CALL IT QUITS

Animals know when to cut their losses, so why do we so often throw good
money after bad, ask Peter Ayton and Hal Arkes

HAVE YOU ever kept a failing relationship tottering along because of the
heartache it's already caused you? Or eaten far too much at an "all you can
eat" fixed-price buffet just to get your money's worth? Were you swayed to
patriotic fever pitch by arguments that the Vietnam War or the troubles in
Northern Ireland must continue because anything less than a total victory
would mean that lives already lost were sacrificed in vain?

If the answer to any of those questions is yes, then you too have been a
victim of what psychologists call the "sunk-cost fallacy"---the human
tendency to judge options according to the size of previous investments
rather than the size of the expected return. Truly rational choices would be
made only after weighing up future costs and benefits. Past costs and
benefits are quite irrelevant.

Psychologists study biases and fallacies in human thinking to get a glimpse
of the hidden mental processes behind decision making. A large literature
testifies both to how often humans fall for the sunkcost fallacy, and to how
fascinating psychologists find it.

In a study by one of us, Hal Arkes, and graduate student Catherine Blumer,
theatregoers who went to buy a $15 season ticket were offered at random a
normalpriced ticket or a discount of $2 or $7. All other costs and benefits
of attending performances (for example, time waiting in traffic jams on the
way to the theatre, or the popularity of the plays) would be about the same
for each of the three groups. What's more, the patrons were unaware that the
tickets had been sold at different rates. Yet those who bought tickets at
either of the cheaper prices attended fewer plays during the subsequent six
months than people who bought tickets at $15. Apparently, theatregoers who
sink the most money into their tickets are the most motivated to attend.

The judgments of professional basketball coaches are also blighted by sunk
costs. They should play and keep their most productive players, but Barry
Staw and Ha Hoang at the University of California in Berkeley found that
players' salaries significantly affected both these decisions. The most
expensive players were given more time on court and kept on the team longer
than cheaper players, even after adjusting for variables such as
performance, injuries and the positions they played.

And it's not just sport and leisure that are riddled with irrational
sunkcost decision making. Entrepreneurs who start a business are more likely
to throw good money after bad than those who buy businesses that are already
under way, according to a study of more than a thousand businesses conducted
by Anne McCarthy at Indiana University in Bloomington. Having been
personally responsible for the birth of a business makes one reluctant to
give up on it even when it might be better to do so.

In one of the earliest studies of the fallacy, Staw asked business school
students to play the role of corporate executives who had to allocate
research and development funds to divisions of their own companies. The
students received feedback on their initial decisions and were then asked to
make a second investment. They put significantly more money into failing
investments than successful ones, and they invested even more money if they
themselves were responsible for the earlier decision rather than another
(unidentified) executive.

That and other studies led Staw to propose that people escalate their
commitment to a sunk cost in the hope of saving face by justifying their
earlier decision---a sort of Nick Leeson effect. A competing explanation for
the sunkcost fallacy is that future investments may seem smaller in the
context of previous investments.

Win or bust

A third idea---and perhaps the most favoured to date---is the so-called
"prospect theory". According to this argument, people are more motivated by
their losses than their gains, and this results in increasingly risky
behaviour as the losses accumulate. For example, long-odds bets are more
popular in the last horse race of the day than the first. By the end of the
day, the punters have lost most of their gambling money and hope to win it
all back with a single long-shot bet that they wouldn't dream of taking in
the first race.

Now we believe we have an even better explanation of why supposedly rational
humans fall prey to the sunk-cost fallacy.

It all started with a chance remark by Oxford University zoologist Alex
Kacelnik at the 1996 British Psychological Society conference called
"Thinking". Kacelnik had made a passing reference to something called the
"Concorde fallacy". To our astonishment, we discovered that ethologists had
been studying an animal version of the sunk-cost fallacy for the past twenty
years, only they called it the Concorde fallacy---named after the supersonic
airliner that was financed even after it became clear that its future
prospects meant it should be abandoned.

