equality preferences in different experimental contexts

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Equality Preferences in Different Experimental Contexts

Ross Hoffman

Spring 2009

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NOTE: This experiment was not actually conducted. It was submitted as the final paper for my

Experimental Economics class in the Spring 2009 Quarter.

Abstract

A binary voting mechanism is used to test for preferences for income equality when the

perceived source of inequality is varied. After receiving an initial income, individuals choose

between two distributions of additional money that will have an equalizing or polarizing effect.

Treatments vary whether positions are justified (through the use of a quiz) or random, and

whether initial payoffs are equal or varied. In the treatments using the quiz, the additional

benefits to the group will be directly generated by individual performance, creating an

environment where inequality may be more justified. The plans are structured so that one plan

evenly distributes the group fund to each participant, while the other divides it according to

different proportions. The model will examine the sensitivity of preferences for equality to

context effects of income being warranted or random.

Introduction

How do perceptions of the causes of inequality influence preferences for fairness in

distribution of income? If differences in income are seen as justifiable based on the conditions

that created it, observed preferences for equality may decrease in favor of outcomes that appear

merit-based. It is clear that some people desire more equal outcomes in a variety of situations,

even at a cost to themselves. Redistributive policies in developed nations support low income

individuals at the expense of more stable and successful taxpayers. However, support for these

programs may be strongly dependent on the perceived causes of inequality. Individuals who

believe that luck is largely responsible for anothers fate will be more receptive to mechanisms

that reduce inequality, while those that feel the distribution of income is largely derived from

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individual effort and achievement will be less interested in redistribution. If a situation can be

created to induce a perception that income is either earned or lucky, individual preferences for

equality can be compared in different conditions.

Literature Review

Alesina and Angeletos (2005) construct a macroeconomic model that attempts to link

these perceptions of deservingness or luck to the different redistributive environments present in

Europe and America. In Europe, poverty is seen as something that is very difficult to escape

from, while Americans tend to think the poor are responsible for their state due to poor decisions

or lack of effort. Likewise, Americans view success as the result of individual skill and hard

work, while Europeans attribute it more to luck, birth, connections, and corruption. There is a

strong correlation between social spending as a percentage of GDP in a country and the

percentage of citizens that believe luck determines income. This disparity in perceptions results

in different preferences for fairness in the form of redistribution, resulting in two possible

equilibria. In one case, taxes will be low, individual investment and effort will be high,

inequality will be higher, and luck has a low role in determining income. In the other

equilibrium, which captures the environment in Europe, taxes are higher, investment and effort

are lower, but since income is more influenced by luck, preferences for equality through

redistribution are higher. Another study by Alesina, Di Tella, and MacCulloch (2003) examines

the link between the level of inequality in a society and individual well-being, based on extensive

survey data from Europe and America. They find that people are less likely to identify

themselves as happy when income inequality is high. However, there are interesting

differences between the groups. In Europe, the poor and left-leaning individuals are most

dissatisfied with inequality, while in the United States, the wealthy are more averse to inequality.

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These differences are mostly the result of contrasting perceptions of social mobility. Americans

believe society is more mobile, so the poor should be able to achieve stability, while Europeans

are thought to be trapped in poverty, thus making inequality less tolerable.

Some experimental evidence of preferences for equality is presented by Clark (1998). A

voting mechanism is used to simulate the use of referendums in the provision of public goods,

such as at the state and local level. Using groups of 8, after dividing subjects into even groups of

low or high initial incomes, individuals vote on two alternate plans of redistribution. While

members of each group receive the same benefit from a group fund, the higher income group

pays more in Plan A and the lower income group pays more in Plan B. Plan B is essentially a

regressive taxation, since the low income subjects contribute more but only receive benefits

equal to the high income subjects. By creating a well-balanced utility function, the model

isolates preferences for equality to see if individuals will choose the more equal or more

personally beneficial plan, mainly focusing on the decisions of the high income group. The

results indicate that there is a significant preference for equality with such a setup, both when

initial positions were random or earned through performance on a quiz. The data from the

treatments when group placement was earned suggests that inequality aversion may decrease

when inequality is the result of a justifiable difference rather than random causes. This paper

will attempt to further investigate the effect of the perceived causes of inequality.

