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TRANSCRIPT
Primary Social Goods and the Rawlsian Difference Principle
Joshua Chen-Yuan Teng, Joseph Tao-yi Wang and C. C. Yang1
Abstract: While most economists view the relationship between equality and efficiency as a
tradeoff or conflict, Rawls (1971) saw it differently according to his proposed difference
principle: equality has priority over efficiency in essence. Previous experimental studies lend
little support to the importance of the difference principle -- subjects whose social
preferences obey the difference principle represent only a small minority in the sample. This
paper finds a much stronger support -- a salient majority of subjects whose social preferences
obey the difference principle. A key to our departure from previous studies lies in that
allocating monetary payoffs between subjects in our experimental design embodies not
simply choosing the distribution of payoffs but more importantly the distribution of Rawls's
so-called “primary social goods,” which serve as instruments critical to the fulfillment of
people's rational desire.
1Teng: Department of Public Finance, National Taipei University (corresponding author, email: [email protected]); Wang: Department of Economics, National Taiwan University (email: [email protected]); Yang: Institute of Economics, Academia Sinica; Department of Public Finance, National Chengchi University; Department of Public Finance, Feng Chia University (email: [email protected]). This research is supported by The National Science Council, Taiwan, grant 101-2410-H-305-002-.
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I. Introduction
A fundamental tradeoff in policy or institutional design in economics is between equality
and efficiency. On the one hand, we would like to have a pie produced as large as possible.
On the other hand, we would also like to divide the pie among individuals as equal as
possible. Unfortunately, an equal division of a pie will generally dull individual incentives to
work hard; as a result, the equality goal and the efficiency goal are often in conflict. A
tradeoff between these two goals seems inevitable, and the focus of policy or institutional
design is on the tradeoff.
Rawls (1971) saw the relationship between equality and efficiency differently: equality
has priority over efficiency in essence. He proposed the difference principle (popularly
known as the maximin criterion), arguing that efficiency is desirable only if it is beneficial to
the least advantaged. Papers including Johannesson and Gerdtham (1995), Beckman et al.
(2002), Charness and Rabin (2002), Johansson-Stenman et al. (2002), Carlsson et al. (2003),
Engelmann and Strobel (2004), Traub et al. (2005) and Schildberg-Hörisch (2010), have
conducted experiments to test, among other things, the importance of the Rawlsian difference
principle. Overall, it receives little support -- subjects whose social preferences obey the
difference principle represent only a small minority in the sample. For example, this
proportion of subjects is found to be lower than 14% in Schildberg-Hörisch (2010), and 9%
in Traub et al. (2005), both are well below the majority.2
In this paper we re-conduct test on the difference principle and find a much stronger
support -- a salient majority of subjects whose social preferences obey the principle. A key to
the departure from previous studies is that our experimental design introduces the so-called
“primary social goods,” a critical concept emphasized by Rawls (1971) in his arguments for
2Besides incentivized experiments, Konow (2009) used a survey approach and found that people would apply divergent principles under various described circumstances. For example, the efficiency principle will be adopted in business administration, but people would allocate enough money to satisfy necessary means of students.
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the difference principle.
Primary social goods
Rawls (1971) used a contractarian approach to develop his theory of justice. He
perceived that everyone would agree to construct principles of justice behind “the veil of
ignorance”, that is, no one knows “his fortune in the distribution of natural assets and
abilities, his intelligence, strength, and the like.” (p. 12) Then the “two principles of justices”
that would be agreed by everyone arise (p. 302):
1. First principle: “Each person is to have an equal right to the most extensive total system
of equal basic liberties compatible with a similar system of liberty for all.”
2. Second principle: “Social and economic inequalities are to be arranged so that they are
both: (a) to the greatest benefit of the least advantaged, consistent with the just savings
principle,3 and (b) attached to offices and positions open to all under conditions of fair
equality of opportunity.”
The one that is subject to tests most frequently in economics is part (a) of the second
principle -- the difference principle. Below we often appeal to Rawls's (1971) original quotes
for the purpose of persuading readers that the category of primary social goods is the main
domain to which the difference principle is supposed to apply.
