Moral Costs and Rational Choice:
Theory and Experimental Evidence
James C. Cox, John A. List, Michael Price,
Vjollca Sadiraj, and Anya Samek
Dictator Games
• Hundreds of dictator games in the past 30 years provide
evidence for altruism or warm glow
• In standard dictator games
~60% of subjects pass positive amounts of money;
allocating ~20% of endowment (Camerer, 2003)
• Changing the give vs. take action set produces some
different results:
 Allowing taking significantly decreased transfers (List, 2007;
Bardsley, 2008)
 Take option effect is robust to heterogeneous adult subjects
with earned endowments (Cappelen, et al., 2013)
 Take vs. give option effect is robust to charitable contributions
(Grossman & Eckel, 2015)
 Recipients earn more in a take game than in a payoff
equivalent give game (Korenok, Millner & Razzolini, 2014)
Possible Interpretations
• Not a “real behavioral phenomenon”; an effect of
an artificial environment such as:
 “Hawthorn effect”?
 “Experimenter demand effect”?
 “Framing effect”?
 Other artificial environment effect?
• Or maybe a Kitty Genovese effect?
Possible Interpretations (cont.)
• A “real behavioral phenomenon” that is:
 Inconsistent with convex preference theory?
 Inconsistent with rational choice theory?
Possible Interpretations (cont.)
List (2007)
50%
45%
40%
Percentage
35%
30%
25%
Baseline
20%
15%
10%
5%
0%
−1
0
0.5
1
1.5
2
2.5
Amount Transferred
3
3.5
4
4.5
5
Take $1
Theoretical Interpretation of List (2007) Data
• In order for the data to be consistent with
convex preference theory:
 The height of the blue bar at 0 must equal the
sum of the heights of the red bars at -1 and 0
 The heights of the blue and red bars must be the
same at all other transfer numbers
• In order for the data to be consistent with
extant rational choice theory:
 No red bar to the right of -1 can be taller than the
corresponding blue bar
List (2007), Bardsley (2008),
Cappelen, et al. (2013)
• Data from these experiments are:
– Inconsistent with convex preference theory
(including “social preferences” models)
– Almost completely consistent with extant rational
choice theory
• These experiments:
– Stress-test convex preference theory
– Endowments and action sets are not well suited to
stress-test rational choice theory
Outline of Contents
• Report an experimental design to stress-test rational
choice theory
• Report an experiment with children
• Review properties of conventional theory
– Convex preference theory (including “social preferences”)
– Rational choice theory
• Develop a modified form of rational choice theory,
with moral reference points, that explains:
– Dependence on irrelevant alternatives (“contraction
effects”)
– Dependence on give vs. take action sets (“framing
effects”)
• Use child experiment data and data from college
student experiments to test alternative theories
Our Experiment
• 329 children, ages 3-7 (Average age: 5, min. 3.5; max.
7.4)
• Treatments include variations in:
– Action sets: Give, Take, Symmetric
– Initial endowments: Inequality, Equal, Envy
Treatments: Varying Endowments and Action Sets
• Compare Give, Take, Symmetric to investigate the effect of the
action set on final outcomes.
• Across Inequality, Equal, Envy: compare the final allocation within
action sets.
Feasible Budget Sets
• Give and Symmetric start at B
• Take starts at A
Equal Treatments
Inequality Treatments
Envy Treatments
Randomization to Treatment
• Between subjects: 3 – 4 year olds randomized
to Inequality, Equal, or Envy
• Within subjects: Plays each of Give, Take,
Symmetric in random order
Payoff accumulates after each decision (PAS)
In the main text we report only the decision from
the dictator game
o when it is played first
o and the existence of the second and third choices is
unknown to the child
Appendix D reports tests with all of the data
Average Allocations
Extant Rational Choice Theory
• The Chernoff (1954) contraction axiom (also
known as Property α from Sen (1971) states:
Property α: if G  F then F   G  G 

f
• In words, a most-preferred allocation from
feasible set Fis also a most-preferred allocation
in any contraction G of the set F that contains

the allocation f
Q*j
Explanation for Dictator Games
• For singleton choice sets: If Qj , that is chosen
from opportunity set [A j ,C j ] , belongs to the