Experimental Design

Using a voting model similar to that used by Clark (1998), the decisions presented to

individuals will attempt to examine how preferences for equality and redistribution can be

affected by perceptions of income being earned or the result of chance. The participants will be

recruited from the pool of undergraduate students at The Ohio State University. In groups of 10,

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the students will convene in a computer lab and read instructions on their computer screens that

are also read aloud by the experimenter (see attached Instructions). Treatments will vary the

initial income distribution and the mechanism used for sorting individuals into groups. The

initial distribution will be equal in two treatments, and will vary in the other two. Individuals

will be assigned a position from 1 to 10, and then separated into three groups, consisting of

positions 1-3, 4-7, and 8-10. The assignments will be determined either randomly or using the

results from a quiz, ranking each person according to their score. The quiz will consist of 20

multiple choice questions covering a variety of subjects at high school and university levels.

Each participant will receive the same questions, with performance judged based on the number

of correct answers. Potential ties will be broken based on the elapsed time of taking the quiz,

with faster times taking precedence.

After the positions and groups are established, the subjects will be informed that an

additional amount of money, designated the group fund, is available for distribution to all

members. A subjects position will determine the potential proportions of benefits received from

the group fund, and it will also determine initial income in treatments where the distribution is

not equal. They will be given two plans to consider, Plan A and Plan B. Plan A distributes 15%

of the additional benefits to each individual in the high ranking group (Positions 1-3), 10% to

each middle member (4-7) and 5% to each person with a low ranking (8-10). Plan B evenly

distributes 10% of the surplus to each person, regardless of position. When each person is ready,

they will anonymously cast their vote for whatever plan they prefer via computer. The plan

receiving the majority of votes will be adopted as the actual distribution of benefits. In the case

of a tie, a coin will be flipped. Participants will be paid according to their position and the

winning plan.

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The experiment has 4 treatments, labeled T1 to T4. All treatments will be between

subjects. In Treatment 1, initial incomes are equal and positions are determined randomly. In

T2, initial income varies by position and the positions are determined randomly. The initial

distribution consists of three high incomes of $9 (Positions 1-3), four middle amounts of $6 (4-

7), and three low incomes of $3 (8-10). In the third treatment (T3), initial incomes are equal but

positions are based on the quiz results. Finally, in T4, initial incomes are structured in the same

way as T2, but the positions are established using the quiz. This is a 2x2 treatment model that

attempts to isolate the sensitivity of preferences for equality to context effects of initial

distribution and positions being earned rather than the result of chance. Each treatment will be

run using 5 different groups, for a total of 20 experimental trials. The treatment structure is

summarized in the following table:

Equal 3 Levels

Random T1 T2

Quiz T3 T4

Initial Payoff

Sorting

Mechanism

When the quiz is used, not only will individual performance determine the positions, but

it will also determine the size of the group fund. For each correct answer, 30 cents is added to

the group fund. This is a key aspect of the experiment, since the top performers will generate the

most group revenue and therefore be most responsible for the benefits received by all. Individual

quiz scores will be displayed along with the voting options. This may create a situation where

the top performers are seen as more deserving of high incomes, and low performers may be less

deserving. The presence of a middle group with equal benefits from either plan creates a clean

trade-off between equality and favoring the benefit-generating group. There is a good chance

that the middle group will determine the outcome since they do not have any self-interest in the

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decision. The tension between preferences for equality and the appearance that the inequality

may be justified will be an important factor in the final outcome.

