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Preference, Belief, and Similarity: Selected Writings

Amos Tversky and Eldar Shafir (ed)

Tversky, Amos; Eldar Shafir (ed);

Preference, Belief, and Similarity: Selected Writings

MIT Press (Bradford books), 2004, 1023 pages

ISBN 026270093X, 9780262700931

topics: |  psychology | cognitive |

How we delude ourselves

When I play squash, there are days when I find that every shot becomes a
winner, I am invincible.  Many others have had this feeling.  We justify
it by saying that the mind wields a lot of power on our body.  But is it
really true?
(Of course this "feeling" can't build up against much stronger players).

Tversky and Gilovich show - quite convincingly, that at least for
basketball - that this may be a cognitive illusion.

The second excerpt below presents this debate : does an athlete
have periods where he is "hot" - where anything he does, just works?
Particularly in basketball, there is a belief in "hot hands" - among
audiences, coaches, and players.  But Tversky finds that this is a
cognitive illusion - possibly caused by the fact that moments of success
are more salient - rather than any underlying reality.

What is interesting is that this initial work was challenged by an alternate
approach who produced differing statistics based on limiting the time
duration over which a "hot hand" even is detected.  But in the end, Tversky
and Gilovich show that even for the new data, there is no strong
correlation between a past set of scores and a new shot.

As with any random process it may happen that a player gets nine shots out
of ten in a row.  However, they show that this sort of series would arise in
any probabilistic process - and that there is no correlation between success
in previous shots and success in the next.  However, as they clarify
in their analysis, while the probability of success does not change
much, perhaps the player is more energized into attempting more shots
than he would have otherwise.

	As a result, a player may score more points in one period than in
	another not because he shoots better, but simply because he shoots
	more often. The absence of streak shooting does not rule out the
	possibility that other aspects of a player’s performance, such as
	defense, rebounding, shots attempted, or points scored, could be
	subject to hot and cold periods.

In later work, Tversky identified the clustering illusion as a tendency to
erroneously find "streaks" or "clusters" in small samples from random
distributions.  This is a result of a human tendency to underpredict the
amount of variability likely to appear in a small sample of random or
semi-random data.


Discovering the failures of the mind

This is but one of the many psychological aberrations that Tversky has
ferreted out over a relatively short career. (d. 1996, at age 59)

Tversky is one of the giants of cognitive psychology.  His work has
debunked many myths about how humans function, and has led to new areas
such as behavioural economics and decision theory.  His work underlined the
role of the subconscious in modifying deliberative models that we think are
the main wellsprings of behaviour.  His work has identified many crucial
"psychological tendencies and processes that intrude upon and shape
behavior, independently of any deliberative intent." (p.xi)



Excerpts



9 Extensional vs. Intuitive Reasoning: The Conjunction Fallacy


full title:
Extensional vs. Intuitive Reasoning: The Conjunction Fallacy in
   Probability Judgment p. 221
 	Amos Tversky and Daniel Kahneman


Cognitive Illusions


Our studies of inductive reasoning have focused on systematic errors because
they are diagnostic of the heuristics that generally govern judgment and
inference. In the words of Helmholtz (1881/1903), "It is just those cases
that are not in accordance with reality which are particularly instructive
for discovering the laws of the processes by which normal perception
originates." The focus on bias and illusion is a research strategy that
exploits human error, although it neither assumes nor entails that people are
perceptually or cognitively inept. Helmholtz’s position implies that
perception is not usefully analyzed into a normal process that produces
accurate percepts and a distorting process that produces errors and
illusions. In cognition, as in perception, the same mechanisms produce both
valid and invalid judgments.