[A
,B
]
Q
subset j j then j is chosen when the
the opportunity set is [A j ,B j ]
• This means that no striped bar should be taller
than corresponding bars in the intersection of
feasible sets in the following figure
Q*j
Explanation for Dictator Games
• For singleton choice sets: If Qj , that is chosen
from opportunity set [A j ,C j ] , belongs to the

[A
,B
]
Q
subset j j then j is chosen when the
the opportunity set is [A j ,B j ]
• This means that no striped bar should be taller
than corresponding bars in the intersection of
feasible sets in the following figure
Example of Observed Contraction Effects
Inequality
70%
60%
Percentage
50%
40%
Give
30%
Take
Symmetric
20%
10%
0%
0
1
2
3
4
5
6
Final Payoff to Dictator
7
8
9
10
11
12
Introduction of Moral Reference Points
• We extend rational choice theory to include
objectively-defined moral reference points.
• We here consider the N = 2 case needed for
dictator games in the give vs. take literature:
– Let (m,y) denote an ordered pair of money payoffs
for the dictator m = “my payoff” and the recipient
y = “your payoff”
– Let F denote the dictator’s compact feasible set
o
– Let mo and y denote maximum feasible payoffs:
mo ( F )  sup{m | (m, y )  F }and y o ( F )  sup{ y | (m, y )  F }
Theory Generalization (cont.)
• The minimal expectations point M is:
mo ( F )  sup{m | (m, y o ( F ))  F } and yo ( F )  sup{ y | (mo ( F ), y )  F }
• The moral reference point depends on M and the
dictator's endowment:
f r  ( mo ( F )  (1   )em , yo ( f ))
• Any   (0,1) is consistent with contraction and action
set effects. In the paper, we use the value   1/ 2
Graphical Depiction of Examples
y
AQ = Take Endowment
10
BQ = Give Endowment
= Symmetric Endowment
6
CQ
2
2
4
6
10
m
Moral Monotonicity Axiom
• Let R denote “not smaller” or “not larger”
• For every agent i one has:
Moral Monotonicity Axiom (MMA):
If G  F , g R f i and g  f
r
i


r

i
r
i


r
i
f  F  G  g R f i , g  G
then

Implications of MMA
• MMA is a sufficient condition for the choice set to
satisfy contraction and expansion axioms (analogs
of Sen’s properties  and  ) if opportunity sets
preserve a moral reference point:
r
r