To motivate the difference principle, Rawls first discussed concepts of welfare.
Specifically, Rawls adopted Aristotle’s thought of welfare: “A person’s good is determined by
what is for him the most rational long-term plan of life given reasonably favorable
circumstances. A man is happy when he is more or less successfully in the way of carrying
out this plan. To put it briefly, the good is the satisfaction of rational desire.” (pp. 92-93)
Postulating that people have this concept of welfare, Rawls reasoned that they would “prefer
3The aim of the just saving principle is to realize justice between generations. Rawls believed that it can be formulated behind the veil of ignorance, that is, no one knows to which generations she belongs. For more details, see Rawls (1971, pp. )
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more primary social goods” (p. 142), which are defined as “Things that every rational man is
presumed to want. These goods normally have a use whatever a person’s rational plan of life.
For simplicity, assume that the chief primary goods at the disposition of society are rights,
liberties, and opportunities, and income and wealth.” (p. 62) In fact, Rawls explicitly wrote:
“The difference principle is a very special criterion: it applies primarily to the basic structure
of society via representative individuals whose expectations are to be estimated by an index
of primary goods.”4
Note that Rawls did not specify what kinds of expectations or plans in life people would
or should pursue. Instead, “Only the most general assumptions are made about the aims of
the parties, namely, that they take an interest in primary social goods …To suppose, then
that the parties want these goods, and to found a conception of justice on this presumption,
is not to tie it to a particular pattern of human interests as these might be generated by a
particular arrangement of institutions. The theory of justice does, indeed, presuppose a
theory of the good, but within wide limits this does not prejudge the choice of the sort of
persons that men want to be.” (p. 260)
Behind the veil of ignorance, one of the reasons for which people would adopt the
difference principle is that it is too risky to gamble on primary social goods: “…the person
choosing has a conception of the good such that he cares very little, if anything, for what he
might gain above the minimum stipend that he can, in fact, be sure of by following the
maximin rule. It is not worthwhile for him to take a chance for the sake of a further
advantage, especially when it may turn out that he loses much that is important to him.” (p.
4 See Rawls (1999, p. 72), the revised edition of A Theory of Justice. In this edition, Rawls disagreed with economists’ view of seeing the maximin preference as a result of extreme risk aversion, and argued that the difference principle is a fairness idea.
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154)5
To our understanding of these quotations, Rawls seemed to suggest that the difference
principle is applicable to the allocation of primary social goods, which serve as instruments
to fulfill “the most rational long-term plan of life”; indeed, “The difference principle ...
applies primarily to the basic structure of society via representative individuals whose
expectations are to be estimated by an index of primary goods.” Naturally, the difference
principle is not applicable to the distribution of final outcomes resulting from “the
satisfaction of rational desire” since the theory of justice “within wide limits ... does not
prejudge the choice of the sort of persons that men want to be.”
5 People may not even know the distribution of their social positions behind the veil of ignorance. This nature of uncertainty makes it very risky to choose principles other than the difference principle. Gerber et al. (2013) tested this by giving subjects full or partial or no information of their social positions (defined by differences in productivities). They found higher demand for redistribution under the no and partial information than under the full information.
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Previous experimental tests on the difference principle typically ask subjects to choose
the distribution of monetary payments, which designate as the distribution of final
outcomes. As such, these tests may fail to catch a critical point of the Rawlsian difference
principle, that is, it is the distribution of primary social goods (serving as instruments to
fulfill “the most rational long-term plan of life”) rather than the distribution of final
outcomes that really matters. This paper builds on and extends previous work, exploring
implications of this plausible thought on the Rawlsian difference principle.
The rest of the paper is organized as follows. Section II introduces our experimental
design. Section III reports the results and Section IV concludes.