Scouring the literature revealed that we weren't alone in our ignorance.
Neither the researchers into animal behaviour nor the researchers of human
judgment ever refer to each other's work. After an exhaustive search, we
found that not one reference cited by those who study the Concorde fallacy
is also cited by those who study the sunk-cost fallacy and vice versa; they
are two mutually exclusive ghettos of literature, publishing in different
journals and using different terminology.

We also learnt that at least one prominent biologist argues pretty
convincingly that, theoretically, it is impossible that animals should fall
for the Concorde fallacy. This argument turned out to be a key to our
understanding of the mental processes that underpin the sunk-cost effect in
humans.

Abandoned partners

First, back a step. For ethologists, the Concorde fallacy originally arose
in the context of arguments about evolution. To reproduce successfully, an
animal has to accomplish various tasks such as seeking a mate, building a
nest and rearing and defending its young. While performing any of these
tasks, an animal will incur costs and will have to decide whether to
continue with the present task or abandon it and start anew.

Back in 1972, evolutionary theorist Robert Trivers of Rutgers University in
Newark, New Jersey, pointed out that either member of a mated pair could
exploit the other by deserting, leaving the partner to finish the job of
rearing the young alone. He argued that the parent who had invested least
(usually the father) would be most likely to desert.

Richard Dawkins and one of his Oxford students, Tamsin Carlisle, soon
spotted that Trivers's argument implied that animals should "value" options
according to the extent of their prior investment rather than their future
benefits. Evolutionarily speaking, that argument had to be wrong. Such a
fallacy may well affect the reasoning of theoretical biologists, argued
Dawkins and Carlisle, but it could not affect the actions of animals.
Natural selection could only support desertion by the parent who has most to
gain by deserting---regardless of who has invested most. It could not work
against the prospects of effective procreation. In their article, published
in 1976, the year Concorde went into service, Dawkins and Carlisle coined
the term "Concorde fallacy".

A few years later, Dawkins was alarmed to discover what looked like Concorde
fallacy behaviour in female digger wasps. These wasps paralyse katydids---a
sort of grasshopper---with a sting, and drag the bodies to their burrows.
Once they have collected four or five katydids, they lay a single egg that
hatches and feeds on the paralysed but still living katydids. Sometimes
there's a mix-up and two wasps end up putting katydids in the same burrow.
When they eventually bump into one another, they fight for the right to lay
their egg in the burrow. Fights end when the loser gives up and retreats.

According to observations made by Jane Brockmann of the University of
Florida in Gainesville, how long the losing wasp keeps fighting depends on
how many katydids she has already placed in the burrow---that is, the
investment to date--- rather than the total number of katydids in the
burrow. The second option would be the rational basis for such a decision
because it alone dictates how much future effort the wasp must make to fully
stock its larder.

When Dawkins and Brockmann put their heads together, they came up with
another explanation for the wasps' apparently irrational behaviour. Plainly
each wasp knows how many katydids she placed in her burrow because that
dictates how long she fights. (She probably doesn't actually count the
number of katydids, but assesses it indirectly, perhaps by sensing how much
time she spent flying back and forth from the burrow.) She is, however,
unable to tell whether another wasp is stashing katydids in her burrow until
she meets her rival, so it's probably safe to say that she has trouble
counting the total number of katydids that are there. As the wasp cannot be
said to be ignoring information she does not have access to, she can hardly
be held to be committing a fallacy. The two researchers concluded that the
number of katydids each wasp puts in its burrow is simply the best estimate
of the burrow's future worth. In that case, it makes sense for a wasp to
fight longer the more katydids it has put in.

But not everyone has been swayed by Dawkins's arguments that animals should
not commit the Concorde fallacy. In fact, since Dawkins first published on
the subject, claims of such behaviour have been popping up all over. We
scrutinised those reports, and in each case we found alternative
explanations for the animals' seemingly irrational behaviour.

For example, according to a study by Robert Lavery at Queen's University at
Kingston, Ontario, cichlid fish that have had three previous broods defend
their current brood more aggressively against a fake predator than those
protecting their first brood. In his 1995 report in Behavioral Ecology and
Sociobiology (vol 36, p 193), Lavery favoured the idea that the fish were
exhibiting the Concorde fallacy---those that had made the largest investment
increased their expenditure in terms of aggression.

