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The Linda experiment and other probabilistic tasks in the heuristics and biases programme ask participants to assess the probability of a single event (e.g., the probability of Linda being a feminist bank teller). However, according to a frequentist interpretation of probability, it is hard to make sense of the probability of a single event.

According to the (simple) frequency interpretation, a claim about the probability of an event (e.g., the probability of winning a coin toss is 0.5) is understood as talking about the frequency of the event relative to the relevant reference class (e.g., the frequency of winning relative to the total number of tosses of that particular coin). The Linda experiment asks the probability of Linda being a feminist bank teller. On a frequentist interpretation, this amounts to asking the frequency of Linda being a feminist bank teller. What does that mean? The frequency of Linda being a feminist bank teller relative to the total cases of her being a feminist bank teller in her life would be 1. Does that mean, then, that the probability of Linda being a feminist bank teller is 1?

Gigerenzer’s objection is that asking the probability of a single, non-repetitive event – like Linda being a feminist bank teller – is an ill-formed question. Since the question is ill formed and meaningless, there is no correct answer to it. Thus, it is not a mistake to assign a higher probability to Linda being a feminist bank teller than to Linda being a bank teller.

The philosophical and statistical distinction between single events and frequencies clarifies that judgments hitherto labeled instances of the ‘conjunction fallacy’ cannot be properly called reasoning errors in the sense of violations of the laws of probability. (Gigerenzer 1994, 144)

Moreover, as we have already seen (Fiedler 1988), when questions are explicitly framed in the format of frequency with a clearly specified reference class (‘Among the 100 people who fit Linda’s description, how many are bank tellers and how many are feminist bank tellers?’), participants’ performance improves. This reveals that people make apparent ‘mistakes’ when the question is ill formed (asking the probability of a single event with no specified reference class), but do not make mistakes when the question is well formed (asking the frequency of something being the case among a specified reference class). It would seem, then, that people are far from being irrational.

What we call the ‘meaninglessness objection’ can be developed in at least two ways. In other words, there are at least two versions of it. The first version, the ‘factual version’, states that the frequency interpretation of probability is true as a matter of fact and, hence, the probabilistic questions in the heuristics and biases experiments are nonsense as a matter of fact. The second version, the ‘psychological version’, states that frequentism is psychologically true in the sense that the information about probability is represented in the frequentist format in the mind of human agents. Hence, the probabilistic questions in the heuristics and biases experiments are nonsense psychologically (i.e., the participants cannot make sense of the questions).

The factual version of the meaninglessness objection is philosophically bold; it presupposes the truth of the frequency interpretation of probability. The interpretation of probability is a highly contested topic in philosophy, which goes beyond the scope of this book. But it is worth pointing out that the factual version involves a controversial argumentative strategy. After all, (the simplistic version of) frequentism has been criticized exactly because people think that they can meaningfully talk about the probability of a single event (cf., Hajek 2019). It is true that the probability of a single event does not make sense according to frequentism, but it only shows that frequentism is problematic.

The psychological version of the meaninglessness objection is less bold than the factual version. Unlike the factual version, the psychological version is not committed to a particular claim about the interpretation of probability. The problem with the psychological version, however, is that it is not bold enough; if frequentism is not true as a matter of fact but is merely true psychologically, then the probabilistic questions do make sense as a matter of fact and, thus, reasoning biases are real errors as a matter of fact after all. The psychological version is psychologically problematic as well. It is unlikely that the probabilistic questions in the Linda experiment are psychological nonsense. Apparently, participants do not regard the questions as nonsense; after all, they provided meaningful answers to the questions in the experiments, rather than refusing to answer or demanding clarifications (Samuels, Stich, & Bishop 2002).