g

f
• Property M : if G  F and
then
F   G  G
• Property  M : if G  F and g r  f r then
G   F    implies G   F 
Testable Implications Within I, Q & E Treatments
• Let the choice point be t* when the action set is Take and the
opportunity set is [A j ,B j ]
• Let the choice point be g* when the action set is Give and the
opportunity set is [A j ,B j ]
• Let the choice point be s* when the action set is Symmetric and
the opportunity set is [A j ,C j ]
– And assume s* [A j ,B j ]
• Contrasting implications:
 Conventional rational choice theory implies: t* = g* = s*
 Our theory implies: t* northwest g* northwest s*
Within Treatments Take vs. Give Effects
• Result 1: Effects on choices of within-treatment
change from Give to Take action sets are weakly
inconsistent with conventional rational choice
theory but consistent with our model based on
MMA.
Support for Result 1: Take vs. Give
Table 3: Comparisons of Give vs. Take Action Sets
Average marginal effects from the Hurdle model (Cragg, 1971).
Dependent Variable
Dictator Payoff
Conditional mean estimates of
Give Action [+]
Observations
Means {Take, Give}
Nobs {Take, Give}
(Kruskal-Wallis) Chi-Squared
(1)
Inequality
(2)
Equal
(3)
Envy
0.400*
(0.216)
0.246
(0.326)
1.174**
(0.458)
103
57a
46
{6.16, 6.51}
{4.60, 5.06}
{2.84, 3.38}
{50, 53}
{25, 33}
{25, 21}
2.51
3.26*
2.88*
Note: ademographics missing for one child. Predicted sign by MMA in square brackets. Standard errors in parentheses. Choice at the highest dictator’s payoff is
treated as hurdle. Includes Experimenter fixed effects and demographics (child age, race and gender). Take action set is the omitted category, and childrens’ choices
Within Treatments Contraction Effects
• Result 2: Effects on choices from within-treatment
contractions of feasible sets are inconsistent with
conventional rational choice theory but consistent
with our model based on MMA.
Support for Result 2: Contraction
Table 4: Contraction of the Symmetric Set (within treatment)
Average marginal effects from the hurdle model (Cragg, 1971).
Dependent Variable
Dictator Payoff
Give Action [-]
Take Action [-]
Observations
Means (Take, Give, Symm.)
Nobs (Take, Give, Symm.)
(Kruskal-Wallis test)
Chi-Squared
(1)
Inequality
(2)
Equal
(3)
Envy
-0.930***
(0.263)
-1.293***
(0.245)
-1.585***
(0.532)
-1.782***
(0.522)
-0.570
(0.482)
-1.477***
(0.440)
143a
73a
64
(6.16, 6.51, 7.83)
(4.60, 5.06, 5.94)
(2.84, 3.38, 3.94)
(50, 53, 41)
(25, 33, 16)
(25, 21, 18)
52.07***
15.51***
12.25***
Note: MMA predicted sign in square brackets. Standard errors in parentheses. Includes Experimenter fixed effects and children demographics (gender, age,
race). The Symmetric action set is the omitted category. Only choices from [A, B] are included. Choice at the highest dictator’s payoff is treated as hurdle. ***
Implications for Data from other Experiments
• Korenok, Millner & Razzolini (2014)
– Their Contraction data are consistent with warm glow
model reported in Korenok, Millner & Razzolini (2013)
– Their Give vs. Take (“framing”) data are inconsistent
with their theoretical model and Property alpha
– We show that their data are consistent with MMA
• Andreoni & Miller (2002)
– They ask whether their data are consistent with GARP
– We show MMA places tighter restrictions on their
data than does WARP
Give vs. Take Action Sets in Korenok, et al. (2014)
Action Sets in Korenok, et al. (cont.)
• Endowments are at points 1, 3, 6, 8, and 9
• Korenok, et al. theory and conventional rational
choice theory imply choices invariant to these
endowment (and give vs. take action set) changes
• The moral reference points for our theory are
shown at points f j for j = 1, 3, 6, 8, and 9
• MMA implies that choice points move
northwesterly along with endowments
Implications of Data from Korenok, et al.
• The average recipient payoffs for the five
scenarios are: S1($4.05), S3($5.01), S6($5.61),
S8($6.59) and S9($6.31).
• The data are inconsistent with Korenok, et al.
theory and with conventional rational choice
theory
• The data support predictions of MMA except for
the change from $6.59 to $6.31, which is
insignificant
Some Feasible Sets from Andreoni & Miller
Recipient’s Payoffs
B
A
fa
a
fb
b
Dictator’s Payoffs
MMA and WARP
