unable to show a card with a higher number and, therefore, the sentence ”I have a card with the number 59” means that ”The highest number appearing on the cards in my hand is 59.”

30In the second story, after the listener tells the petitioner that the case of Bangkok does not support his position, the petitioner is expected to refer to Manila, the only city on the list that can be said to be geographically close to Bangkok. The most convincing argument is: ”the level of education in Manila has risen.” That is, if the petitioner had argued for example, ”the level of education in Brussels has risen”, this statement would have been interpreted as if he had presented a weaker argument, ”the level of education has risen in Brussels, but not in Manila.”

Criticism (1)

31Of course, I am happy about the faith that you, the readers, have shown in me by unquestioningly accepting the survey results I reported. But what do you know about the method by which the survey was conducted? Who were the respondents and to what extent do the responses of several hundred students reflect the general population? Do I also report experiments that did not succeed or only those whose results support what I want to show? Don’t you have a sneaking feeling that I have an interest in bending the results a bit in order to appear – to myself as well as to you – as more persuasive?

32In fact, you the readers and I are involved in a persuasion situation right now. I want to convince you that the results of the survey support the thesis that I am presenting here. I must not lie, but I can choose to highlight only the findings that support my thesis and to hide the less favorable ones. This is the situation in all experimental and empirical work. The researcher wants to appear wise, correct and original – regardless of the quality of his research.

33If we are interested in verified facts, we should look at findings with a measure of skepticism. But most of us prefer not to delve into the experimental and empirical data or examine how researchers reached their conclusions. The culture of relying on someone is especially prevalent in the interdisciplinary realms. We are not sufficiently critical when we cite research conducted in another field, because we are not knowledgeable enough to do so; often the citation is just intended to demonstrate the breadth of our horizons. We are also insufficiently critical in regard to citations from our own field, perhaps because we are interested in impressing researchers from other fields, and fear that by criticizing the works of other economists we may harm ourselves too.

34If economists would write models describing the research in economics and would include economists among the decision makers, they would certainly adopt the approach that the conclusions should not be taken at face value, and that the interests of the researchers should be taken into account. Economists would discuss the incentives they face when they collect, analyze and publish findings. They would also speak about the common interests of the members of the economics club to praise themselves in front of spectators from the other clubs. But the economists do not write models about economists. Only rarely have I heard an economist complain that a colleague who had announced a great discovery in his famous article, had been selective in his choice of the findings he presented, and had omitted data that was not quite consistent with his discovery. In other words, we have encountered another trap.

Trap 2: We are unduly impressed by studies published in the professional journals and pay too little attention to the personal interests of the researchers.

The economists are coming

35What principles determine the difference between a convincing and a non-convincing statement? Let’s return to my study with Kobi. The basic premise of our approach is that there is truth in the world. If the listener knew this truth, there would be no need for a persuasion process and the listener would adopt or reject the petitioner’s position in accordance with the truth and according to his preferences. However, the truth is not known to the listener. Only the petitioner knows the relevant facts and, independent of the truth, he is always interested in convincing the listener of something. The listener, on the other hand, would like to be persuaded by the petitioner’s arguments only under certain conditions. The situation becomes charged with tension similar to that present in many typical economic situations. The petitioner and the listener have common interests, as there are circumstances in which it is beneficial for the listener to accede to the petitioner. But there are also conflicts of interest, and there are circumstances in which it is best for the listener to reject the petitioner’s arguments. This is why Grice’s cooperative principle is not a reasonable basis for a theory explaining the rules used to interpret statements in a persuasion situation. We will therefore try to formulate an alternative principle that can explain the rules people use naturally when interpreting a petitioner’s arguments in a persuasion situation.

36In our approach, the purpose of the persuasion process is to enable the listener to extract from the petitioner as much of the information he needs as possible. We assume that a social designer implanted in human beings the rules with which they interpret the arguments and evidence presented in a persuasion situation. The designer assumed that the petitioner would act in a rational way and that the listener would listen to the petitioner and act according to the rules of persuasion implanted in him by the designer. The designer chose rules of persuasion that maximize the chance that the listener will reach the correct conclusion from his own perspective.

37The social designer determines which arguments will convince the listener and which will not. He must take into consideration certain limitations: time limitations – the listener has very little spare time; and cognitive limitations – there is a limit to the listener’s ability to absorb and digest data and draw conclusions. As we know, even the judicial system is cognizant of the severe time constraints in which the courts operate and the limits of judge’s ability to absorb and process information, even in a life and death situation.

