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In front of and behind the veil of ignorance: an analysis of motivations for redistribution

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Abstract

This paper uses a laboratory experiment to explore individuals’ motivations for redistribution. The laboratory results show that as income uncertainty diminishes, participants become more extreme in their preferences for redistribution. The findings suggest that for most people, the motivation for redistribution is financial self-interest—namely as insurance against future bad luck—rather than furthering equity. However, a non-negligible group of participants propose redistribution levels inconsistent with financial self-interest, where this group is primarily made up of those with the least to lose financially from making such a proposal, and the size of this group increases when participants can communicate prior to proposing. Survey data from the National Longitudinal Survey of Youth and General Social Survey show that these experimental findings may help shed light on the way preferences for redistribution evolve with age in the real world.

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Notes

  1. For example, behavior is drastically different when the dictator’s decision is framed as taking rather than giving (List 2007), when dictators are also given the option of taking some of their partner’s allotment rather than just sharing some of their own allotment with their partner (Bardsley 2008), whether the allotments to be shared are “produced” or “earned” rather than just randomly allocated (Cappelen et al. 2007; Krawczyk 2010), how many people will benefit from the redistribution decision (Andreoni 2007), when subjects are placed in identifiable groups together (Klor and Shayo 2010), when the recipient is generally agreed to be “more deserving” (Eckel and Grossman 1996), how much of the “endowment” is initially allocated to the dictator versus the “receiver” (Hayashi 2013), and when the dictator is guaranteed greater anonymity (Hoffman et al. 1996).

  2. This is sometimes known as a “random dictator” mechanism and is meant to ensure that it is in each player’s best interest to truthfully reveal his or her preferred redistribution rule.

  3. Specifically, they observe a list of everyone’s earnings that round from smallest to largest with their own earnings highlighted, as well as the mean earnings that round.

  4. In a 2009 Gallup Poll of the US population, 9  % described themselves as “very conservative,” 31  % “Conservative,” 35  % “Moderate,” 16  % “Liberal,” 5  % “Very Liberal,” and 4  % “No Opinion.”

  5. The instruction script that was read to the participants in the Earnings Unknown treatment are included in the Appendix. Instructions that were read to participants in the other treatments are very similar and available from the author upon request.

  6. See Appendix for screen shots showing the re-distribution proposal screen (for the Earnings Known treatment) and the end of round results screen.

  7. The F-test jointly tested the null hypothesis of equality for each of the deciles in the two distributions. Standard errors, and therefore statistical significance levels, were adjusted for the fact that each individual provided multiple data points by clustering at the individual level. Such a clustering adjustment was done for all the statistical tests that follow in this paper.

  8. Earnings are shown in tokens, which was how they were revealed to participants during the course of the experiment. However, participants were explicitly told at the outset of each session the that each token would be worth $0.10.

  9. Specifically, subjects were asked what they would be willing to pay to participate in a coin flip gamble where they would win $100 if the coin landed on heads and nothing if it landed on tails.

  10. Table 7 in the Appendix shows that very similar conclusions are drawn when using “proposed no redistribution (p \(= 0\))” and “proposed full redistribution (p \(= 1\))” are used as the dependent variable.

  11. In order to see if earnings variation in the previous rounds were correlated with proposed levels of redistribution, the regressions in Table 5 only use data from rounds 3–6.

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Authors and Affiliations

  1. Claremont McKenna College, 500 East Ninth St., Claremont, CA, 91711, USA

    David Bjerk

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  1. David Bjerk
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Corresponding author

Correspondence to David Bjerk.

Additional information

Thank you to UCLA’s CASSEL for providing the research facilities to perform this work, as well as the Lowe Institute for Political Economy and the Dean of Faculty’s Office at Claremont McKenna College for their generous financial assistance, and seminar participants at UQAM for helpful comments. Thanks to Myles MacDonald for research assistance.

Appendices

Appendix 1: Examples of questions asked in “task” completion component of game

(i) Examples of GRE Math Type Questions:

Question 1: :

Which of the following is a solution to x(1+ x) = 1? (a) 4 (b) -1 (c) 0 (d) 1/2 (e) 1 (f) none of the above

Question 2: :

In a certain shop, notebooks that normally sell for 59 cents each are on sale at 2 for 99 cents. How much can be saved by purchasing 10 of these notebooks at the sale price? (a) 85 cents (b) 95 cents (c) 1.50 dollars (d) 2 dollars

Question 3: :

Which of the following is equal to 1/4 of 0.01  %? (a) 0 (b) 0.000025 (c) 0.00025 (d) 0.0025 (e) 0.025 (f) 0.25

(ii) Examples of GRE Analogy Type Questions:

Question 1: :

SEDATIVE is to DROWSINESS as: (a) epidemic is to contagiousness (b) vaccine is to virus (c) laxative is to drug (d) anesthetic is to numbness (e) therapy is to psychosis

Question 2: :

