The Reflection Effect
The University of Virginia
October 31, 2002
Michael Loatman
Jason Chin
Simpsons Example

Marge starts off being risk averse.




“I'm not wild about these high-risk ventures.
They sound a little risky.”
“Look at them! They've jumped on the one
franchise I might possibly have considered
thinking about becoming interested in.”
Like our participants, she began to rake
in the money.
When faced with losses from the mob,
she became risk seeking.

"We're going to do what we do everyday. We're
going to make pretzels!"
Background
Reference Point
I.
A.
II.
III.
IV.
Loss aversion and reflection effect
Kahneman and Tversky experiment
(1979)
Holt and Laury critique (2002)
Chin-Loatman critique (2002)
Reference Point

Reference Point


Loss aversion


Point where gains and losses are evaluated
Implies that losses are given more weight in
choices with outcomes that involve both gains and
losses
Reflection effect

Postulates that risk aversion exhibited by choices
when all outcomes are gains will be transformed
into a preference for risk when all outcomes are
losses
Kahneman and Tversky (1979)


Took the following lottery choice
experiment
Lottery S (selected by 80%)
Lottery R (selected by 20%)
3,000 with probability 1.0
4,000 with probability 0.8
0 with probability 0.2
and reflected it around zero to get
losses
Kahneman and Tversky con’t

Resulting in
Lottery S (selected by 80%)
Lottery R (selected by 20%)
minus 3,000 with probability 1.0
minus 4,000 with probability 0.8
0 with probability 0.2


Experimenters found people were risk averse with
positive payoffs and risk seeking with negative
payoffs
Experiment used hypothetical payoffs, did this skew
results?
Holt and Laury Critique
Made changes to Kahneman and
Tversky design




Used real incentives
Allowed participants to earn an initial
stake, a higher one in the loss condition
to hold final wealth constant
Reflected the payoff menu from Chapter
Four around zero
Holt and Laury Cont’d

Payoff menu
Option A
Option B
Decision 1
$40.00 if throw of die is 1
$32.00 if throw of die is 2-10
$77.00 if throw of die is 1
$2.00 if throw of die is 2-10
Decision 2
$40.00 if throw of die is 1-2
$32.00 if throw of die is 3-10
$77.00 if throw of die is 1-2
$2.00 if throw of die is 3-10
Decision 3
$40.00 if throw of die is 1-3
$32.00 if throw of die is 4-10
$77.00 if throw of die is 1-3
$2.00 if throw of die is 4-10
$40.00 if throw of die is 1-10
$77.00 if throw of die is 1-10
…
Decision 10
Holt and Laury Critique Cont’d

Results


Different from what K & T found
Instead of a strong reflection effect, found
that in general people were risk neutral in
the loss domain and risk averse in the gain
domain.
Chin-Loatman Critique

Our intuition about why Holt and
Laury’s data did not match previous
researchers’ data is because Holt and
Laury did not offer a risky choice with a
possibility of a loss of $0.
Procedure




We used the Lottery Choice veconlab program just as
Holt and Laury did.
EXCEPT we changed the risky payoff of $0.10 to $0.
The first four rounds allowed the participants to gain a
large amount of money using scale factors of 1, 45, 90,
and 90. This was important since we wanted to make
sure the participants would have a decent amount of
money to want to protect.
The last four rounds were reflected around zero and
thus used scale factors of –1, -45, -90, and –90.
Payoff Matrix
Holt-Laury
Chin-Loatman
Gains (Scale Factor = 1)
Safe Lottery $2.00 or $1.60
Risky Lottery $3.85 or $0.10
Safe Lottery $2.00 or $1.60
Risky Lottery $3.85 or $0
Losses (Scale Factor = 1)
Safe Lottery -$2.00 or -$1.60
Risky Lottery -$3.85 or -$0.10
Safe Lottery -$2.00 or -$1.60
Risky Lottery -$3.85 or $0
Gains (Scale Factor = 90)
Safe Lottery $180.00 or $144.00
Risky Lottery $346.50 or $9.00
Safe Lottery $180.00 or $144.00
Risky Lottery $346.50 or $0
Losses (Scale Factor = 90)
Safe Lottery -$180.00 or -$144.00
Risky Lottery -$346.50 or -$9.00
Safe Lottery -$180.00 or -$144.00
Risky Lottery -$346.50 or $0
A Risk Neutral Person (Gains)
p
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Option A $180 or $144 Option B $346.50 or $0
147.6
34.65
151.2
69.3
154.8
103.95
158.4
138.6
162
173.25
165.6
207.9
169.2
242.55
172.8
277.2
176.4
311.85
180
346.5