38Who is this super-designer who defines our life for us and whose optimization will be the cornerstone to our analysis? In the best of the economic tradition, we are speaking of a ”virtual” designer. If we insist on removing the mask from this mysterious figure, we will hide behind the term ”evolutionary forces”. In some contexts (for example, when the listener is the boss), we might say that the designer is the listener himself; thanks to his strong position vis-à-vis the petitioner, he is the one who decides on the rules of the game. But, perhaps it is best to admit:

Trap 3: Actually, we are not really sure what we are doing…

39Our approach leads us to clothe the problem of the virtual designer in formal dress. We will then analyze the formal model, swept up in the magic of transforming a mysterious, vague issue into a clear mathematical problem. This is not the place for a detailed description of the formal model – that is the domain of the professional literature. Here, we will suffice with presenting a simple example, just a taste of the model.

40Actually, even if I were to write about this subject in the professional interdisciplinary literature, I would suffice with a concise presentation of the essence of the model. I would not go into great detail on linguistic issues because I am not expert enough to delve into their complexities. I would also not go into too much detail in describing the formal model, because it would deter readers who are not well-versed in economic theory. So, in other words, my own words have led me into another trap.

Trap 4: In the interdisciplinary realms, the presentations must be concise. There is no room for details. We tend to speak about the general picture and often remain there.

Building a model

41A petitioner is interested in persuading a listener about a certain matter. He can make use of the opinions of five experts: A, B, C, D, and E. Each expert has an unequivocal opinion on the matter. He either supports the petitioner’s position, or he opposes it. We will call the description of the opinions of the five experts – the state of affairs. An example of a state of affairs: A, B and D support the petitioner’s position, while C and E oppose it. There are 2 × 2 × 2 × 2 × 2 = 32 possible states of affairs. If the listener were aware of the opinion of the five experts, he would be persuaded only if the majority of experts support the petitioner’s position.

42However, only the petitioner knows the opinion of the experts. In the persuasion process, the petitioner seeks to convince the listener that the state of affairs is such that it is worthwhile for him to accept the opinion of the petitioner. An important premise (and later we will discuss it at greater length) is that the petitioner is allowed to raise an argument that represents the opinion of two experts only. A rule of persuasion defines what is considered a convincing argument and what is perceived as a non-convincing argument. The petitioner, who is aware of the state of affairs and the rule of persuasion, will check whether there is an argument that he is allowed to voice and which will persuade the listener. If there is such an argument, the petitioner will raise it.

43The petitioner is not permitted (in the model) to do anything except present the opinions of the experts. Thus, for example, he cannot curse, bang on the table or open fire… he cannot falsely claim that a certain expert supports his position when the expert does not support him. This is particularly relevant in a situation in which, beyond mere words about the experts’ views, the petitioner must substantiate his statements with the reasoned declarations of the experts.

44Finally, we come to that mysterious designer – the one responsible for choosing the rule of persuasion. The rule of persuasion he chooses will apply in all states of affairs (since the listener, who uses the rule, does not distinguish between different states of affairs). In order to assess a rule of persuasion, the designer identifies the states of affairs in which the listener makes a decision that from the listener’s perspective is the wrong one. The designer counts as a mistake (i) every state of affairs in which the listener does not want to be persuaded, yet the petitioner is able to persuade him to accept his position; and (ii) every state of affairs in which the listener would want to be persuaded, yet the rule of persuasion does not allow the petitioner to present a combination of convincing arguments. The designer does not distinguish between mistakes in the various states of affairs and attributes equal weight to each mistake. The central assumption of the model is that the designer chooses the rule of persuasion that minimizes the number of states of affairs in which the listener makes a decision that is wrong from his own perspective.

45As stated, we allow the petitioner to present arguments that include the opinions of only two experts. The model would be uninteresting if we were to allow the petitioner to present the opinions of three experts. If that were the case, the social designer would determine that a convincing argument must cite three experts who support the petitioner. This rule of persuasion would always lead to the correct outcome from the listener’s perspective. The premise of the model, stipulating that the petitioner can only refer to two experts, reflects the listener’s limitations and prevents the social designer from imposing the full burden of proof on the petitioner.

