**
Judgment Under Uncertainty **

(Intuitive statistics; ecological rationality; optimal foraging; heuristics and biases; fast & frugal heuristics)

**Are humans rational? By
what standard should we decide?**

One argument has been that human thought is rational to the extent that it conforms to normative theories drawn from mathematics and logic. During the 1970s and 1980s, Amos Tversky, Daniel Kahneman, and their colleagues pursued this approach, developing experiments to see whether people's responses on tasks requiring probability judgments conformed to various normative theories of probability: Bayes' rule (for calculating conditional probabilities), the law of large numbers, and, more generally, subjective expected utility theory and the Savage axioms. Compared to these normative theories, people's performance looked irrational (or, at least, poorly designed). A large body of research, known as the heuristics and biases school, emerged, demonstrating how people's judgments deviate from the dictates of probability theory. The claim was made that the human mind does not contain any algorithms that embody aspects of a calculus of probability: Probability judgments are made instead by a collection of rules of thumb that produce judgments that do not closely track any normative theory. It was suggested that people use quick rules of thumb to make such judgments because the mind is so limited in its ability to process information (on analogy to a computer with a tiny RAM).

Yet behavioral ecologists who study foraging in insects and birds had found evidence of mechanisms that make rather accurate probability judgments, e.g., judgments that satisfy the constraints of Bayes’s rule, as well as normatively appropriate risk-sensitive foraging decisions. How can the fact that bird brains and insect minds make well-calibrated probability judgments be reconciled with a human mind that is "too limited"?

**Absolute frequencies: An
ecologically valid format. **Humans, like other animals, evolved as foragers.
Thus we thought it unlikely that they would be substantially worse “intuitive
probabilists” than other animals. Our initial work in this area (Cosmides
& Tooby, 1996), along with that of Gerd
Gigerenzer, showed that the format in which the probabilistic information
is presented creates huge differences in performance. People appear to be poor
at Bayesian reasoning (just as Tversky & Kahneman claim) when they are given
problems that express the relevant information as percents and that ask them
to judge the probability of a single event (e.g., “What is the chance that a
person who tests positive for the disease actually has it?”). But a different
picture emerges when information is presented in a more ecologically valid format.

Probabilities of single events are
a byproduct of modern statistical and data-gathering techniques (ever wonder
what a "60% chance of rain today" means?). No hunter-gatherer ever
encountered a probability of a single event (it either rains today or it doesn't).
Instead, hunter-gatherers encountered statistical information in the same format
that other species do: in the form of the actual frequencies of encountered
events (e.g., It rained 6 out of the last 10 days; *Not*: there is a
60% chance of rain *today*). If so, then mechanisms designed to make
well-calibrated statistical judgments might exist, but they might require information
to be in a format that they can “read” to give the right output. To test this,
we translated the same standard problems into frequency formats and asked for
the answer as a frequency (e.g., how many people who test positive for the disease
actually have it? ___ out of ___) rather than as the probability of a single
event. Whereas only 12-36% of untutored undergraduates gave the correct Bayesian
response when the problem was phrased in the single event format, 76-92% gave
the right answer when the problem had a frequency format. This suggests that
the mind does indeed have mechanisms that embody aspects of a calculus of probability.
Gigerenzer has gone on to show that what matters are absolute frequencies (not
relative frequencies), and that these are well-adapted to a natural sampling
scheme. (In natural sampling (e.g., walking through a forest in which you encounter
apple and cherry trees, some with red fruit on them others not), base rates
become irrelevant because information about rarity or abundance is implicit
in the absolute encounter frequency. If you want to know the probability that
a tree with red fruit on it is an apple tree and you know the absolute frequency
of apple trees with red fruit (hits) and other trees with red fruit (false alarms),
then the answer is simple: hits / hits + false alarms. For discussion, see Brase,
Cosmides & Tooby, 1998.)** **We expect mechanisms to be *ecologically
rational*: designed to work well in the ecological circumstances for which
they were designed.

**Frequency computation and
object perception**. How does the frequency computation system interact
with object perception? The object perception system is designed to parse and
(token) individuate some aspects of the world, but not others (e.g., it will
automatically individuate a leaf, but not the sides of a leaf). A frequency
computation system depends on the ability to count, and items cannot be counted
unless they are first individuated as tokens (and not just as types). Following
this logic, Brase, Cosmides,
and Tooby (1998) showed that people respect Bayes’s rule when a correct
solution requires that one assess the frequency of items that their object perception
system is designed to token individuate (whole objects). But they make errors
when a correct solution requires counting over items that the system does not
individuate (e.g., inseparable aspects of objects, such as sides of a card or
ends of a rod). Following an ecological rationality approach, we argued that
debates over whether people are “rational” should be reframed. Instead, one
should expect to find human probability judgment mechanisms that produce well-calibrated
and adaptive judgments when operating within the parameters for which they were
designed by selection. (See Kahneman
2003 on natural assessments.)

