80 E.E. Rutström, M.B. Williams J. of Economic Behavior Org. 43 2000 75–89
the entitlement is independent of which allocation rule is used, either random or earned; in particular, it is independent of the performance in the earned allocation rule. Hoffman and
Spitzer find a high proportion of equal-split outcomes in the random allocation treatment, even though an equal split makes the controller worse off than with the initial entitlement
value that would apply under a disagreement outcome. Hoffman and Spitzer find some reduction in this type of non-self-interested behavior when using the earned allocation rule,
but the outcomes are still mixed.
Hoffman and Spitzer emphasize the importance of effort in determining whether an individual deserves the entitlement in a Lockean sense. “The Lockean theory posits that an
individual deserves, as a matter of natural law, a property entitlement in resources that have been accumulated or developed through the individual’s expenditure of effort” p. 264 and,
hence, Lockean desert appears to be consistent with equity theory p. 265. Nevertheless, Hoffman and Spitzer also “think that a Lockean theory of property has room within it for
differences in efficacy of effort: even if two people spend the same amount of time or try as hard, the person who does a better job still deserves the resource” p. 273. In the Hoffman
and Spitzer experiments the role of controller is allocated according to performance as a measure of effort. Thus, in their design effort is defined as productivity.
The experimental design in Burrows and Loomes 1994 consists of a two-person trading environment. As in Hoffman and Spitzer, the decision-making power over redistributions
rests with the holding of initial income entitlements. Unlike Hoffman and Spitzer, however, the dollar value of entitlements depend on performance in the earnings phase. Burrows
and Loomes also find that allocating entitlements according to a task, rather than just ran- domly, affects bargaining outcomes. When initial entitlements are unequal, the proportion
of bargaining outcomes yielding equal splits of final payoffs falls when entitlements are earned relative to when they are random. At the same time, however, the proportion of equal
splits of the gains from trade increases. Burrows and Loomes suggest that their results may support a slightly revised version of Lockean desert theory, which they refer to as “two-part
desert”; desert derives not only from the effort that produces the allocation of initial entitle- ments, but also from effort in the bargaining process itself. Equal splits of gains from trade
correspond to a notion of just desert if the effort in the bargaining process is perceived to be equal across subjects.
3. Experimental design
In the present design we incorporate two treatments where initial income entitlements are earned. We distinguish between effort-based earned entitlements and productivity-based
earned entitlements. As an additional robustness test of earnings-based justice motives, we also include a simplified design with a random income entitlement allocation.
The productivity and effort treatments both consist of two phases.
10
Phase I is the performance phase: subjects perform a task which determines their initial income for the
second phase of the experiment. In Phase I subjects know only that their performance in
10
A web-appendix summarizes our instructions which contain more detail on the design. The appendix can be found at http:theweb.badm.sc.edulisaequity.htm.
E.E. Rutström, M.B. Williams J. of Economic Behavior Org. 43 2000 75–89 81
Phase I will determine their initial income in Phase II; they are not told how their income will be determined. In Phase II subjects are brought back into groups of 12 and are informed
of their initial income and its relationship to their performance in Phase I. Subjects are then asked to choose a distribution rule.
11
We take great care to ensure anonymity throughout the experiment, but do not implement a double-blind design as we wish to control for subjects’
socio-demographic characteristics, which must be elicited and matched to individual subject responses. Subjects generally know who is in their group, but do not know the initial income
of others or their choices. Subjects are identified by randomly assigned Subject ID numbers only. The experimenter is unable to attach an ID number to an individual. Final payoffs are
known only to the subject and a “payment clerk” who is not present during the experiment.
In the performance phase subjects are given 30 minutes to solve a computerized version of the Tower of Hanoi problem. Subjects are encouraged to solve the problem more than
once. The task can be described as follows: there are k pegs and n disks. The disks are of different sizes and arranged in a pyramid on one peg the source peg. The object is to move
the stack of disks from the source peg to another specified peg the goal peg, moving only one disk at a time and never placing a larger disk onto a smaller disk. In our experiment
the number of pegs is three and the number of disks is five, yielding a rather difficult solution which requires a minimum of 31 moves to solve. We choose this particular task
because it allows us to observe both effort and productivity with no change in experimental instructions. Therefore, there is no difference between treatments in the performance phase.