II. Experimental Design
In Schildberg-Hörisch (2010), a subject in the “allocation stage” must choose one
distributional allocation from the 13 possible ones shown in Table 1. After decisions are
made, all subjects are randomly divided into groups of two, and roles (Player 1 or Player 2)
are then randomly assigned to each group member as “the veil of ignorance” would be. It is
clear from Table 1 that Alternative 1 is the most efficient allocation, from which Player 1’s
payoff equals the largest amount 240 (in terms of experimental standard currency, ESC)
whereas Player 2 receives nothing. The next distributional allocation, Alternative 2, yields
220 for Player 1 and 10 for Player 2, indicating an efficiency loss of 50% when transferring
20 ESC from Player 1 to Player 2. In fact, every time when we move to the next higher
numbered Alternative, Player 1’s payoff is reduced by 20 ESC but Player 2 will only gain
10 ESC. Put differently, there exists tradeoff or conflict between efficiency and equality in
choosing different distributional allocations in Table 1. Note that choosing Alternatives 10
to 13 is not rational, in that it sacrifices efficiency without gaining equality. No subject
chose any of these alternatives in our experiment. So, we confine our analysis to
Alternatives 1-9 for the rest of the paper.
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[Insert Table 1 about here]
As far as the allocation stage is concerned, we adopt the same setup represented by
Table 1 as in Schildberg-Hörisch (2010). Our innovation is to add a “real effort stage” right
after the allocation stage. In the real effort stage, subjects perform the slider task devised by
Gill and Prowse (2012). They earn 30 ESC for each successful task and, within 120
seconds, there are total 48 slider tasks to be completed by a subject. Each slider is initially
positioned at 0. To accomplish a task successfully, the subject has to use the mouse to
position the slider exactly at 50. There are two different working environments under which
subjects can carry out the task. The first is the environment in which the current position of
a slider is displayed with a numerical scale so that subjects can adjust the slider to the
correct position without errors; see Figure 1a. The second is the environment in which the
current position of a slider is displayed without any numerical scale so that subjects face
difficulty in adjusting the slider to the correct position; see Figure 1b.
[Insert Figure 1 about here]
To which environment a subject is applied, it hinges completely upon whether the
monetary payoff received by the subject in the allocation stage is no less than some
threshold or not. If the threshold criterion is met in the allocation stage, a subject will carry
out the task in the first environment with scales displayed; however, if the threshold
criterion is not met, a subject must carry out the task in the second environment without
scales displayed. To accomplish the task successfully, it is obvious that the display of
numerical scales for the current position of a slider serves as a critical instrument for
subjects. It is important to recognize that once the threshold is met, no subject is in a better
position than others in terms of advantage or disadvantage in carrying out the task in the
real effort stage. Subjects are “all under conditions of fair equality of opportunity” as Rawls
(1971, p. 266) would put it. By means of this experimental design, we tie the monetary
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payoffs received in the allocation stage tightly to the concept of primary social goods in the
real effort stage. More specifically, if a subject’s payoff received in the allocation stage is
below the threshold, the amount of primary social goods owned by the subject in the real
effort stage will be insufficient and, consequently, he or she has to implement the task in the
real effort stage in the absence of “reasonably favorable circumstances.” On the other hand,
all of those who meet the threshold will own sufficient primary social goods or means to
make money in the real effort stage, and all are under conditions of fair equality of
opportunity to realize “the most rational long-term plan of life”.
Allocating resources between subjects in the allocation stage in Schildberg-Hörisch
(2010) and other similar studies is to determine the distribution of final outcomes, which
directly dictate subjects' well-being. Allocating resources between subjects in the allocation
stage here is to mainly determine the distribution of social primary goods in the real effort
stage, which only indirectly dictate subjects' well-being. It is indirect because primary social
goods serve as instruments, not ends, in the real effort stage.
We conduct a between-subject experiment with three different thresholds in the
allocation stage: 75, 35 and 0. These three thresholds represent different critical levels of
redistribution in the allocation stage such that once the thresholds are met, the resulting
distributions of primary social goods will enable subjects to face “reasonably favorable
circumstances” and have “conditions of fair equality of opportunity” in the real effort stage.
The 0 threshold serves the benchmark or control. Because choices in the allocation stage
have no impact whatsoever on the real effort stage when the threshold is 0, the result of this
treatment is expected to be similar to that of Schildberg-Hörisch (2010).