46The social designer in the model must choose one rule of persuasion from a large number of possibilities. Here are three examples of simple rules of persuasion:

471. The listener is convinced by the arguments of the petitioner if the petitioner can cite any two experts who support his position.

48This rule of persuasion leads to an undesirable outcome from the perspective of the listener in 10 of the 32 states of affairs:

  • In every state of affairs in which the listener would like to be persuaded – that is, when at least three of the five experts support the petitioner’s position, the petitioner can convince the listener.
  • The rule of persuasion prevents the petitioner from persuading the listener in the five states of affairs in which only a single expert supports the petitioner, as well as in the state of affairs in which all five experts oppose the petitioner’s position. And indeed, the listener would not want to be persuaded in these six states of affairs.
  • In the 10 states of affairs in which exactly two of the five experts support the petitioner, the petitioner can convince the listener to accept his position, despite the fact that the latter would prefer not to be persuaded.

492. Let’s assume that the five experts are naturally arranged in the minds of the petitioner and the listener in the order A, B, C, D, E, as they appear, for example, in the directory of certified experts.

50According to this rule of persuasion, the petitioner is not only required to cite two experts who support his position, but the two experts must also be ”neighbors” (A and B, B and C, C and D, or D and E).

51The rule of persuasion leads to a wrong result from the perspective of the listener in only five states of affairs:

  • The petitioner can persuade the listener in all states of affairs in which three or more experts support his position, except for the one state of affairs in which only the experts A, C and E support him. (In this state of affairs, he cannot argue that some pair of neighboring experts supports his position.)
  • The rule of persuasion prevents a mistake in the six states of affairs in which there is no pair of experts who support the petitioner.
  • Of the 10 states of affairs in which only two experts support the petitioner, in four of them the experts are neighbors and the petitioner can convince the listener, despite the fact that he was not supposed to do this; in the other six states of affairs, the experts who support the petitioner are not neighbors and he has no way to convince the listener.

523. Let us assume that the five experts are arranged in the minds of the petitioner and the listener in two groups. A, B and C are in one group, and D and E in the second. This is the situation, for example, when the five experts are similar in every way, except for the fact that three of them are men and two are women. The rule of persuasion requires the petitioner to provide evidence pertaining to two aspects of a same group (two men or two women). Citing the supporting opinions of B and C will convince the listener; on the other hand, citing the supporting opinions of A and D will not do so.

53The third rule of persuasion limits the number of mistakes to 4:

  • The petitioner can persuade the listener in all states of affairs in which at least three experts support him, because either two of the three are men or two of them are women.
  • There are four problematic states of affairs in which the petitioner can convince the listener to accept his position, despite the fact that in these states of affairs the listener would prefer not to be persuaded: these four states of affairs are when exactly two experts support the petitioner’s position and both of them are of the same sex (A and B, A and C, B and C, or D and E).
  • In all of the other states of affairs, the number of experts supporting the petitioner is not greater than two; and if there are two experts who support the petitioner, they come from different groups. In these states of affairs, the petitioner has no way of persuading the listener and no mistake is generated. What is the optimal rule of persuasion? It can be proven (we will not do this here) that every rule of persuasion involves at least four states of affairs in which the outcome of the persuasion situation will be wrong. Thus, third rule of persuasion, which is based on a division of the experts into two groups – one of three experts and the other of two experts – and which requires the petitioner to cite the views of two experts from the same group, is a rule of persuasion that minimizes the number of errors.

54According to this optimal rule of persuasion, the argument citing the opinions of B and C in support of the petitioner convinces the listener, while the argument citing the opinions of B and D in support of the petitioner does not. The two arguments seemingly convey equal information (two of the five experts support the petitioner), but nonetheless are not equally convincing. When the social designer adopts the third rule of persuasion, the argument that cites B and D in support of the petitioner’s position becomes more informative than it appears. The argument that B and D support the petitioner is interpreted as also admitting that there is no pair of supporting experts from the same group.

55As noted, our approach is that the prevalent rules of persuasion in the real world derive from the maximization performed by the social designer. If there is any truth in our approach, we would expect to find the third rule of persuasion in persuasion situations in which there is a clear division of the experts into two groups, one of three and one of two. In the absence of such a single natural division, it will not be clear to the petitioner and the listener whether or not the two experts the petitioner cites come from the same group.