Indeed, the evidence does not seem to support a "truth plus error" model,
which assumes a coherent system of beliefs that is perturbed by various
sources of distortion and error. Hence, we do not share Dennis Lindley’s
optimistic opinion that "inside every incoherent person there is a coherent
one trying to get out," (Lindley, reference note 3) and we suspect that
incoherence is more than skin deep (Tversky & Kahneman, 1981).  It is
instructive to compare a structure of beliefs about a domain, (e.g., the
political future of Central America) to the perception of a scene (e.g., the
view of Yosemite Valley from Glacier Point). We have argued that intuitive
judgments of all relevant marginal, conjunctive, and conditional
probabilities are not likely to be coherent, that is, to satisfy the
constraints of probability theory. Similarly, estimates of distances and
angles in the scene are unlikely to satisfy the laws of geometry. For
example, there may be pairs of political events for which P(A) is judged
greater than P(B) but P(A/B) is judged less than P(B/A)—see Tversky and
Kahneman (1980).  Analogously, the scene may contain a triangle ABC for which
the A angle appears greater than the B angle, although the BC distance
appears to be smaller than the AC distance.

The violations of the qualitative laws of geometry and probability in
judgments of distance and likelihood have significant implications for the
interpretation and use of these judgments. Incoherence sharply restricts the
inferences that can be drawn from subjective estimates. The judged ordering
of the sides of a triangle cannot be inferred from the judged ordering of its
angles, and the ordering of marginal probabilities cannot be deduced from the
ordering of the respective conditionals. The results of the present study
show that it is even unsafe to assume that P(B) is bounded by PðA&BÞ.
Furthermore, a system of judgments that does not obey the conjunction rule
cannot be expected to obey more complicated principles that presuppose this
rule, such as Bayesian updating, external calibration, and the maximization
of expected utility.

The presence of bias and incoherence does not diminish the normative force of
these principles, but it reduces their usefulness as descriptions of behavior
and hinders their prescriptive applications. Indeed, the elicitation of
unbiased judgments and the reconciliation of incoherent assessments pose
serious problems that presently have no satisfactory solution (Lindley,
Tversky & Brown, 1979; Shafer & Tversky, reference note 4).

The issue of coherence has loomed larger in the study of preference and
belief than in the study of perception. Judgments of distance and angle can
readily be compared to objective reality and can be replaced by objective
measurements when accuracy matters. In contrast, objective measurements of
probability are often unavailable, and most significant choices under risk
require an intuitive evaluation of probability.

In the absence of an objective criterion of validity, the normative theory of
judgment under uncertainty has treated the coherence of belief as the
touchstone of human rationality. Coherence has also been assumed in many
descriptive analyses in psychology, economics, and other social
sciences. This assumption is attractive because the strong normative appeal
of the laws of probability makes violations appear implausible. Our studies
of the conjunction rule show that normatively inspired theories that assume
coherence are descriptively inadequate, whereas psychological analyses that
ignore the appeal of normative rules are, at best, incomplete. A
comprehensive account of human judgment must reflect the tension between
compelling logical rules and seductive nonextensional intuitions.

1. Lakoff, G. Categories and cognitive models (Cognitive Science Report
No. 2). Berkeley: University of California, 1982.
2. Beyth-Marom, R. The subjective probability of conjunctions (Decision Research Report No. 81–12).
Eugene, Oregon: Decision Research, 1981.


10 The Cold Facts about the "Hot Hand" in Basketball

			Amos Tversky and Thomas Gilovich


	You’re in a world all your own. It’s hard to describe. But the basket
	seems to be so wide. No matter what you do, you know the ball is
	going to go in.
			— Purvis Short, of the NBA’s Golden State Warriors

This statement describes a phenomenon known to everyone who plays or watches
the game of basketball, a phenomenon known as the "hot hand." The term
refers to the putative tendency for success (and failure) in basketball to be
self-promoting or selfsustaining.  After making a couple of shots, players
are thought to become relaxed, to feel confident, and to "get in a groove"
such that subsequent success becomes more likely. The belief in the hot hand,
then, is really one version of a wider conviction that "success breeds
success" and "failure breeds failure" in many walks of life.



What People Mean by the "Hot Hand" and "Streak Shooting"


[again, a sample of 100 avid basketball fans from Cornell and Stanford;
and also the players from Philadelphia 76ers.]

Does a player have a better chance of making a shot after having just made
his last two or three shots than he does after having just missed his last
two or three shots?

	Yes 91%
	No 9%

When shooting free throws, does a player have a better chance of making his
second shot after making his first shot than after missing his first shot?