When the critical level of redistribution in the allocation stage reaches 75 as required in
the 75-threshold treatment, Alternative 9 in Table 1 is the only distribution in the allocation
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stage that meets the threshold for both players.6 Subjects who choose Alternative 9 in the
allocation stage in this treatment reveal their maximin social preferences.
The critical level of redistribution in the 35-threshold treatment is located between the
two treatments above. Alternatives including 5 to 9 in Table 1 all meet the 35 threshold. 7 It
is interesting to know how subjects would trade off equality against efficiency in their
choices once the critical level is met. The results from the 35-threshold treatment serve the
purpose for this investigation.
In order to let subjects have some concrete idea about impacts of the two different
working environments in the real effort stage, we conduct a pilot with two rounds of the real
effort task before the allocation stage -- one in the environment with scales displayed while
the other in the environment without scales displayed. The order of the two rounds is
randomly assigned to each subject. To avoid the wealth effect, subjects are paid randomly
only in one of the two rounds. We also conduct the experiment as in Holt and Laury (2002)
to elicit subjects’ risk attitudes before the pilot. This elicitation is to control for subjects' risk
attitudes in our later analysis since they might play a role in the allocation stage. Again, to
avoid the wealth effect, subjects are paid only 50% of the time. Finally, according to their
choices and the number of tasks completed, subjects are always paid in the allocation stage
and the one round of the real effort stage.
Figure 2 illustrates the procedure of our experiment.
[Insert Figure 2 about here]
We conducted a total of 14 sessions of experiments in May and June, 2014. Each lasting
within an hour. A total of 202 National Taiwan University students were recruited via the
6We use 75 instead of 80 as the threshold so that subjects would not choose Alternative 9 (where both players receive 80) simply because 80 is mentioned so as to become the focal point.7 Remember that choosing Alternatives above 9 is not rational, and that none of subjects chosen Alternatives above 9 in our experiment.
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Taiwan Social Science Experimental Laboratory (TASSEL) online recruiting website.8 3 ESC
in the experiment is equal to one NT$. The average payment was NT$483 (approximate
US$16.32), ranging from NT$147 (US$ 4.97) to NT$925 (US$ 31.30).
A possible scenario
Here we provide a concrete scenario for our abstract experimental design.
Consider two families: one is rich (Player 1) while the other is poor (Player 2). The rich
leave some bequest to their children, whereas the poor leave none. How much bequest left by
the rich depends on how high the inheritance tax is imposed. The amount of the inheritance
tax collected will be transferred to children of the poor family. Table 1 documents all possible
distributions of outcomes. For example, if there is no inheritance tax, the amount of bequest
left will equal 240 (Alternative 1). However, if the inheritance tax imposed is high enough, the
amount of bequest left will equal 160, which is divided equally between rich and poor children
through transfer (Alternative 9). Previous studies elicit individual social preferences over the
imposed inheritance tax by sampling how subjects would make choices behind the veil of
ignorance when they face alternatives shown in Table 1.
Our experimental design does not elicit individual social preferences solely based on
Table 1 (the allocation stage). We further explore the plausible possibility that children
expectations of their life (the real effort stage) critically depend on the amount of initial capital
owned at the beginning of their career. Initial capital is called “income and wealth” in Rawls
(1971) and viewed by him as one of the chief primary social goods. It serves as an important
instrument for the fulfillment of the most rational long-term plan of children life. When the
distribution of primary social goods rather than simply the distribution of outcomes is
8 Two subjects’ data are dropped in our data analysis. A subject participates in this experiment twice. We drop the data of his second attendance, which is the session of the 75-threshold treatment. Another subject participating in the 35-threshold treatment uses right and left buttons on the keyboard to conduct slider tasks. We disable these buttons but he somehow enables them, and complete lots of tasks in both rounds. Since the primary social goods manipulation does not work for him, we drop his data.
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involved in Table 1, we elicit individual social preferences over the imposed inheritance tax
behind the veil of ignorance.