But Lavery also acknowledged that prior investment could be a good indicator
of future reward if the past efforts reduce the fish's ability to procreate
in the future. In that case, aggression that could put the fish's life in
jeopardy would become "cheaper" because fewer potential future broods would
be at risk. The fish would be quite rational to defend its later broods more
aggressively.

Similarly, Patrick Weatherhead at Carleton University in Ottawa has found
that Savannah sparrows defend their nests ever more aggressively as the
brood hatches and grows. Once again, Weatherhead suggests that this is
Concorde fallacy behaviour. But once again, there is an alternative
explanation: with time, not only does past investment increase, but also the
future cost of brood-rearing diminishes. Consequently, you could just as
easily argue that the future benefit to cost ratio of the sparrow's
defensive behaviour increases with brood development. Once again, the
behaviour is entirely rational.

In fact, just as Dawkins might have predicted, we found that every one of
the dozen or so reports of Concorde fallacy behaviour in animals could be
attributed to the reasoning of the researchers as they struggle to tease
apart past investment and future benefit, or fail to adequately take into
account the fact that sunk costs can sometimes predict future benefits.

There are several other studies which show that animals as cognitively
humble as ducks, blackbirds and mice make perfectly rational decisions on
the basis of the expected future benefit, not past investment. House mouse
mothers, for example, protect small litters less aggressively than bigger
ones, even when they have started out investing resources in a larger litter
which has then been reduced in size.

Spilt milk

So why are people less rational than animals? We are products of evolution
too, so why do we alone appear to find it so difficult to resist the
sunk-cost fallacy?

First of all, for humans as for animals, sunk costs may occasionally predict
future benefits, although this certainly isn't the case with the examples of
sunk-cost reasoning that psychologists study. We would argue that in these
cases, the explanation lies with the human brain's unique ability to make up
and apply abstract rules: "wise" generalisable rules that can often be
expressed proverbially such as "No use crying over spilt milk", "A stitch in
time saves nine", and "Don't put the cart before the horse". Abstract rules
and generalisations have enabled humans to respond effectively to an
enormously wide range of situations, but they can also catch us out if we
overgeneralise.

More than child's play

Take the rule "Waste not, want not". If that is applied to a situation where
investing more in an attempt not to "waste" a previous investment does not
produce greater benefits, the sunk-cost fallacy emerges. Lower animals lack
the intellectual capacity to create abstract rules, let alone overgeneralise
them, and can only respond using instincts or simple learnt behaviours.
Neither could lead to Concorde-type reasoning.

If the sunk-cost fallacy is a by-product of abstract thought then you might
expect younger children to be less susceptible to it than adults and older
children. And that's exactly what happens. At the European Association for
Decision Making conference in Leeds, in August 1997, economic psychologist
Paul Webley reported that in a group of five-year-old children, those who
had been asked to imagine that they had bought and then lost a fairground
ticket were no more likely to say that they would buy another one than those
who had not been asked to imagine the loss of a ticket. By contrast,
eight-year-olds who were asked to imagine that they had lost a ticket were
more likely to say they would buy another one.

So next time you fall prey to the sunk-cost fallacy and find yourself making
entirely illogical decisions about how to invest your money, affection or
time, you can at least take some comfort from this: it's the price you pay
for being smart enough to reason abstractly.
.......
Peter Ayton is a reader in psychology at City University, London, and a
member of the European Association for Decision Making.

Hal Arkes is professor of psychology at Ohio University and a past president
of the Society for Judgment and Decision Making

Further Reading:

"The Psychology of Waste" by H .R. Arkes, Journal Of Behavioral Decision
Making, vol 9, p 213 (1996).

"Quasi-rational Economics" by R H. Thaler, Russell Sage Foundation, New
York, 1991
"Parental Investment, Mate Desertion and a Fallacy" by R. Dawkins and T. R.
Carlisle, Nature, vol 262, p 131 (1976)

"The road to Desert Storm" by R Lipshitz, Organization Studies, vol 16, p
243 (1995)

Checked-by: "R. Lake"