**Optimal foraging theory.**
With Catrin Rode,
we tested predictions from optimal foraging theory (Rode,
Cosmides, Hell, & Tooby, 1999). This paper suggests that two phenomena –
loss aversion and ambiguity avoidance – are byproducts of statistical inference
mechanisms that conform to normative principles drawn from optimal foraging
theory, according to which decisions should take into account not only the expected
value and variance associated with a resource, but the need level of the decision-maker.
Most research on judgment under uncertainty does not consider the need level
of the subject (and implicitly assumes it is zero), and in these cases, people
usually prefer low variance options. But consider a bird who is deciding to
forage on one of two patches, which have the same expected value (mean) but
different variances. If the amount the bird needs to live another day is below
the expected value, the safest bet is to forage on the low variance patch. But
the high variance patch is a better bet if the bird needs to gather an amount
greater than the expected value. Following predictions such as these from the
behavioral ecology literature on risk-sensitive foraging, we varied people’s
need levels, using a betting task involving drawing from urns with different
distributions of black and white balls (representing different variances and
expected values). Like the birds, human subjects preferred the low variance
option only when the number of balls needed to win was lower than the expected
value; when the number needed to win exceeded the expected value of two alternative
urns, subjects preferred the higher variance option. Moreover, we were able
to show that when need levels are low, people will prefer an ambiguous option
as long as there is reason to think it is the lower variance alternative (thereby
showing that, contrary to claims in the literature, there is no general tendency
to avoid ambiguity). Most striking (and spooky) were tests in which we used
a wide variety of distributions, expected values, and need levels. In these
experiments, using probability theory to explicitly calculate which options
have the higher probability of success is arduous (for the experimenter); nevertheless,
the subjects’ intuitively-made choices closely tracked these probabilities.
For more research on risky decision making and optimal foraging theory in humans,
see the interesting evolutionary psychological research done by X-T
Wang.

**Relevance to debates about
human rationality**. Philosophers, economists, and legal scholars have
developed an interest in CEP work on judgment under uncertainty and on social
exchange, because it leads to different views of reasoning and rationality.
First, it suggests that it is a mistake to define rationality narrowly, as reasoning
in accordance with the rules of logic or probability theory (e.g., our cheater
detection work eliminated the hypothesis that the results were caused by the
activation of rules of logical inference. The algorithms involved embody an
adaptive logic that does not map onto formal – that is, content-free – logical
rules). Second, it suggests that you cannot determine whether the mind does
in fact reason in accordance with probability theory (or whatever the normative
theory might be) unless you provide information in a format the mind was designed
to read, and consider what adaptive problems (such as risk-sensitive foraging)
the mechanisms were designed to solve. A plethora of papers in behavioral economics
and in law assume that people are poor intuitive statisticians--and make policy
recommendations based on this view (often involving taking choice away from
lay people and putting it in the hands of technocrats). But the research by
Gigerenzer's group on fast-and-frugal
heuristics (decision rules that work quickly and well, based on limited
information), as well as the research above, suggest that there are ways of
presenting information about probability and risk that can activate well-calibrated
probability judgments, even in lay people.

Gerd Gigerenzer's **Center for
Adaptive Behavior and Cognition** at the Max Planck Institute for Human Development
in Berlin has a wealth of resources on this topic.
http://www.mpib-berlin.mpg.de/en/forschung/abc/index.htm

**Martie
Haselton**** **of UCLA has interesting work on error
management theory, according to which certain biases in judgment reflect mechanisms
designed to minimize the probability of making the more costly error. See especially
**The
Paranoid Optimist **and **Error
Management Theory.**

Cosmides, L. & Tooby, J.
(1996). **Are humans good
intuitive statisticians after all?: Rethinking some conclusions of the literature
on judgment under uncertainty.** * Cognition, 58,* 1-73.

Brase, G., Cosmides, L., & Tooby,
J. (1998). **Individuation,
Counting, and Statistical Inference: The role of frequency and whole object
representations in judgment under uncertainty.** *Journal
of Experimental Psychology: General, 127,* 1-19.

Rode, C., Cosmides, L., Hell, W.,
& Tooby, J. (1999). **When
and why do people avoid unknown probabilities in decisions under uncertainty?
Testing some predictions from optimal foraging theory.** *Cognition,
72,* 269-304.