LAWYER is to COURTROOM as: (a) participant is to team (b) commuter is to train (c) gladiator is to arena (d) senator is to caucus (e) patient is to ward

Question 3: :

CURIOSITY is to KNOW as: (a) temptation is to conquer (b) starvation is to eat (c) wanderlust is to travel (d) humor is to laugh \({\vert }\)(e) survival is to live

(iii) Examples of General Trivia Questions

Question 1: :

What famous document begins: “When in the course of human events...”? (a) The Magna Carta (b) The United States Constitution (c) The Declaration of Independence (d) The Oslo Accords

Question 2: :

What current branch of the U.S. military was a corps of only 50 soldiers when World War I broke out? (a) The U.S. Air Force (b) The U.S. Army (c) The U.S. Navy (d) The U.S. Marines

Question 3: :

What president was shot while walking to California Governor Jerry Brown’ office? (a) Ronald Reagan (b) Jimmy Carter (c) John F. Kennedy (d) Gerald Ford

(iv) Examples of Entertainment Trivia Questions

Question 1: :

What movie has Anthony Perkins explain: “Understand, I don’t hate her. I hate what she’s become. I hate her illness”? (a) Carrie (b) Psycho (c) Terms of Endearment (d) Ordinary People

Question 2: :

Who was the first person since Orson Welles to be up for four Oscars in a single year, in 1982? (a) Jack Nicholson (b) Clint Eastwood (c) Warren Beatty (d) Martin Scorcesse

Question 3: :

What was the first Arnold Schwarzenegger movie to win four Academy Awards? (a) Terminator (b) Terminator 2 (c) True Lies (d) Rocky

(v) Examples of GRE Type Sentence Completion Questions

Question 1: :

Nonviolent demonstrations often create such tensions that a community that has constantly refused to————its injustices is forced to correct them: the injustices can no longer be————. Choose option that best completes sentence) (a) acknowledge...ignored (b) decrease...verified (c) tolerate...accepted (d) address...eliminated (e) explain...discussed

Question 2: :

Since 1813 reaction to Jane Austen’s novels has oscillated between ———— and condescension; but in general later writers have esteemed her works more highly than most of her literary —————-. Choose option that best completes sentence) (a) dismissal...admirers \({\vert }\) adoration...contemporaries (b) disapproval...readers (c) indifference...followers (d) approbation...precursors

Question 3: :

There are, as yet, no vegetation types or ecosystems whose study has been ———— to the extent that they no longer ———— ecologists. (Choose option that best completes sentence) (a) perfected...hinder (b) exhausted...interest (c) prolonged...require (d) prevented...challenge (e) delayed...benefit

(vi) Examples of Sports Trivia Questions

Question 1: :

What racket sport can be played with four balls of differing bouncing qualities? (a) Tennis (b) Squash (c) Basketball (d) Cricket

Question 2: :

What pro athlete is nicknamed “The Dream”? (a) Clyde Drexler (b) Michael Jordan (c) Hakeem Olajuwon (d) Scottie Pippen

Question 3: :

What Giant’s bone-crushing 1985 tackle ended Joe Theismann’s career? (a) Lawrence Taylor (b) Michael Strahan (c) Reggie White (d) Bruce Smith

Appendix 2: Instructions to participants for Earnings Unknown Treatment

Instructions to Participants

Thank you very much for your participation. Please read the following instructions closely. They describe the game you will be playing and how your final payoff for participating in the experiment will be determined. At no time will you be lied to or misled at any point in the experiment regarding how the experiment will proceed and how your final payoff will be determined.

The Experiment

This experiment will consist of a practice round and six real rounds. In each real round you will be presented a series of questions and given 4 min to answer as many as you can. For each question you answer correctly, you will earn some amount of tokens, where the number of tokens you earn for each correct answer is said to be your “rate-of-return” (ROR) and is a randomly determined number between 2 and 17, which will be revealed to you prior to your answering of questions. So, your earnings in a given round in tokens will equal the number of questions that you answer correctly times your realized ROR for that round. At the end of the experiment, each token will be worth $0.10. This means each correct answer can earn you between $0.20 and $1.70 depending on your realized ROR.

After your 4 min for answering questions are up you will learn your total earnings (in tokens) for that round, as well as where your earnings fit in the overall distribution of all participants’ earnings for that round.

However, the key component of this game is that prior to answering any questions or knowing your ROR in a given round, you will be asked to propose a re-distribution rule p, where p is a number between zero and one. Your choice of p works as a re-distribution rule in the following way: at the end of a round, the re-distribution rule p that is proposed by one of the participants in this room will be randomly selected, revealed to all participants, and then implemented by the experiment administrator. If we denote the implemented re-distribution rule as \(p^{*}\), then implementation means that a fraction \(p^{*}\) of each participant’s earnings for that round will be taken from each of participant and split evenly across all of the participants here today.