Subjects do not know which treatment they are in during Phase I, nor do they know that we have two treatments in Phase II.
Productivity is measured via the number and quality of solutions. For each solution found, subjects receive 62 “units”, but then lose one unit for each move that particular solution uses
in excess of the minimum number of moves 31. Thus, it is possible to solve the problem yet earn zero units if the solution requires 93 62+31 or more moves. Subjects are given 10
points for each solution found, plus 1 point for each unit received. Points are then positively related to income. In addition, we let the size of the total group entitlement depend on the
average productivity in the group. This is quite distinct from the effort treatment where the total group income is kept constant. This design feature should strengthen the expression
of productivity-based distributive preferences, since low productivity individuals receive a higher income when teamed up with high productivity individuals.
Effort is measured as the total number of moves the subject makes within the allotted 30 minutes. Total group income is predetermined in the effort treatment, and subjects are
assigned places in the income distribution according to their level of effort. Contrary to the productivity treatment in which individual earnings decrease in the number of moves, here
individual earnings increase in the number of moves. The relative position of players into income classes based on the number of moves they performed is therefore inverted across
these two treatments. There is no reason, therefore, to expect that our subjects would equate
11
The two phases of the earned income entitlement treatments were conducted on separate days and all Phase I sessions were completed before beginning Phase II. This was necessary in order to avoid contamination of the
subject pool. In addition, subjects were recruited and scheduled for both phases simultaneously in order to avoid the potential perception that the experimenters were manipulating outcomes by basing committee assignments in
Phase II on performance in Phase I.
82 E.E. Rutström, M.B. Williams J. of Economic Behavior Org. 43 2000 75–89
Table 1 Initial income shares
Share of total group income Number of people
Income group 1 40
3 Income group 2
30 3
Income group 3 20
3 Income group 4
10 3
effort and productivity when they consider how worthy other subjects are of compensation. This allows us to test whether the amount of effort, independent of the productivity of that
effort, increases a person’s worthiness for compensation. We recognize that there are other types of effort the subject might put into solving a task, but physical effort, such as moving
disks, is the one which is most easily observable and quantifiable.
An important experimental control is to preserve the redistribution rules and to ensure budget balance across the experimental sessions. If we do not maintain redistribution rules
we cannot compare the results of the treatments, and if we do not impose budget balance we are not ensuring that all transfers are financed by participating subjects.
12
Our solution to this design problem involves defining income classes and redistribution rules in terms
of percent allocation of the total initial income for the group. This makes the definition of income class comparable across treatments, but allows total income in the productivity
treatment to vary with aggregate performance in the group.
In Phase II, subjects are randomly sorted into groups of 12 across treatment conditions. We explain to them how point earnings are determined. Subjects are then informed that
the total group income is divided among four initial income categories. We explain that the three individuals who earned the most points will together receive an initial income of
40 percent of the total income, to be divided equally among those three individuals. The three individuals who earned the fewest points will together receive an initial income of
10 percent of the group income. The remainder of the group income is divided similarly, as illustrated in Table 1. We then distribute income slips which inform each subject of his
point earnings and his place in the initial income distribution. Once subjects receive their income slips, they are presented with four distribution rules as shown in Table 2. Subjects
are informed that the group will choose one rule which will determine their final payoffs. Distribution rules are presented as income class shares in aggregate group income, and
we explain to subjects that this share will be divided equally among the three individuals in each initial income class. Because the translation of shares into final dollar payoffs for
the productivity treatments is dependent upon aggregate production in Phase I and which
12
If we use redistribution rules that apply the same tax and subsidy rates across treatments, we cannot ex ante ensure budget balance because we cannot determine the group income before knowing which of our recruits will
actually turn up to any particular group in Phase II. Budget balance would then require that we determine tax and subsidy rates after subjects have arrived at the Phase II session. Then, for example, if all participants are clustered
together around some intermediate initial income level, budget balance would require a low percentage rate for taxes and subsidies. If, on the other hand, participants experience considerable variation in initial income, budget
balance will require a higher percentage rate of transfers. If we instead use a redistribution rule based on fixed dollar amount transfers, there is a risk that the ex post redistribution will reverse the ranking of some individuals,
introducing additional factors that could influence preferences.