For Treatments 1 and 3, a sample of voting options using simulated data follows:

Plan A $35.70

Rank 10 9 8 7 6 5 4 3 2 1

Quiz Score 5 7 7 10 12 12 13 16 17 20

Initial Income 6 6 6 6 6 6 6 6 6 6

Benefit $1.79 1.79 1.79 3.57 3.57 3.57 3.57 5.36 5.36 5.36

Contribution $1.50 2.10 2.10 3.00 3.60 3.60 3.90 4.80 5.10 6.00

Final Pa yoff $7.79 7.79 7.79 9.57 9.57 9.57 9.57 11.36 11.36 11.36

Group Fund:

Plan B $35.70

Rank 10 9 8 7 6 5 4 3 2 1

Quiz Score 5 7 7 10 12 12 13 16 17 20

Initial Income 6 6 6 6 6 6 6 6 6 6

Benefit $3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57Contribution $1.50 2.10 2.10 3.00 3.60 3.60 3.90 4.80 5.10 6.00

Final Payoff $9.57 9.57 9.57 9.57 9.57 9.57 9.57 9.57 9.57 9.57

Group Fund:

Treatments 2 and 4 will resemble this format:

Plan A $35.70

Rank 10 9 8 7 6 5 4 3 2 1

Quiz Score 5 7 7 10 12 12 13 16 17 20

Initial Income 3 3 3 6 6 6 6 9 9 9

Benefit $1.79 1.79 1.79 3.57 3.57 3.57 3.57 5.36 5.36 5.36

Contribution $1.50 2.10 2.10 3.00 3.60 3.60 3.90 4.80 5.10 6.00

Final Pa yoff $4.79 4.79 4.79 9.57 9.57 9.57 9.57 14.36 14.36 14.36

Group Fund:

Plan B $35.70

Rank 10 9 8 7 6 5 4 3 2 1

Quiz Score 5 7 7 10 12 12 13 16 17 20

Initial Income 3 3 3 6 6 6 6 9 9 9

Benefit $3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57 3.57

Contribution $1.50 2.10 2.10 3.00 3.60 3.60 3.90 4.80 5.10 6.00

Final Pa yoff $6.57 6.57 6.57 9.57 9.57 9.57 9.57 12.57 12.57 12.57

Group Fund:

The Contribution is determined by multiplying a subjects quiz score by 30 cents per

correct answer. This does not come at a cost to an individual, but it does indicate how much of

the common pool was generated by each subject. A subjects benefit is calculated as a

percentage of the sum of the contributions, identified as the Group Fund. Consistent with the

proportions described earlier, Plan A distributes 15% of the group fund to each of ranks 1-3, 10%

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each to positions 4-7, and 5% each to ranks 8-10. Plan B pays out 10% of the group fund to each

player. The sum of a persons initial income and their benefit from the group fund gives the total

payoff received from each plan.

Since positions are assigned randomly in T1 and T2, the rows for Quiz Score and

Contribution are not relevant and will not be displayed. However, the total amount of the

group fund will still be displayed. The size of the group fund (and thus the resulting benefits) for

these treatments will be derived using data from matching treatments when positions are earned.

This will allow for more meaningful cross-treatment comparisons to examine the effect of

random versus earned roles. For example, if the size of the fund is $25 in a trial of T3, T1 will

be run using that value as the predetermined group fund. For this reason, T3 will need to be run

before T1 and T4 before T2 in order to generate data to use for the random treatments

Hypotheses

The final payoffs to participants will be somewhat volatile since the size of the group

fund is dependent on the quiz results. However, this may be beneficial in generating a variety of

interesting situations with the same treatment. Depending on whether the results within a group

are relatively equal, polarized, or skewed in one direction, the trade-offs faced by individual

voters will be slightly varied.

In T1 and T3, subjects with a high ranking (1-3) face a trade-off between higher

individual income in Plan A and maintaining income equality in Plan B. While some members

in both treatments will likely choose the equal outcome at a cost to themselves, the use of the

quiz in T3 may reinforce a feeling of entitlement and induce more subjects to vote according to

self-interest if their position is earned. The middle ranked (4-7) voters are indifferent to each

plan in terms of personal income, since they receive 10% of the group fund in either case.