• Consider the WARP violation shown by choices A and B
• Note that the shaded quadrilateral (SQ) is a contraction of
each budget set
• Looking at SQ as a contraction of the “steeper set”:
– MMA (see Proposition 1) requires that A also be chosen from
SQ because the sets have the same moral reference point
• Looking at SQ as a contraction of the flatter set:
– MMA requires that the choice from SQ is northwest of B
because f a is to the left of f b
• But this contradicts the choice of A from SQ
• Thus, any pair of choices of type A and B violate MMA
• MMA places tighter restrictions on the data than does
WARP (in the figure, WARP implies B must be southeast of
the intersection; MMA says it must be east of A)
Summary
• Data from List, Bardsley, and Cappelen, et al.
contradict convex preference theory
• Data from our experiment and Korenok, et al.
contradict
– Conventional rational choice theory
– Warm glow theory of Korenok, et al.
• Our theory with MMA is consistent with data
– From Take vs. Give
– From (“proper”) Contraction
Summary (cont.)
• Our theory with MMA is clearly testable, e.g.:
o It places tighter restrictions on data than does
WARP in some dictator experiments
o It places restrictions across play in moonlighting and
investment games
Making the Decision
“First, you and the other boy will get some stickers to start.”
“With the stickers on these plates, you still get to decide -- how many you
want to keep, and how many you want the other boy to keep.”
Daniel’s plate (Variable endowment)
“Here are more stickers – they are
yours now.”
Other boy’s plate (Variable
endowment) “Here are even more
stickers – they are his now.”
Daniel’s box (Fixed endowment)
“These are the stickers you
definitely get to take home.”
Other boy’s box (Fixed endowment)
“These are the stickers he definitely
gets to take home.”
Fig. 5: Reference Points for Proper Contractions
Table 5: Contraction of the Symmetric Set (across treatments)
Average marginal effects from the hurdle model (Cragg, 1971).
Dependent Variable
Dictator Payoff
Give Action
Take Action
Observations
Means (Take, Give, Symm.)
Nobs (Take, Give, Symm.)
(Kruskal-Wallis test)
Chi-Squared
(1)
Symmetric Equal
Inequality Take/Give
(2)
Symmetric Envy
Inequality Take/Give
0.082
(0.277)
-0.286 [-]
(0.289)
1.301*** [+]
(0.296)
0.875*** [+]
(0.320)
127
133
(6.16, 6.51, 6.42)
(6.16, 6.51, 5.37)
(50, 53, 24)
(50, 53, 30)
2.81
11.67***
Convex Preferences on Discrete
Choice Sets
Strictly convex preferences
on a discrete choice set
• The most preferred set is either a singleton or a set
that contains two adjacent feasible points
• If Q* not in [Aj, Bj] is chosen from [Aj, Cj] then Bj will
be chosen from [Aj, Bj] because:
o Bj is a convex combination of Q* (that belongs to
[Bj, Cj]) and X , for any given X in [Aj, Bj]
o Since Q* is preferred to X in [Aj, Cj], by strict convexity
Bj is strictly preferred to X
Proof of Proposition 1
Proof of Properties  M and  M
Let f belong to both F and G . Consider any g from G  .
As G and F have the same moral reference point, g r  f r ,
MMA requires that gi  fi and fi  gi , i . These inequalities
can be simultaneously satisfied if and only if g  f ,
i.e. f belongs to G  which concludes the proof for property
 M . Note, though, that any choice g from G  must
coincide with f , an implication of which is G  must be a
singleton. So, if the intersection of F  and G is not empty
then choices satisfy property  M .
Both Axioms from Conventional
Rational Choice Theory
Properties  and 
• Samuelson (1938), Chernoff (1954), Arrow (1959),
Sen (1971, 1986)


• Property  : if G  F then F  G  G
A most-preferred allocation f *  F * from feasible
set F is also a most-preferred allocation in any
contraction G of the set F that contains the
*
f
allocation .
Properties  and  (cont.)
• For non-singleton choice sets one also has
• Property β: if G  F and G  F    then G  F 
*
F
If the most-preferred set for feasible set F
contains at least one most-preferred point from the
contraction set G then it contains all of the mostpreferred points of the contraction set.
• For finite sets, Properties α and β are necessary
and sufficient conditions for a choice function to
be rationalizable by a weak (complete &
transitive) order (Sen, 1971)