III. Results
We first compare results from treatments (35- and 75-threshold) with those from control
(0-threshold). We then consider an empirical model to investigate motivations underlying
subjects' choices
A. Treatments against control
The focus of our analysis is on the allocation stage, which involves the distribution of
primary social goods in the real effort stage. Table 2 reports the summary statistics of subjects'
choices, and Figure 3 plots the frequency distributions.
[Insert Table 2 and Figure 3 about here]
We first compare the results of the 75-threshold treatment with those of the 0-threshold
treatment, which serves as the benchmark or control. In order to meet the critical level of
resource allocation for both players, it is crucial to recognize that all distributional allocations
in Table 1 are satisfied in the 0 treatment, whereas only Alternative 9 is satisfied in the 75
treatment. When the threshold is 0, it is found that merely 14.29% (10/70) of subjects chose
Alternative 9. This percentage is not salient compared with many other chosen percentages, as
can be seen from Figure 3. Indeed, our result of 14.29% is comparable to the result of 13.7%
(18/131) in Schildberg-Hörisch (2010).
By contrast, the percentage of subjects who chose Alternative 9 jumps to 54.10% (33/61)
when the threshold is 75. This percentage represents the mode of the subject-choice
distribution and is clearly salient compared with any other chosen percentages, as can be
visibly seen from Figure 3. Table 3 reports that the rise in the percentage compared to the
control is statistically highly significant at p < 0.0001 (the p-value of one-tail test). Thus, a
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salient majority of subjects are significantly willing to sacrifice efficiency and act according to
the difference principle when: (i) monetary payoffs that they can obtain in the allocation stage
are tightly tied to the concept of primary social goods in the real effort stage (instruments for
future success in the subsequent slider task), and (ii) the maximin of resource allocation in the
allocation stage represents the critical level of redistribution of primary social goods needed
for meeting conditions of fair equality of opportunity in the real effort stage. Table 4 makes
comparison between the results of the two treatments using two standard tests: the Wilcoxon–
Mann–Whitney rank sum test yields Z = 3.53 (p<0.001), and the Epps-Singleton test gives
W2=34.33 (p<0.0001). The difference between the two treatments is highly significant. It is
interesting to note from Figure 4 that the frequency distribution of the 75 treatment
stochastically dominates that of the 0 treatment in the strict sense. This dominance implies that
subjects tend to choose more equally distributional allocations in the 75 treatment than the 0
treatment. There is no such dominance in the 35 treatment, as we show below.
[Insert Tables 3 and 4 about here]
[Insert Figure 4 about here]
We next compare the results of the 35-threshold treatment with those of the 0-threshold
treatment, which again serves as the benchmark or control. To meet the critical level of
resource allocation for both players in the 35 treatment, Alternatives equal to or above 5 in
Table 1 are all satisfied. Table 4 reports that both the Wilcoxon–Mann–Whitney test (Z = 0.39
and p=0.6940) and the Epps-Singleton test (W2=2.13 and p=0.7117) indicate no significant
difference in frequency distribution between the 35 treatment and the 0 treatment.
Nevertheless, careful examination of the data reveals some important information. Table 2
reports that while the proportion of subjects who chose Alternatives 1-4 is 32.86% in the 0
treatment, it reduces to 27.54% in the 35 treatment. Since the proportion of subjects who
chose Alternatives 7-9 is also decreased as noted below, this implies that, as the threshold level
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raises from 0 to 35, the decrease in the proportion of subjects who chose Alternatives 1-4 must
shift to contribute to the increase in the proportion of subjects who chose Alternative 5-6. This
result is consistent with our previous finding: subjects are more willing to sacrifice efficiency
when monetary payoffs that they can obtain in the allocation stage are associated with the
availability of “reasonably favorable” primary social goods in the real effort stage.
A new finding, which is absent previously, is that the proportion of subjects who chose
Alternatives 7-9 is decreased from 44.29% in the 0 treatment to 34.78% in the 35 treatment.