	Yes 68%
	No 32%

Is it important to pass the ball to someone who has just made several (2, 3,
or 4) shots in a row?

	Yes 84%
	No 16%

Consider a hypothetical player who shoots 50% from the field.  What is your
estimate of his field goal percentage for those shots that he takes after

a) having just made a shot?

	Mean : 61%

b) after having just missed a shot?

	Mean : 42%


Misconceptions of Chance Processes


One reason for questioning the widespread belief in the hot hand comes from
research indicating that people’s intuitive conceptions of randomness do not
conform to the laws of chance. People commonly believe that the essential
characteristics of a chance process are represented not only globally in a
large sample, but also locally in each of its parts. For example, people
expect even short sequences of heads and tails to reflect the fairness of a
coin and to contain roughly 50% heads and 50% tails. Such a locally
representative sequence, however, contains too many alternations and not
enough long runs.

This misconception produces two systematic errors. First, it leads many
people to believe that the probability of heads is greater after a long
sequence of tails than after a long sequence of heads; this is the notorious
gamblers’ fallacy. Second, it leads people to question the randomness of
sequences that contain the expected number of runs because even the
occurrence of, say, four heads in a row—which is quite likely in even
relatively small samples—makes the sequence appear non-representative.
Random sequences just do not look random.

Perhaps, then, the belief in the hot hand is merely one manifestation of
this fundamental misconception of the laws of chance. Maybe the streaks of
consecutive hits that lead players and fans to believe in the hot hand do
not exceed, in length or frequency, those expected in any random sequence.

To examine this possibility, we first asked a group of 100 knowledgeable
basketball fans to classify sequences of 21 hits and misses (supposedly
taken from a basketball player’s performance record) as streak shooting,
chance shooting, or alternating shooting.

[Finds that] people perceive streak shooting where it does not exist. The
sequence of p(a) = .5, representing a perfectly random sequence, was
classified as streak shooting by 65% of the respondents. Moreover, the
perception of chance shooting was strongly biased against long runs: The
sequences selected as the best examples of chance shooting were those with
probabilities of alternation of .7 and .8 instead of .5.

What is even more interesting than this quantitative study are the answers by
the fans. (above)

If a player is occasionally "hot," his record must include more
high-performance series than expected by chance. The numbers of high,
moderate, and low series for each of the nine Philadelphia 76ers were
compared... The results provided no evidence for non-stationarity or streak
shooting as none of the nine chi-squares approached statistical
significance.


The Hot Hand as Cognitive Illusion


To summarize what we have found, we think it may be helpful to clarify what
we have not found. Most importantly, our research does not indicate that
basketball shooting is a purely chance process, like coin
tossing. Obviously, it requires a great deal of talent and skill.

What we have found is that, contrary to common belief, a player’s chances
of hitting are largely independent of the outcome of his or her previous
shots. Naturally, every now and then, a player may make, say, nine of ten
shots, and one may wish to claim — after the fact — that he was hot. Such
use, however, is misleading if the length and frequency of such streaks do
not exceed chance expectation.

Our research likewise does not imply that the number of points that a
player scores in different games or in different periods within a game is
roughly the same. The data merely indicate that the probability of making a
given shot (i.e., a player’s shooting percentage) is unaffected by the
player’s prior performance. However, players’ willingness to shoot may well
be affected by the outcomes of previous shots. As a result, a player may
score more points in one period than in another not because he shoots
better, but simply because he shoots more often. The absence of streak
shooting does not rule out the possibility that other aspects of a player’s
performance, such as defense, rebounding, shots attempted, or points
scored, could be subject to hot and cold periods.



Larkey etal's Challenge: It’s Okay to believe in the hot hand


Larkey, Smith, and Kadane (1989)].  summary by Eldar Shafir.

	This critique proposes "a different conception of how observers’
	beliefs in streak shooting are based on NBA player shooting
	performances."  Tversky and Gilovich, they suggest, are taking
	isolated individual-player shooting sequences, whreas the observers
	in a real game would be seeing "how that player’s shooting activities
	interact with the activities of other players."  For example, LSK
	propose that two players both with five consecutive field goal
	successes will be perceived very differently if one’s consecutive
	successes are interspersed throughout the game, whereas the other’s
	occur in a row, without teammates scoring any points in between.