Thus, if there were three participants and if a participant i’s earnings in a given round are denoted \(E_{i}\), then for a given implemented distribution rule p, participant 1’s final payoff from that round will be equal to (\(1-p)\hbox {E}_{1}+p(\hbox {E}_{1} +\hbox {E}_{2}+\hbox {E}_{3})/3\). Note that this is equivalent to (\(1-p)\hbox {E}_{1}+p\hbox {E}_{\mathrm{Avg}}\). Therefore, if the implemented p is zero, each person’s final payoff for that round simply equals his or her earnings from that round. Alternatively, if the implemented p equals one, each person’s final payoff for that round will all be identical and equal to the average earnings over all participants in that round. Obviously, if the implemented p is greater than zero and less than one, each person’s final payoff for that round will be between his or her own earnings from that round and the average earnings over all participants in that round. Therefore, the lower the implemented re-distribution rule p, the closer each participant’s final payoff for that round will be to his or her earnings from that round, while the higher the implemented p, the more equal each participants’ final payoff will be to the average earnings across all participants.

To help illustrate how this game works more concretely, consider the following example. Suppose there are three participants: Annie, Bill, and Charlie. In a given round, Annie drew a rate-of-return of 8 and answered 5 questions correctly, meaning her earnings for that round were 40 tokens. Similarly, suppose Bill drew a rate-of-return of 4 and answered 8 questions correctly. This would mean his earnings that round were 32 tokens. Finally, suppose Charlie drew a rate-of-return of 2 and answered 10 questions correctly, meaning his earnings for that round were 20 tokens.

Now, suppose Annie proposed a re-distribution rule p equal to 0, Bill proposed a p equal to 0.25, and Charlie proposed a p equal to 0.75. Given these choices and the above earnings, if Annie’s proposed p (equal to 0) turns out to be the randomly selected re-distribution rule that is implemented, no tokens will be re-distributed. Therefore, in this scenario, each person’s final payoff from that round will simply equal his or her earnings from that round, meaning Annie will have a payoff of 40 tokens that round, Bill will have a payoff of 32 tokens that round, and Charlie will have a payoff of 20 tokens that round.

Alternatively, if Bill’s proposed p (equal to 0.25) is randomly selected to be the redistribution rule that is implemented, then 25  % of each person’s earnings are re-distributed equally to everyone, so Annie’s payoff for that round will equal \((1-0.25)^{*}40 + 0.25^{*}(32 + 40 + 20)/3 = 37.67\) tokens, Bill’s payoff for that round will equal \((1-0.25)^{*}32 + 0.25^{*}(32 + 40 + 20)/3 = 31.67\) tokens, and Charlie’s payoff for that round will equal \((1-0.25)^{*}20 + 0.25^{*}(32 + 40 + 20)/3 = 22.67\) tokens.

Finally, if Charlie’s proposed p equal to 0.75 is randomly selected to be the redistribution rule that is implemented, then 75  % of each person’s earnings are re-distributed to everyone, so Annie’s payoff for that round will equal \((1-0.75)^{*}40 + 0.75^{*}(32 + 40 + 20)/3 = 33\) tokens, Bill’s payoff for that round will equal \((1-0.75)^{*}32 + 0.75^{*}(32 + 40 + 20)/3 = 31\) tokens, and Charlie’s payoff for that round will equal \((1-0.75)^{*}20 + 0.75^{*}(32 + 40 + 20)/3 = 28\) tokens.

This example is summarized in the table below. Please take a minute to look it over.

     

Final payoff in tokens for this round

 

Rate-of-return

Correct answers

Earnings

Chosen p

If Annie’s p is selected

If Bill’s p is selected

If Charlie’s p is selected

Annie

8

5

40

0

40

37.67

33

Bill

4

8

32

0.25

32

31.67

31

Charlie

2

10

20

0.75

20

22.67

28

Round progression and final payoff for participation in this experiment

As stated previously, this experiment will consist of one practice round and six “real” rounds. Each round will follow the procedure listed above. The only difference across rounds will be the type of questions asked. While the practice round will contain all types of questions, in the subsequent real rounds, questions will all be of a certain type for a given round but will differ across rounds. For example, questions in one round may all relate to vocabulary, while in the next round may all relate to mathematics, and the next round may all relate to movie trivia. Furthermore, rounds will all be completely independent. Your performance, your ROR, or your choice of a re-distribution rule in one round will have no relation to what happens in subsequent rounds.

At the end of all the rounds, one of the “real” rounds will be randomly selected to be the one that “counts,” meaning each participant will receive his or her payoff from that round as his or her final payoff for the experiment, where each token is worth $0.10. You will also earn a $5 participation fee just for being here today.

Appendix 3: Screen shots of experiment interface (EarningsKnown treatment)

figure a

Appendix 4: Additional table

See Table 7.

Table 7 Regression analysis (OLS)
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Bjerk, D. In front of and behind the veil of ignorance: an analysis of motivations for redistribution. Soc Choice Welf 47, 791–824 (2016). https://doi.org/10.1007/s00355-016-0992-x

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