Since the proportion of subjects who chose Alternatives 1-4 is also decreased as noted above,
this implies that, as the threshold level raises from 0 to 35, the decrease in the proportion of
subjects who chose Alternatives 7-9 must shift to contribute to the increase in the proportion
of subjects who chose Alternative 5-6. This kind of shift in subjects' choices from Alternatives
7-9 to 5-6 can be ascribed to the plausible interpretation that once fair equality of opportunity
for future success is guaranteed, subjects become more willing to trade off equality for
efficiency.
Subjects who chose Alternatives 5-6 increase from 22.86% to 37.68% as the threshold
level raises from 0 to 35. Table 3 reports that this increase is significant with p=0.0286. It is of
no surprise to find that the 14.82 percentage-point increase for Alternatives 5-6 is almost equal
to the sum of the 5.32 percentage-point decrease for Alternatives 1-4 plus the 9.51 percentage-
point decrease for Alternatives 7-9. Suppose our samples are representative of the population.
Then, as the threshold level raises from 0 to 35, the overall picture revealed indicates that
those who used to emphasize efficiency in the absence of primary social goods (i.e., those who
chose Alternatives 1-4 in the 0 treatment) become more willing to place priority on equality,
while those who used to emphasize equality in the absence of primary social goods (i.e., those
who chose Alternatives 7-9 in the 0 treatment) become more willing to sacrifice equality for
efficiency. In fact, Figure 3 shows that Alternative 5, which is the least numbered alternative
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that meets the 35 threshold, becomes the focal point and is the mode in the 35-threshold
treatment.
To sum up, our experiment yields three main results:
1. When monetary payoffs that subjects can obtain in the allocation stage have little to do
with the availability of “reasonably favorable” primary social goods in the real effort stage
(the 0-threshold treatment), the proportion of subjects whose social preferences obey the
Rawlsian difference principle is not salient at all and lower than 15%. This result is
comparable with previous experimental findings in the absence of the role for primary social
goods
2. When (i) monetary payoffs that subjects can obtain in the allocation stage are tightly
tied to the concept of primary social goods in the real effort stage, and (ii) the maximin of
resource allocation in the allocation stage represents the critical level of redistribution of
primary social goods needed for meeting conditions of fair equality of opportunity in the real
effort stage (the 75-threshold treatment), a salient majority of subjects are significantly willing
to sacrifice efficiency and act in accordance with the Rawlsian difference principle.
3. Once the availability of “reasonably favorable” primary social goods or the equality of
opportunity for future success is guaranteed (the 35-threshold treatment), subjects place less
priority on distributional equality and are more willing to trade off equality for efficiency.
On the specialty of the 75-threshold
Our experimental design considers three thresholds, 0, 35 and 75 in the allocation stage.
Once the thresholds are met in our experiment, the distribution of primary social goods can
generate “reasonably favorable circumstances” and meet “conditions of fair equality of
opportunity” for subjects in the real effort stage. A question remains unanswered: which
threshold is more realistic? Consider our concrete scenario in which primal social goods are
identified with “income and wealth.” In this context, the distribution of monetary payoffs in
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the allocation stage can be viewed essentially the same as the distribution of primary social
goods in the real effort stage. As such, it seems that the 75-threshold is the only threshold out
of three that is really capable of generating “reasonably favorable circumstances” and meeting
“conditions of fair equality of opportunity” for subjects in the real effort stage. The assertion is
logical in view of Rawls's reasoning that every rational man would “prefer more primary
social goods” and that these goods “normally have a use whatever a person’s rational plan of
life.” This suggests the specialty of the 75-thredhold in our experiment, and explains why the
Ralwsian difference principle is uniquely associated with the maxmin criterion.
B. An empirical model
To better understand motivations underlying subjects' choices in the allocation stage, we
estimate a conditional logit model. Our estimation use separate data from different treatments,
not pooled data from all treatments. As will be seen, motivations underlying subjects' choices
differ qualitatively across treatments. The model is built on Engelmann and Strobel (2004)
with the important modification of: (i) incorporating the impact of primary social goods, and
(ii) focusing on the element of trading off between equality and efficiency as in our
experiment and so concerns other than this element such as inequality aversion in Fehr and
Schmidt (1999) and Bolton and Ockenfels (2000) are not considered.
