## Biases in Reasoning

A common bias in inductive reasoning is the confirmation bias, the tendency to seek confirming evidence and not to seek disconfirming evidence. In one study, subjects who were presented with the numbers (2, 4, 6) determined what rule (concept) would allow them to generate additional num bers in the series. In testing their hypotheses, many subjects produced series to confirm their hypotheses—for example, (20, 22, 24) or (100, 102, 104)— of "even numbers ascending by 2," but few produced series to disconfirm their hypotheses—for example, (1, 3, 5) or (20, 50, 187). In fact, any ascending series (such as 32, 69, 100,005) would have satisfied the general rule, but because subjects did not seek to disconfirm their more specific rules, they did not discover the more general rule.

Heuristics also lead to biases in reasoning. In one study, subjects were told that bag A contained ten blue and twenty red chips, while bag B contained twenty blue and ten red chips. On each trial, the experimenter selected one bag; subjects knew that bag A would be selected on 80 percent of the trials. The subject drew three chips from the bag and reasoned whether A or B had been selected. When subjects drew two blues and one red, all were confident that B had been selected. If the probability for that sample is actually calculated, however, the odds are 2:1 that it comes from A. People chose B because the sample of chips resembles (represents) B more than A, and ignored the prior probability of 80 percent that the bag was A.

In another experiment, subjects were shown descriptions of "Linda" that made her appear to be a feminist. Subjects rated the probability that Linda was a bank teller and a feminist higher than the probability that Linda was a bank teller. Whenever there is a conjunction ofevents, however, the probability of both events is less than the probability of either event alone, so the probability that Linda was a bank teller and a feminist was actually lower than the probability that she was only a bank teller. Reliance on representativeness leads to overestimation of the probability of a conjunction of events.

Reliance on representativeness also leads to the "gambler's fallacy." This fallacy can be defined as the belief that if a small sample is drawn from an infinite and randomly distributed population, that sample must also appear randomly distributed.

Consider a chance event such as flipping a coin. (H represents "heads"; T represents "tails.") Which sequence is more probable: HTHTTH or HHHHHH? Subjects judge that the first sequence is more probable, but both are equally probable. The second sequence, HHHHHH, does not appear to be random, however, and so is believed to be less probable. After a long run ofH, people judge T as more probable than H because the coin is "due" for T. A problem with the idea of "due," though, is that the coin itself has no memory of a run of H or T. As far as the coin is concerned, on the next toss there is .5 probability of H and .5 probability of T. The fallacy arises because subjects expect a small sample from an infinitely large random distribution to appear random. The same misconceptions are often extended beyond coin-flipping to all games of chance.

In fallacies of reasoning resulting from availability, subjects misestimate frequencies. When subjects estimated the proportion of English words beginning with R versus words with R as the third letter, they estimated that more words begin with R, but, in fact, more than three times as many words have R as their third letter. For another example, consider the following problem. Ten people are available and need to be organized into committees. Can more committees of two or more committees of eight be organized? Subjects claimed that more committees of two could be organized, probably because it is easier to visualize a larger number of committees of two, but equal numbers of committees could be made in both cases. In both examples, the class for which it is easier to generate examples is judged to be the most frequent or numerous. An additional aspect of availability involves causal scenarios (sometimes referred to as the simulation heuristic), stories or narratives in which one event causes another and which lead from an original situation to an outcome. If a causal scenario linking an original situation and outcome is easily available, that outcome is judged to be more likely.