	For their revised analyses, LSK devise a statistical model of
	players’ shooting behavior in the context of a game. They find that
	Vinnie Johnson — a player with the reputation for being "the most
	lethal streak shooter in basketball" — "is different than other
	players in the data in terms of noticeable, memorable field goal
	shooting accomplishments," and reckon that "Johnson’s reputation as
	a streak shooter is apparently well deserved." "Basketball fans and
	coaches who once believed in the hot hand and streak shooting and who
	have been worried about the adequacy of their cognitive apparatus
	since the publication of Tversky and Gilovich’s original work,"
	conclude LSK, "can relax and once again enjoy watching the game."
	Reference Larkey, P., Smith, R., and Kadane, J. B. (1989). "It’s
	Okay to Believe in the Hot Hand," Chance, pp. 22–30.
		(from Editor’s Introductory Remarks to Chapter 11)



11 The "Hot Hand": Statistical Reality or Cognitive Illusion?

	Amos Tversky and Thomas Gilovich

Myths die hard. Misconceptions of chance are no exception. Despite the
knowledge that coins have no memory, people believe that a sequence of heads
is more likely to be followed by a tail than by another head. ...

Larkey, Smith, and Kadane (LSK) challenged our conclusion [that the
probability of hitting a shot is not higher following a hit than following a
miss... and that belief in the "hot hand" or "streak shooting" is a
cognitive illusion.]

Like many other believers in streak shooting, they felt that we must have
missed something...  LSK collected a new data set consisting of 39 National
Basketball Association (NBA) games from the 1987–1988 season and analyzed the
records of 18 outstanding players.

LSK's [analysis focuses on] "cognitively manageable chunks of shooting
opportunities" on which the belief in the hot hand is based.  Their argument
confounds the statistical question of whether the hot hand exists with the
psychological question of why people believe in the hot hand — whether it
exists or not. We shall address the two questions separately, starting with
the statistical facts.  LSK argue, in effect, that the hot hand is a local
(short-lived) phenomenon that operates only when a player takes successive
shots within a short time span. By computing, as we did, a player’s serial
correlation for all successive shots, regardless of temporal proximity, we
may have diluted and masked any sign of the hot hand.  The simplest test of
this hypothesis is to compute the serial correlation for successive shots
that are in close temporal proximity. LSK did not perform this test but they
were kind enough to share their data. Using their records, we computed for
each player the serial correlation r1 for all pairs of successive shots
that are separated by at most one shot by another player on the same
team. This condition restricts the analysis to cases in which the time span
between shots is generally less than a minute and a half. The results,
presented in the first column of table 11.1, do not support the locality
hypothesis. The serial correlations are negative for 11 players, positive
for 6 players, and the overall mean is -.02. None of the correlations are
statistically significant.

The comparison of the local serial correlation r1, with the regular serial
correlation r, presented in the second column of table 11.1, shows that the
hot-hand hypothesis does not fare [sic fair] better in the local analysis
described above than in the original global analysis. (Restricting the
local analysis to shots that are separated by at most 3, 2, or 0 shots by
another teammate yielded similar results.)




Contents


Introduction and Biography 						ix
Sources 								xv

Similarity


1 Features of Similarity 						7
	Amos Tversky
2 Additive Similarity Trees 						47
	Shmuel Sattath and Amos Tversky
3 Studies of Similarity 						75
	Amos Tversky and Itamar Gati
4 Weighting Common and Distinctive Features in Perceptual and
  Conceptual Judgments
	Itamar Gati and Amos Tversky
5 Nearest Neighbor Analysis of Psychological Spaces 			129
	Amos Tversky and J. Wesley Hutchinson
6 On the Relation between Common and Distinctive Feature Models 	171
	Shmuel Sattath and Amos Tversky

