06.FALLACIES & BIASES

Transcription

1 Methods in Philosophical and Instructor: Carlo Martini T.A.: Rami Koskinen Critical Thinking 06.FALLACIES & BIASES Except where otherwise noted, Methods in Philosophical and Critical Thinking by Carlo Martini is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

2 Why should we study fallacies? Just like we d like to know what makes an argument valid, we d like to know what makes an argument invalid. Being able to idendfy incorrect reasoning is just the other side of the medal. In theory: correct reasoning < > not-incorrect reasoning CORRECT REASONING REASONING INCORRECT REASONING In pracdce, things are a bit more complicated.

3 A fallacious argument All science is essendally materialisdc. Karl Marx, a very influendal philosopher of the XIX century was certainly a materialist; therefore, he must certainly have been sciendfic. IF sciendfic THEN materialisdc, materialisdc THEREFORE sciendfic Compare: All dogs are mammals, X is a mammal THEREFORE X must be a dog. Fallacy: Affirming the consequent

4 Formal and informal fallacies Formal fallacies are misuses of some of the inferendal rules of a given formal methods: e.g. misuses of the logical rules of inference, or misuses of the probability calculus. Informal fallacies are more commonly found in verbal arguments. Informal fallacies are harder to detect, and the principle of charity should apply: our logical standards should be high, but our applicadon of those standards to arguments in ordinary life should also be generous and fair. (Copi, Cohen p. 110) In other words, when reconstrucdng/analyzing an argument, we should avoid making it trivially fallacious: Perhaps the argument can be expressed in a way that patches some of the obvious fallacies that the author could not possibly have commiaed.

5 Categorizing fallacies Categorizing fallacies is helpful because it allows us to recognize paierns of incorrect reasoning, not just single instances. Compare: Everyone wears jeans. You should wear jeans too. We all think that religious beliefs should be respected. It is immoral to denigrate religions. If we see the mistake in both arguments, it is not because each is mistaken in their own respect, but because both contain a fallacious paiern of reasoning: All do X, it is right to do X. Compare: Paaerns of correct reasoning Paaerns of incorrect reasoning

6 Why are fallacies fallacious? What is it that makes a fallacy a mistake in reasoning? Fallacies are such only to a normadve standard. But what normadve standards we choose may depend on a number of factors. N.B.: The word fallacy usually refers to logical thinking, the word bias is more general, and refers to thinking, judgment, decision making. We can safely use the two words interchangeably.

7 Fallacies and normative reasoning. Immagine the following: you are feeling sick, you know it s not something that you had before, you think you need medicadons. What do you do? Imagine the following: your car broke down. What do you do?

8 Fallacies and normative reasoning. Most people would reply to the previous quesdons with: I would go to the doctor. And I would call a mechanic. But now imagine you were asked by your friend: why are you taking this and that medicadon? or why did you have this and that components of your car replaced? You would probably reply because the doctor said so and because the mechanics advised so. From a purely logical point of view, those would be argument by authority. In fact, in most of our daily judgments and arguments we do rely on authority. So is authority a good guide to life? What normadve model do we take to jusdfy or otherwise reject arguments by authority?

9 Fallacies and normative reasoning. Unlike many other fields of psychology, such as the study of percepdon, where the emphasis is on finding out how it works, much of the study of thinking is concerned with comparing the way we usually think with some ideal. (Baron, p. 32) Ideal: normadve vs. prescripdve Part of our subject maaer is therefore the quesdon of how we ought to think. If we know this, we can compare it to the way we do think. Then, if we find discrepancies, we can ask how they can be repaired. [ ] we shall have to discuss models or theories of how we ought to think, as well as models of how we do think. Models of how we ought to think will fall, in our discussion, into two categories: prescripdve and normadve. (Baron, p. 32)

10 Prescriptive and normative models of thinking PrescripDve models: tell you how you ought to think may consist of heurisdcs, rules of thumb, etc. are fast and frugal (cf. Gigerenzer) NormaDve models: evaluate our radonal and decision making processes reladve to given goals and means they are osen complex (e.g. probability theory, logic) we normally do not use them in daily acdvides Example: How do you decide whether to take a rain jacket before going out? How do you decide how to price a product you plan to sell?