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However, they must make a decision between income inequality in Plan A and maintaining

equality in Plan B. These subjects are very likely to vote for the equal distribution in T1 when

positions are random. However, when the quiz is used in T3 to generate the group fund and

positions, subjects may be more willing to reward the top scorers, especially since they are

more responsible for the benefits. Low ranked members receive a higher payoff from the equal

distribution of Plan B, so preferences for self-interest and for equality will complement each

other. For this reason, they will be extremely likely to vote for Plan B, even when positions are

earned.

Treatments two and four follow a similar dynamic in terms of the trade-offs faced by

subjects in each position. However, since initial incomes are not equal, the distribution of the

group fund will either increase inequality with Plan A or decrease inequality with Plan B. For

T2, the more equal Plan B is likely to receive strong support from all positions since the

inequality is based on chance. In Treatment four, when positions are earned, high ranking

subjects may be more willing to vote for Plan B compared to T2 and T3, since they still receive a

higher total payoff than the other rankings even when the group benefits are equally shared.

Across all treatments, low position subjects receive more income from Plan B and high

position participants earn more when Plan A is adopted. If there are no preferences for equality,

individuals should vote for the plan that maximizes their own payoff. However, based on past

experimental evidence, it is likely that some individuals will vote for an equal outcome even at a

cost to themselves. The middle positions are interesting, since their own payoff is the same

under both plans. Their vote will reveal preferences either for increased equality or a justified

difference in incomes. By carefully examining the data across treatments and within a trial, the

sensitivity of preferences for equality to these context effects can be observed.

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Instructions (NOTE: Use of red indicates commentary that will not actually appear in the

instructions)

Instructions for Treatment 1

Welcome. This is an experiment in economic decision making, involving you and nine

other participants. Please remain quiet during the experiment. If you have questions or need

assistance in any way, raise your hand. Each player will now be credited with $6 in initial

income. There is an additional group fund that is available for distribution to all participants,

totaling $___ (derived from an experimental trial of T3). You will vote on one of two

distribution plans for the group fund. The plan receiving the most votes will be adopted and

subjects will be paid accordingly. In the case of a tie, a coin will be flipped to determine the plan

that is used. In Plan A, individuals 1-3 will each receive 15% of the fund, individuals 4-7 will

receive 10%, and individuals 8-10 will each get 5% of the surplus. In Plan B, each individual

will receive 10% of the group fund. You have been randomly assigned as number __ (1-10). The

voting options will be displayed when you are finished reading these instructions. Take as much

time as you need to consider the two plans. When you are ready, you may submit your vote on

the computer. Individual voting results are strictly anonymous, as experimenters will only use

your group assignment and the winning plan to determine your payoff. They will not know how

participants voted.

(the two plans are displayed to the individual, and subjects submit their votes to the computer)

Plan __ (A or B) has been selected by majority vote. Your total earnings will be $__ (Initial

Income + Benefit). Please wait at your seat while the experimenter distributes payments to each

participant. Thank you for your cooperation.

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assistance in any way, raise your hand. Three individuals will receive an initial income of $3,

four will receive $6, and the remaining three will receive $9 each. You have been randomly

assigned an initial income of $__ (3, 6, or 9). There is an additional group fund that is available

for distribution to all participants, totaling $___ (derived from an experimental trial of T4). You

will vote on one of two distribution plans for the group fund. The plan receiving the most votes

will be adopted and subjects will be paid accordingly. In the case of a tie, a coin will be flipped

to determine the plan that is used. In Plan A, the high income individuals will each receive 15%

of the fund, middle income members will receive 10%, and low income individuals each get 5%

of the surplus. In Plan B, each individual will receive 10% of the group fund, regardless of

initial income. The voting options will be displayed when you are finished reading these

instructions. Take as much time as you need to consider the two plans. When you are ready,

you may submit your vote on the computer. Individual voting results are strictly anonymous, as

experimenters will only use your group assignment and the winning plan to determine your

payoff. They will not know how participants voted.