Judgment


7 Belief in the Law of Small Numbers 					193
	Amos Tversky and Daniel Kahneman
8 Judgment under Uncertainty: Heuristics and Biases 			203
	Amos Tversky and Daniel Kahneman
9 Extensional vs. Intuitive Reasoning: The Conjunction Fallacy in
  Probability Judgment 						221
	Amos Tversky and Daniel Kahneman
10 The Cold Facts about the "Hot Hand" in Basketball 			257
	Amos Tversky and Thomas Gilovich
11 The "Hot Hand": Statistical Reality or Cognitive Illusion? 	269
	Amos Tversky and Thomas Gilovich
12 The Weighing of Evidence and the Determinants of Confidence 	275
	Dale Gri‰n and Amos Tversky
13 On the Evaluation of Probability Judgments: Calibration, Resolution,
   and Monotonicity 							301
	Varda Liberman and Amos Tversky
14 Support Theory: A Nonextensional Representation of Subjective
   Probability 							329
	Amos Tversky and Derek J. Koehler
15 On the Belief That Arthritis Pain Is Related to the Weather 	377
   Donald A. Redelmeier and Amos Tversky
16 Unpacking, Repacking, and Anchoring: Advances in Support Theory 	383
   Yuval Rottenstreich and Amos Tversky

Preference


Probabilistic Models of Choice 411
17 On the Optimal Number of Alternatives at a Choice Point 413
	Amos Tversky
18 Substitutability and Similarity in Binary Choices 419
	Amos Tversky and J. Edward Russo
19 The Intransitivity of Preferences 433
	Amos Tversky
20 Elimination by Aspects: A Theory of Choice 463
	Amos Tversky
21 Preference Trees 493
	Amos Tversky and Shmuel Sattath

Choice under Risk and Uncertainty 547
22 Prospect Theory: An Analysis of Decision under Risk 549
	Daniel Kahneman and Amos Tversky
23 On the Elicitation of Preferences for Alternative Therapies 583
	Barbara J. McNeil, Stephen G. Pauker, Harold C. Sox, Jr., and
	Amos Tversky
24 Rational Choice and the Framing of Decisions 593
	Amos Tversky and Daniel Kahneman
25 Contrasting Rational and Psychological Analyses of Political Choice 621
	George A. Quattrone and Amos Tversky
26 Preference and Belief: Ambiguity and Competence in Choice under
   Uncertainty 645
	Chip Heath and Amos Tversky
27 Advances in Prospect Theory: Cumulative Representation of
   Uncertainty 673
	Amos Tversky and Daniel Kahneman
28 Thinking through Uncertainty: Nonconsequential Reasoning and Choice 703
	Eldar Shafir and Amos Tversky
29 Conflict Resolution: A Cognitive Perspective 729
	Daniel Kahneman and Amos Tversky
30 Weighing Risk and Uncertainty 747
	Amos Tversky and Craig R. Fox
31 Ambiguity Aversion and Comparative Ignorance 777
	Craig R. Fox and Amos Tversky
32 A Belief-Based Account of Decision under Uncertainty 795
	Craig R. Fox and Amos Tversky

Contingent Preferences 823
33 Self-Deception and the Voter’s Illusion 825
	George A. Quattrone and Amos Tversky
34 Contingent Weighting in Judgment and Choice 845
	Amos Tversky, Shmuel Sattath, and Paul Slovic
35 Anomalies: Preference Reversals 875
	Amos Tversky and Richard H. Thaler
36 Discrepancy between Medical Decisions for Individual Patients and for
   Groups 887
	Donald A. Redelmeier and Amos Tversky
37 Loss Aversion in Riskless Choice: A Reference-Dependent Model 895
	Amos Tversky and Daniel Kahneman
38 Endowment and Contrast in Judgments of Well-Being 917
	Amos Tversky and Dale Gri‰n
39 Reason-Based Choice 937
	Eldar Shafir, Itamar Simonson, and Amos Tversky
40 Context-Dependence in Legal Decision Making 963
	Mark Kelman, Yuval Rottenstreich, and Amos Tversky

Amos Tversky’s Complete Bibliography 995


 

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This review by Amit Mukerjee was last updated on : 2015 Sep 15