A risk neutral
person would
pick the option
with the higher
expected
payoff, hence
4 safe choices
and 6 risky
choices (in
bold).
Risk averse
chose more
than 4 safe
choices.
What the class did (gains)
% Safe Choice
Round 3, payoffs scaled x 90
1.2
1
0.8
0.6
0.4
0.2
0
observed
risk neutral
1 2 3 4 5 6 7 8 9 10
Round
•We see risk
aversion
•There is an
incentive
effect—the
greater the
payoffs, more
risk aversion
(not pictured)
A Risk Neutral Person (Loss)
p
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Option A -$180 or -$144 Option B -$346.50 or $0
-147.6
-34.65
-151.2
-69.3
-154.8
-103.95
-158.4
-138.6
-162
-173.25
-165.6
-207.9
-169.2
-242.55
-172.8
-277.2
-176.4
-311.85
-180
-346.5



A risk neutral
person would pick
the option with the
lower expected
loss, hence 6 safe
choices and 4 risky
choices (in bold).
The scale factor
does not change
the number of
safe/risky choices a
risk neutral person
would make.
A risk seeking
person would
chose less than 6
safe choices.
% safe choice
Class results (losses)
1.2
1
0.8
0.6
0.4
0.2
0
observed
risk neutral
1
2
3
4
5
6
round
7
8
9 10
Results
Gains
Spanky
Risk Averse
Kemp
Risk Averse
Oh Canada Risk Neutral
Alexis
Risk Averse
Soupy
Risk Seeking
Jmarsha
Risk Averse
XC
Risk Averse
Jenamy
Risk Neutral
S
Risk Averse
Lins
Risk Averse
CavMan
Risk Neutral
Plankto
Risk Averse
Losses
Risk Seeking
Risk Seeking
Risk Seeking
Risk Seeking
Risk Seeking
Risk Seeking
Risk Seeking
Risk Seeking
Risk Seeking
Risk Averse
Risk Neutral
Risk Seeking
Profit
-$48.90
$155.30
$277.10
$199.40
$233.40
$405.70
$358.35
$418.85
$149.25
$433.40
$524.85
$392.10
Why Are People Risk Seeking
in Losses?
Decision 5


Option A
Option B
-$180.00 if throw of die is 1-5
-$144.00 if throw of die is 6-10
-$346.50 if throw of die is 1-5
-$0.00 if throw of die is 6-10
It is hard to judge why because we are
human and it seems normal to us.
Psychologists, Daniel Kahneman and Amos
Tversky studied these effects and came up
with the most popular theory used to
describe them, Prospect Theory.
Kahneman & Tversky
They ask people:
Imagine an outbreak of an unusual
disease expected to kill 600 people and
you must choose between two public
health programs to combat it.
Kahneman & Tversky

Scenario 1:
If you pick Program A, 200 people will be
saved with 100% certainty.
 If you pick Program B, there is a 1/3
chance of saving all 600 lives and a 2/3
chance of saving no lives.
The expected values are the same, but
people choose A, the sure thing most of
the time, exhibiting risk aversion.

Kahneman & Tversky

If you reframe the last question in terms of
losses (deaths).
If you choose program A, 400 people will die with
100% certainty.
 If you choose program B, there is a 1/3 probability
that no one will die, and a 2/3 probability that 600
will die.
The question is the same as before, but framed in
terms of losses. Now people tend to pick Program
B, thus exhibiting risk seeking behavior

Kahneman & Tversky

Kahneman & Tversky say that people treat
gains and losses differently.


There is a reflection effect as we saw, people are
risk averse in gains and risk seeking in losses
They also show loss aversion, saying that losses
loom larger than gains. For example: most of us
would have no interest in a gamble that yields a
50% chance of gaining or losing $100.
Applications and New Horizons

Economist George Loewenstein applies loss
aversion to his theory, the endowment effect


In one study he gives mugs to half of his class,
and at the end of the class takes them back.
When asked how much they would pay to buy a
mug, the students who once had the mug would
pay more than those who never owned the mug
So, having something and losing it makes you
value it more. Evidence for loss aversion.
Conclusion


Our study shows evidence for the
reflection effect
There are a lot of applications of loss
aversion and the reflection effect to be
explored