Let
i: index of subjects;
j: Alternatives in the allocation stage with j∈{1,2,3 ,. . . ,9};
k: threshold levels with k∈ {0 , 35 ,75 };
V ij : utility representation of subject i's social preferences over Alternative j.
The conditional logit model specifies the probability of subject i's choosing Alternative j as
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pij=exp(V ij )
∑ j=1
9exp(V ij )
where V ij=β1⋅DPij+β2⋅EQij+β3⋅EFij+ β4⋅EU ij+uij , in which the right-hand-side
variables are defined as follows:
(1) DPij : subjects behave in the sense of respecting the threshold of resource allocation such
that
(i) when k=0, DPij=1 all the time;
(ii) when k=35, DPij=1 if j∈{5,6,7,8,9}; DPij=0 otherwise;
(iii) when k=75, DPij=1 if j=9 ; DPij=0 otherwise.
(2) EQij : subjects chose the most equal allocation such that
when k∈ {0 , 35}, EQij=1 if j=9 ; EQij=0 otherwise.
(3) EFij : a measure of efficiency with
EFij=P 1ij+P 2ij , where P 1ij and P 2ij are subject i's two equally likely payoffs in choosing
Alternative j in the allocation stage.
(4) EU ij : subjects behave according to the expected utility hypothesis, that is, maximizing
total payoffs from both the allocation stage and the real effort stage with
EU ij=0 .5⋅(P 1ij+30⋅Taskij )
1−γ i
1−γi+0 . 5⋅
( P 2ij+30⋅Task ij)1−γ i
1−γ i
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where γi is subject i's coefficient of relative risk aversion elicited in accordance with the
experiment of Holt and Laury (2002), Task ij is the number of tasks completed by subject i in
one of the first two rounds slider tasks, dependent on whether she/he will be able to see
numerical scales. Specifically, if DPij =1 (0) , Task ij is the number of tasks complete in the
round where numerical scales can (not) be seen. Recall that subjects earn 30 ESC for each
successful task.
[Insert Table 5 about here]
As in Engelmann and Strobel (2004), we estimate the preferences of an “average
subject.” Table 5 reports the results. When there is no threshold as in the 0 treatment, the
expected utility hypothesis features significantly in explaining subjects' choices as indicated
by the variable EU in Table 5. This implies that subjects behaved by trading off equality
against efficiency or vice versa according to the expected utility hypothesis when primary
social goods are not involved.
By contrast, the expected utility hypothesis represented by the variable EU in Table 5
does not have bites in explaining subjects’ choices in the 35- and 75-threshold treatments,
especially in the case of the 75-threshold treatment. On the other hand, the presence of
thresholds captured by the variable DP in Table 5 explains subjects' choices highly
significantly in both treatments. Moreover, in terms of odds ratio, DP exerts large positive
impact in both treatments, especially in the case of the 75-threshold treatment. The presence of
primary social goods altered subjects’ social preferences over the distribution of payoffs
qualitatively in a significant way.
The efficiency measure represented by the variable EF in Table 5 features significantly
in both the 0- and the 35-threshold treatments. This is in contrast to the finding that the
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efficiency measure is not a critical motive in the 75-threshold treatment. This result suggests
the priority of equality over efficiency as argued by Rawls (1971) when the critical level of
redistribution of primary social goods equals the maximin of distributional allocations as in
the 75-treshold treatment.
The variable EQ represents subjects who chose the most equal allocation, Alternative 9,
regardless of variations in the threshold. However, EQ in Table 5 does not feature importantly
in both the 0- and the 35-threshold treatment, especially in the case of the 0-thresold treatment.
This result is not surprising in view of the significance of the efficiency measure EF in both
treatments -- the significance of EF simply means that subjects would not behave according
to the equality criterion alone.
Overall, the results here complement our previous findings, in support of: (i) the presence
of primary social goods alters subjects' social preferences over the distribution of payoffs
qualitatively, and (ii) the priority of equality over efficiency features significantly in the 75-
threshold treatment.