Plan __ (A or B) has been selected by majority vote. Your total earnings will be $__

(Initial Income + Benefit). Please wait at your seat while the experimenter distributes payments

to each participant. Thank you for your cooperation.


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assistance in any way, raise your hand. Each player will now be credited with $6 in initial

income. You will be taking a quiz containing 20 multiple choice questions covering a variety of

topics at high school and university levels. The results of this quiz will be evaluated relative to

others and will be important later in the experiment. Ties will be broken based on elapsed time

when the final answer is submitted.

(the subjects take the quiz)

You answered __ (1-20) questions correctly. Your score ranking is __ out of 10, with 1

representing the highest score. For each correct answer you gave, 30 cents has been contributed

to a group fund account that will be distributed to all participants. Each correct answer by the

other participants also contributes 30 cents to the same fund. This account contains a total of $__

(the sum of total correct answers multiplied by $0.30). You will vote on one of two distribution

plans for these benefits. The plan receiving the most votes will be adopted and subjects will be

paid accordingly. In the case of a tie, a coin will be flipped to determine the plan that is used. If

Plan A is adopted, those ranked 1-3 will each receive 15% of the group fund, those ranked 4-7

will receive 10% each, and the scorers 8-10 will each receive 5%. If Plan B is used, all

participants will receive 10% of the group fund, regardless of their contribution. The voting

options will be displayed when you are finished reading these instructions. Take as much time

as you need to consider the two plans. When you are ready, you may submit your vote on the

computer. Individual voting results are strictly anonymous, as experimenters will only use your

rank and the winning plan to determine your payoff. They will not know how participants voted.


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assistance in any way, raise your hand. You will be taking a quiz containing 20 multiple choice

questions covering a variety of topics at high school and university levels. The results of this

quiz will be evaluated relative to others and will be important later in the experiment. Ties will

be broken based on elapsed time when the final answer is submitted.

(the subjects take the quiz)

You answered __ (1-20) questions correctly. Your score ranking is __ out of 10, with 1

representing the highest score. This ranking determines your initial payoff. Participants with

ranks 1-3 will earn an initial income of $9, ranks 4-7 earn $6 each, and those ranked 8-10 each

earn $3. For each correct answer you gave, 30 cents has been contributed to a group fund

account that will be distributed to all participants. Each correct answer by the other participants

also contributes 30 cents to the same fund. This account contains a total of $__ (the sum of total

correct answers multiplied by $0.30). You will vote on one of two distribution plans for these

benefits. The plan receiving the most votes will be adopted and subjects will be paid

accordingly. In the case of a tie, a coin will be flipped to determine the plan that is used. If Plan

A is adopted, those ranked 1-3 will each receive 15% of the group fund, those ranked 4-7 will

receive 10% each, and the scorers 8-10 will each receive 5%. If Plan B is used, all participants

will receive 10% of the group fund, regardless of their contribution. The voting options will be

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displayed when you are finished reading these instructions. Take as much time as you need to

consider the two plans. When you are ready, you may submit your vote on the computer.

Individual voting results are strictly anonymous, as experimenters will only use your rank and

the winning plan to determine your payoff. They will not know how participants voted.





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References

Alesina, Alberto and George-Marios Angeletos. Fairness and Redistribution. The American

Economic Review, 2005, 95(4), pp. 960-980. .

Alesina, A., Di Tella, R., MacCulloch, R. Inequality and happiness: are Europeans and

Americans different? Journal of Public Economics, 2004, 88, pp. 2009-2042.

.

Clark, Jeremy. "Fairness in Public Good Provision: An Investigation of Preferences for Equality

and Proportionality." Canadian Journal of Economics, 1998, 31(3), pp. 708-729.

< http://www.jstor.org/stable/136209>.

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equality preferences in different experimental contexts

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