Theory and Experimental Evidence James C. Cox, John A. List, Michael - - PowerPoint PPT Presentation

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.)

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% −1 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 Percentage Amount Transferred

List (2007)

Baseline 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

• when it is played first
• 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 then

• In words, a most-preferred allocation

from feasible set is also a most-preferred allocation in any contraction

• f the set that contains

the allocation

G F 

F G G

 

 

F

G

F

f



f



Explanation for Dictator Games

• For singleton choice sets: If , that is chosen

from opportunity set , belongs to the subset then is chosen when the the opportunity set is

• This means that no striped bar should be taller

than corresponding bars in the intersection of feasible sets in the following figure

* j

Q

j

Q

j

Q

j j

[A ,B ]

j j

[A ,B ]

j j

[A ,C ]

Explanation for Dictator Games

• For singleton choice sets: If , that is chosen

from opportunity set , belongs to the subset then is chosen when the the opportunity set is

• This means that no striped bar should be taller

than corresponding bars in the intersection of feasible sets in the following figure

* j

Q

j

Q

j

Q

j j

[A ,B ]

j j

[A ,B ]

j j

[A ,C ]

Example of Observed Contraction Effects

0% 10% 20% 30% 40% 50% 60% 70% 1 2 3 4 5 6 7 8 9 10 11 12 Percentage Final Payoff to Dictator

Inequality

Give Take Symmetric

Introduction of Moral Reference Points

• We extend rational choice theory to include
• bjectively-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 denote the dictator’s compact feasible set – Let and denote maximum feasible payoffs: and

• m

F

• y

( ) sup{ | ( , ) }

• m

F m m y F   ( ) sup{ | ( , ) }

• y

F y m y F  

Theory Generalization (cont.)

• The minimal expectations point M is:

and

• The moral reference point depends on M and the

dictator's endowment:

• Any is consistent with contraction and action

set effects. In the paper, we use the value

( ) sup{ | ( , ( )) }

• m F

m m y F F  

( ) sup{ | ( ( ), ) }

• y F

y m F y F  

( ( ) (1 ) , ( ))

r

• m
• f

m F e y f     

(0,1)   1/ 2  

Graphical Depiction of Examples

y 10 6 6 10 2 2 4 AQ = Take Endowment BQ = Give Endowment = Symmetric Endowment CQ m

Moral Monotonicity Axiom

• Let R denote “not smaller” or “not larger”
• For every agent i one has:

Moral Monotonicity Axiom (MMA): If then

, and g

r r r r i i i i

G F g R f f

 

 

, g

i i

f F G g R f G

     

    

Implications of MMA

• MMA is a sufficient condition for the choice set to

satisfy contraction and expansion axioms (analogs

• f Sen’s properties and ) if opportunity sets

preserve a moral reference point:

• Property

: if and then

• Property

: if and then implies





M



M



G F 

r r

g f 

F G G

 

 

G F 

r r

g f  G F

 

  

G F

 



Testable Implications Within I, Q & E Treatments

• Let the choice point be t* when the action set is Take and the
• pportunity set is
• Let the choice point be g* when the action set is Give and the
• pportunity set is
• Let the choice point be s* when the action set is Symmetric and

the opportunity set is

– And assume s*

• Contrasting implications:

 Conventional rational choice theory implies: t* = g* = s*  Our theory implies: t* northwest g* northwest s*

j j

[A ,B ]

j j

[A ,B ]

j j

[A ,C ]

j j

[A ,B ] 

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

Dependent Variable (1) (2) (3) Dictator Payoff Inequality Equal Envy Conditional mean estimates of Give Action [+] 0.400* 0.246 1.174** (0.216) (0.326) (0.458) Observations 103 57a 46 Means {Take, Give} Nobs {Take, Give} {6.16, 6.51} {50, 53} {4.60, 5.06} {25, 33} {2.84, 3.38} {25, 21} (Kruskal-Wallis) Chi-Squared 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 in the Symmetric action set are excluded from the analysis. ***p<0.01, ** p<0.05, * p<0.1

Table 3: Comparisons of Give vs. Take Action Sets Average marginal effects from the Hurdle model (Cragg, 1971).

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

Dependent Variable Dictator Payoff (1) Inequality (2) Equal (3) Envy Give Action [-]

• 0.930***
• 1.585***
• 0.570

(0.263) (0.532) (0.482) Take Action [-]

• 1.293***
• 1.782***
• 1.477***

(0.245) (0.522) (0.440) Observations 143a 73a 64 Means (Take, Give, Symm.) Nobs (Take, Give, Symm.) (6.16, 6.51, 7.83) (50, 53, 41) (4.60, 5.06, 5.94) (25, 33, 16) (2.84, 3.38, 3.94) (25, 21, 18) (Kruskal-Wallis test) Chi-Squared 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. *** p<0.01, ** p<0.05, * p<0.1.

Table 4: Contraction of the Symmetric Set (within treatment)

Average marginal effects from the hurdle model (Cragg, 1971).

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 for j = 1, 3, 6, 8, and 9

• MMA implies that choice points move

northwesterly along with endowments

j

f

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 Dictator’s Payoffs fa fb B A b a

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 is to the left of

• 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)

a

f

b

f

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.:
• It places tighter restrictions on data than does

WARP in some dictator experiments

• 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 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.”

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.”

• Fig. 5: Reference Points for Proper Contractions

Dependent Variable Dictator Payoff (1) Symmetric Equal Inequality Take/Give (2) Symmetric Envy Inequality Take/Give Give Action 0.082 1.301*** [+] (0.277) (0.296) Take Action

• 0.286 [-]

0.875*** [+] (0.289) (0.320) Observations 127 133 Means (Take, Give, Symm.) Nobs (Take, Give, Symm.) (6.16, 6.51, 6.42) (50, 53, 24) (6.16, 6.51, 5.37) (50, 53, 30) (Kruskal-Wallis test) Chi-Squared 2.81 11.67***

Note: MMA predicted sign in square brackets. Standard errors in parentheses. Includes Experimenter fixed effects and children demographics (gender, age, race).

Table 5: Contraction of the Symmetric Set (across treatments)

Average marginal effects from the hurdle model (Cragg, 1971).

Convex Preferences on Discrete Choice Sets

Strictly convex preferences

• n 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:

• Bj is a convex combination of Q* (that belongs to

[Bj, Cj]) and X , for any given X in [Aj, Bj]

• 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

Let belong to both and . Consider any from As and have the same moral reference point, MMA requires that These inequalities can be simultaneously satisfied if and only if , i.e. belongs to which concludes the proof for property . Note, though, that any choice from must coincide with , an implication of which is must be a

• singleton. So, if the intersection of

and is not empty then choices satisfy property .

and

M M

 

f

F

G

g

. G G

F

,

r r

g f 

and , .

i i i i

g f f g i   

g f 

f

G

M



g

G

f

G G F 

M



Both Axioms from Conventional Rational Choice Theory

Properties

• Samuelson (1938), Chernoff (1954), Arrow (1959),

Sen (1971, 1986)

• Property : if then

A most-preferred allocation from feasible set is also a most-preferred allocation in any contraction of the set that contains the allocation .

and   

G F 

F G G

 

 

* *

f F 

F G F

*

f

Properties (cont.)

• For non-singleton choice sets one also has
• Property β: if and then

If the most-preferred set for feasible set contains at least one most-preferred point from the contraction set then it contains all of the most- preferred 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)

G F 

G F

 

  

G F

 



*

F

F

G

and  