IV. Conclusion
While most economists view the relationship between equality and efficiency as a
tradeoff or conflict, Rawls (1971) saw it differently according to his proposed difference
principle: equality has priority over efficiency in essence. Previous experimental studies lend
little support to the importance of the difference principle -- subjects whose social
preferences obey the difference principle represent only a small minority in the sample. This
paper finds a much stronger support -- a salient majority of subjects whose social preferences
obey the difference principle. A key to our departure from previous studies lies in that
allocating monetary payoffs between subjects in our experimental design embodies not
18
simply choosing the distribution of payoffs but more importantly the distribution of Rawls's
so-called “primary social goods,” which serve as instruments critical to the fulfillment of
people's rational desire.
The other important finding of our experiment is that once access to primary social goods
is under “reasonably favorable circumstances,” subjects place less priority on distributional
equality and are more willing to trade off equality for efficiency.
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Table 1. Possible distributional allocations in the allocation stage
Alternatives 1 2 3 4 5 6 7 8 9 10 11 12 13
Player 1 240 220 200 180 160 140 120 100 80 60 40 20 0
Player 2 0 10 20 30 40 50 60 70 80 90 100 110 120
Table 2. Summary statistics of subjects' choices in the allocation stage
75-threshold treatment
Alternatives Frequency Percentage Accumulation12
92
14.753.28
14.7518.03
34
13
1.644.92
19.6724.59
56
14
1.646.56
26.2332.75
789
2633
3.289.8454.10
36.0745.09100.00
Total 61 100.00
0-threshold treatment
Alternatives Frequency Percentage Accumulation12
112
15.712.86
15.7118.57
34
28
2.8611.43
21.4332.86
56
88
11.4311.43
44.2955.71
789
13810
18.5711.4314.29
74.2985.71100.00
Total 70 100.00
21
35-threshold treatment
Alternatives Frequency Percentage Accumulation12
102
14.492.90
14.4917.39
34
25
2.907.25
20.2927.54
56
1511
21.7415.94
49.2865.22
789
969
13.048.7013.04
78.2686.96100.00
Total 69 100.00
Table 3. Tests of the effect of primal social goods
Alternative 9 Alternatives 5-6
0 Treatment 10/70
(14.29%)16/70
(22.86%)35 Treatment 26/69
(37.68%)75 Treatment 33/61
(54.1%)
Tests of
differences
z = 4.84
p = 0.0000
z = 1.90
p = 0.0286
Table 4. Tests of differences in frequency distributions
Choice on average
0 Treatment 5.51 5.51
35 Treatment 5.46
75 Treatment 6.82
22
Wilcoxon-Mann-Whitney Z = 3.53
p = 0.0004
Z = 0.39
p = 0.6940
Epps-Singleton W2=34.33
p = 0.0000
W2= 2.13
p = 0.7117
Table 5. Results for the conditional logit model
Treatment
75 0 35
Odds ratio p-value Odds ratio p-value Odds ratio p-value
11.31 <0.0017.36 <0.001
1.00 0.9601.02 0.012 1.00 0.275
1.01 0.4580.98 0.024 1.03 0.013
0.96 0.930 1.82 0.253
23
24
blank
Panel a. Scales displayed Panel b. No scales displayed
Figure 1. Two different working environments in the real effort stage
Figure 2. Experimental procedure
25
Elicit risk attitude(paid 50% of the time)
Two rounds of the pilot slider task (paid randomly one of two rounds)
Allocating stage (always paid)
One round of the slider task (always paid)
blank
26
020
4060
Per
cent
1 2 3 4 5 6 7 8 9Distribution
75-threshold treatment (n=61)
020
4060
Per
cent
1 2 3 4 5 6 7 8 9Distribution
0-threshold treatment (n=70)
Figure 3. Frequency distributions of subjects’ choices
Figure
4.
27
020
4060
Per
cent
1 2 3 4 5 6 7 8 9Distribution
35-threshold treatment (n=69)
Cumulative distributions of subjects’ choices
28