11 Quick and slow modes of argument evaluation How do evaluate an argument or an acdon? Even if the calculadons somedmes yielded beaer choices than the choice than the heurisdcs would yield, the difference between the two choices in desirability usually would be too small to make the calculadon worthwhile as a general policy. (Baron, p. 33) E.g. when should I carry a rain jacket for outdoors acdvides? Always

12 Normative, descriptive and prescriptive models In short, normadve models tell us how to evaluate judgments and decisions in terms of their departure from an ideal standard. DescripDve models specify what people in a pardcular culture actually do and how they deviate from the normadve models. PrescripDve models are designs or invendons, whose purpose is to bring the results of actual thinking into closer conformity to the normadve model. If prescripdve recommendadons derived in this way are successful, the study of thinking can help people to become beaer thinkers. Baron, p.34

13 Descriptive models of thinking Study the way people think, not they way they should think; or the way people use arguments and words, not the way they should use them. E.g. Kathy and Tom got married and had a baby. This implies that fallacies are not only faulty reasoning paaerns but, somedmes, also quick ways of reasoning. SomeDmes reasoning that is fallacious under a given normadve model, can make us achieve the same results that we would have achieved, had we applied the full normadve model, but much faster. Osen, however, fallacious reasoning and biased reasoning can take us astray when the condidons are such that we should apply a fully normadve model for the kind of reasoning, or decision-making we are faced with.

14 Fast thinking or normative model ROYAL FLUSH highest-ranking standard poker hand 4 possible r. flushes in a deck of cards FLUSH fourth highest ranking poker hand 5108 possible straight flushes in a deck of cards Which sequence is more likely in Poker?

15 Fast thinking or normative model Compare: Baron, p. 31 All families with six children in a city were surveyed. In seventy-two families, the exact order of births of boys (B) and girls (G) was G B G B B G. What is your esdmate of the number of families surveyed in which the exact order of births was B G B B B B? This was a real experiment, and most people tend to reply that the second sequence is less likely. What is the probability of each birth? What is the probability of each sequence?

16 Categorizing biases Most studies on biases are just long lists of the thousands of ways our reasoning in argumentadon or in decision-making can go the wrong way. Is there any unifying principle behind biases? A bias or a fallacy, is a deviadon from a normadve model of reasoning or decision making. Biases call for: A descripdon (what the bias is, how people reason, as a maaer of fact) A normadve model (how people ought to think/decide, given a certain goal) An explanadon (why there is a deviadon between the descripdve and the normadve e.g. limited cognidon, fast thinking, use of heurisdcs, etc.).

17 Categorizing biases From Baron, Table 2.1

18 The study of biases experiments and theory

19 Biases and fallacies A fallacy is a schema of incorrect reasoning: We commit a fallacy when we violate a rule of reasoning (e.g., we infer the antecedent ). A bias is more general: it is a tendency towards systemadc error* in reasoning, behavior, etc. E.g. We can be biased against a minority when we systemadcally give the majority a beaer treatment. E.g. We are biased when we tend to commit the conjuncdon fallacy when evaluadng probabilisdc events. A bias can be the result of commicng a fallacy of reasoning (logical, probabilisdc, etc.), but not necessarily. Here we focus on biases that are the result of fallacious reasoning (e.g. no moral biases).

20 A geography quiz hap://

21 Overconfidence Overconfidence: tendency to overesdmate the true value of a certain quandty, typically in favor of one s own standing on a certain ranking, one s own ability at a certain task, etc.

22 Calibration Overconfidence is lack of calibradon in one direcdon, underconfidence is lack of calibradon in the opposite direcdon. Suppose that I am a weather forecaster. Over the span of a year, I give probability esdmates of rain, and I say that there is a 75% probability of rain for some of the days of the year. On some days it will rain, on some it won t. If my probability judgments are calibrated, it should rain on 75% of those days for which I forecast rain with probability 75%. It should also rain on 100% of the days for which I claim there is a 100% probability of rain, 50% of the days for which I claim there is a 50% probability, and so forth. Baron, Thinking and Deciding, CUP (2008)

23 Calibration the Cooke method

24 Is overconfidence real? Are people really overconfident? Are people overconfident under specific experimental condidons? Are there demographic differences in confidence levels?