E.E. Rutström, M.B. Williams J. of Economic Behavior Org. 43 2000 75–89 83
Table 2 Distribution rules for effort and productivity treatments
Initial income group Distribution rule
A B
C D
I: 40 40
35 30
25 II: 30
30 28
27 25
III: 20 20
22 23
25 IV: 10
10 15
20 25
subjects show up for Phase II, they cannot be calculated in advance of the experimental session. Therefore, subjects in each experimental session are shown via blackboard how
income shares translate into final dollar payoffs. The distributions of final payoffs for each session are presented in Appendix A.
As detailed in the following section, we observe a predominance of behavior consistent with self-interest across both of our earned entitlements treatments. Accordingly, we de-
cided to implement an additional treatment designed to test a random income entitlement rule. Our hypothesis under random entitlements is that advantaged subjects should favor
more redistribution than in the earnings treatments and that low income subjects will reveal a preference for full redistribution. To give this hypothesis its best shot, we utilize a single
phase design with two income classes involving only the most and the least advantaged agents. Subjects are assigned a high 40 or low 0 initial income by means of a lot-
tery, where the probability of receiving either income is 50 percent for each subject. The distribution rules incorporated in this treatment are presented in Table 3.
To ensure truth-telling we use the Random Dictator decision rule, which is theoretically incentive compatible. Subjects make their choices anonymously and one individual is ran-
domly and anonymously chosen to be the dictator. This individual’s choice determines the distribution rule to be used. Because only one individual’s choice determines the outcome,
subjects cannot gain by engaging in strategic behavior. This decision mechanism also has the property that the probability of becoming the dictator is equal across all subjects, and
the dictator is not selected until after distribution choices are made. To ensure that subjects understand their incentives, we explain by way of example why truth-telling is their best
strategy. In addition, we conduct a Random Dictator trainer which involves a choice over four different types of candy. The candy chosen in the trainer is distributed to all participants.
Finally, we gather information on age, sex, household size, household income, country of birth, race and education.
Table 3 Distribution rules for random treatment
a
Initial income group Distribution rule
A B
C D
High: 100 100
75 62.5
50 Low: 0
25 37.5
50
a
n= 19 in each income classgroup.
84 E.E. Rutström, M.B. Williams J. of Economic Behavior Org. 43 2000 75–89
Table 4 Total group and initial incomes
a
Session Total committee income
High initial income Low initial income
Productivity 1 437.00
58.00 14.50
Productivity 2 337.00
45.00 11.00
Productivity 3 172.00
23.00 6.00
Productivity 4 120.00
16.00 4.00
Effort 1, 2, 3 264.00
35.00 9.00
Random 760.00
40.00 0.00
a
n= 12 for all productivity and effort sessions; n=38 for random session.
Based on the shares presented in Tables 2 and 3 we can specify our hypotheses as follows: under hypothesis H
1
, subjects will not always choose the payoff-maximizing alternatives, where payoffs are maximized under distribution rule A for the higher income classes Initial
Income Groups “I” and “II” in the earnings treatments and “high” in the random treatment, and distribution rule D for the lower income classes Initial Income Groups “III”, “IV” and
“low”. Our experiment is not designed to reject this hypothesis, but we could reject its alternative, self-interested payoff maximization, if we observe a significant proportion of
choices other than A for the higher income groups and other than D for the lower income groups. Under hypothesis H
2 ,
1 ,
we would expect significantly fewer subjects to choose redistribution in the effort treatment than in any other treatment because more participants
would consider the high income subjects worthy. This hypothesis can therefore only be rejected based on a comparison of behavior across treatments. Hypothesis H
2 ,
2
, similarly, predicts that significantly fewer subjects will choose redistribution in the productivity treat-
ment compared to all the other treatments. If, for example, we find that all subjects in the higher income groups choose C in the productivity and random treatments, but A in the
effort treatment, and all subjects in the lower income groups choose D in the productivity and random treatments, but B in the effort treatment, we would reject hypothesis H
2 ,
2
but not hypothesis H
2 ,
1
.
4. Results