The model and reality

56Is there really a connection between the optimal rule of persuasion and what people consider to be convincing? When a group of experts can be divided naturally into two groups of two and three experts, do people really find that citing testimony from two experts from the same group is more persuasive than citing testimony from two experts from different groups?

57The third story does not deal with experts, but it is still easy to see the resemblance between the story and the model.

Third story: An exam consists of five questions printed on two separate pages, three on one page and two on the other. The questions were administered to many examinees and it was found that:

  1. The fact that a person knows one answer does not indicate whether he knows another answer; and
  2. About 50 % of the examinees know the answer to every question.

58You want to determine whether an examinee’s ability is above the average in the population – that is, whether he is able to answer at least three questions. Due to time constraints, the examinee is asked to choose and answer only two questions.

Compare the following two events in terms of their ability to convince you that the examinee’s knowledge is above average:

Event A: The examinee chose two questions, one from each page, and answered them correctly.

Event B: The examinee chose two questions from the page containing three questions and answered them correctly.

59In the third story, each question reflects the examinee’s level. In other words, each question functions like an expert in the model. The examinee is the petitioner and the examiner is the listener. The examinee’s ability or inability to answer a question correctly is analogous to a situation in which an expert supports or opposes the petitioner’s position. The examinee tries to persuade the examiner via the answers to only two questions that he knows the answers to at least three of the questions.

60There is ostensibly no difference between the information received if the examinee answers two questions given on two different pages or if he answers two questions from a single page. Therefore, it would be possible to expect that the examiner would form the same opinion regardless of whether the examinee correctly answers two questions from two separate pages or two questions from the same page. However, according to our approach, an examinee who correctly answers two questions written on the same page should be considered more persuasive that an examinee who correctly answers two questions written on separate pages.

61We presented the story to students and lecturers around the world. We asked them to compare the persuasiveness of Event A and Event B. We also allowed them to say that they find the two events equally persuasive. We expected to find that Event B would be perceived as more persuasive than Event A. Of 1,300 respondents, 28 % found Event B to be more persuasive and 19 % found Event A to be more persuasive.

62Since the sample was a large one and 28 % is much higher than 19 %, it could be said that we received support for the conjecture that a correct answer on two questions from the same page is more convincing. But it can also surely be said that the results of the survey do not support our assumption because more than half of the respondents found the two events to be equal in terms of their persuasive power.

Criticism (2)

63Our discussion focuses on a very specific case and therefore sheds little light on the rules of pragmatics in persuasion situations. Furthermore, the discussion lacks the depth and understanding necessary to try to formulate and explain the natural rules that guide us in understanding utterances in persuasion situations.

64While recognizing the limitations of the model and the discussion, I found myself speaking about this study not only to economists and philosophers, but also to lawyers. Words such as: discussion, evidence, arguments and petition tempted me to hint about the possible implications of this approach for legal theory. I have nothing at the moment to contribute to legal thought, but this has not prevented me from reciting for years (and again, here and now) the mantra that it might be interesting to view legal procedure and the laws of evidence through the lenses of economic theory. While jumping from economics to linguistics, and from linguistics to the legal world, I recognized another trap.

Trap 5: The interdisciplinary worlds are like the universe. They have a tendency to expand nonstop.

65And, incidentally, there is another troublesome aspect of this interdisciplinary expansion. Under pressure from the audience and market forces, universities are dragged into approving interdisciplinary programs of study at too early a stage in the student’s academic career. In my view, an undergraduate student does not need to specialize. Instead, he should study a large number of areas from a list of basic fields such as: mathematics, philosophy, biology, history, physics, art, law and perhaps even economics. Challenging and provocative interdisciplinary studies should play a prominent role only in the course of studies for higher degrees, after the student has absorbed the forms of thinking from the basic fields.

Trap 6: The attractiveness of interdisciplinary studies leads students to engage in them at too early a stage in their studies, and thus prevents them from building a broad base of studies that can support a solid interdisciplinary pyramid.

Last trap

66We have encountered six traps, jumped from economics to language and back, formulated bold assumptions (on a narrow base of knowledge) and played with a model. I will conclude the discussion with the last and most frightening trap of all.

Trap 7: Engaging in interdisciplinary realms without deep knowledge of the basic fields raises suspicion of charlatanism.

67Now, it remains for me to wonder, perhaps in this chapter I fell into Trap 7 myself.


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