25 Daniel Kahneman The heurisdcs and biases program. Many decisions are based on beliefs concerning the likelihood of uncertain events such as the outcome of an elecdon, the guilt of a defendant, or the future value of the dollar. These beliefs are usually expressed in statements such as "I think that...," "chances are...," "it is unlikely that...," and so forth. [ ] What determines such beliefs? How do people assess the probability of an uncertain event or the value of an uncertain quandty? This ardcle shows that people rely on a limited number of heurisdc principles which reduce the complex tasks of assessing probabilides and predicdng values to simpler judgmental operadons. In general, these heurisdcs are quite useful, but somedmes they lead to severe and systemadc errors.

26 Gerd Gigerenzer HeurisDcs are not faults in reasoning, they are strategies. We should not believe that human thinking is riddled with irradonal cognidve biases. We should conceive radonality as an adapdve tool, different from the rules of formal logic or the probability calculus. Overconfidence, for example, is not a real phenomenon, it is induced by the experimental design.

27 Different ways of being calibrated Confidence: refers to the probability we aaribute to the occurrence of a single event. Frequency: refers to the probability we aaribute to the occurrence of an event in a long run of trials. According to J.S. Mill there is a disdncdon between the two, and we tend to exaggerate the former, rather than the laaer, in our judgments. Much later, in 1991, Gerd Gigerenzer (Max Planck, Berlin) and his collaborators worked out an experimental set-up to test the two condidons under which calibradon (and, possibly, overconfidence) is measured.

28 John Stuart Mill on biases Unfortunately for the good sense of mankind, the fact of their [people s] fallibility is far from carrying the weight in their pracdcal judgment, which is always allowed to it in theory; for while every one well knows himself to be fallible, few think it necessary to take any precaudons against their own fallibility, or admit the supposidon that any opinion of which they feel very certain, may be one of the examples of the error to which they acknowledge themselves to be liable. John Stuart Mill, On Liberty

29 How do we measure calibration? Measuring confidence and measuring frequency are two very different things. Frequency: Aser asking a number of true/false quesdons, you try to esdmate the number of quesdons you answered correctly. Measuring frequency is equal to measure your confidence on the overall run of the test you have taken. Confidence: How do we measure single-event confidence on a whole test run? If we only have truth values, we can take the average of our confidence over each item If we have probabilisdc events, we need a more complex method: Cooke s probability bins method

30 Normativity and overconfidence What is the normadve theory behind the measurement of overconfidence? Should we expect frequency and esdmadon to be the same? How do we select the kind of problems we test overconfidence with?

31 Gigerenzer s psychological model People s miscalibradon on probability judgments is not a fallacy of reasoning, but rather the result of the way they process informadon when answering probability quesdons. According to Gigerenzer, there are two psychological factors that determine the way we answer quesdons about the probability of a certain event: e.g. the probability that we answered a quesdon, or a set of quesdons, correctly. Whether we are asked to esdmate the frequency of a certain event over a long run of events (e.g. the frequency of correct answers over a long run of quesdons&answers) Whether the set of quesdons we are asked is representadve of the knowledge one would need to answer quesdons about the topic we are being tested on.

32 Representative and unrepresentative sets When researchers pick quesdons for tests, they tend to pick hard quesdons, such that the set of quesdons they present to the subject is not representadve of the topic the subject is being tested on. How to build a representadve set? north All Italian cides with more than inhabitants. Q: Is X north of Y? Q-easy: Is Venice north of Perugia? Q-hard: Is Venice north of Milan? south

33 Building a representative set. 1. Find a set: e.g. Wikipedia, list of most populous cides. 2. Randomizer: have a random number generator generate a random subset the set you have. 3. List all the possible pairwise comparisons of the items in your subset Is 3 f of 10? Is 3 f of 8? Is 3 f of 25? Is 25 f of 58?

34 Results?