Equity and Fairness: Easy as Pie? |
Dividing resources fairly is a difficult task.
People often rely on intuition and narrow self-interest.
Marginal gains from cooperation should be divided equally.
Tous pour un, un pour tous [All for one, one for all]. ― Alexandre Dumas, The Three Musketeers
Achieving fairness when dividing resources presents a perennial challenge. Sometimes this is easy. When Adele and Billy are invited to divide six peanuts, all they need to do is count to three, unless there are other considerations, such as when it was Adele who had planted and harvested the peanuts while Billy did nothing.
When the resource does not break down into countable units, the task is tricky. A classic solution is to tell one person to make the division, e.g., by cutting the proverbial pie, and the other to pick one of the pieces. The ancients, we are told, used a version of this method when dividing up land (Brams & Taylor, 1996). The residual challenge is how to decide who will do the cutting. The cutter can anticipate being at a slight disadvantage, as any departure from perfect even-handedness will be their loss. A third-party authority is needed to appoint the roles of cutter and chooser, or this could be made a matter of chance.
Most people facing division tasks experience a conflict between self-regard (greed) and the wish to maintain a moral reputation (fairness). This conflict comes into play even when resources can be counted. If fairness dominates, an even split is the way to go, but equalitarianism often prevails even when a rational and balanced decision rule suggests unequal division (Krueger, 2000). Writing for a business audience, Nalebuff and Brandenburger (2021) presented the intriguing case of a division problem where a particular kind of equalitarian decision rule would be fair and rational, and yet is overlooked by most untrained observers, such as their MBA students.
Nalebuff and Brandenburger (NB) propose that in a negotiated agreement, what matters are the marginal gains; these, they argue, should be split equally regardless of any inequality that would prevail if the two players failed to reach an agreement. NB describe their reasoning with a pizza-sharing scenario. Adele gets four pieces, and Billy gets two pieces if they can’t agree on how to split the entire pizza of 12 pieces. One scheme says each should get six pieces, so that Adele would gain two and Billy would gain four pieces. Another scheme awards eight pieces to Adele (a gain of four) and four to Billy (a gain of two). This scheme, which is popular among MBA students, preserves the proportionate inequality remaining if no agreement is reached. In contrast to these two schemes, NB suggest the gain of six pieces should be evenly divided so that Adele ends up with seven (4 + 3) and Billy with five (2 + 3) pieces.
Now suppose Adele and Billy have different sums of money to invest and stand to benefit from the highest interest rate only if they pool their investments. NB propose that the additional, or marginal, gain obtained with this higher interest rate should be split evenly, ignoring any difference in the invested capital. MBA students’ intuitions bristle because a larger investment is seen as deserving a larger piece of the pie, but the pie at issue is the marginal gain, that is, the gain beyond what individual investing would yield.
NB’s solution is counterintuitive because it asks decision-makers to treat the invested money as being inert. This money may not be sunk, but it does not do anything once invested. Both players’ capital input is equally necessary for the marginal gain to be achieved. Each player has the same veto power to withdraw their investment and eliminate the marginal gain. To illustrate the irrelevance of the invested capital with regard to marginal gains, imagine a rich person and a poor person finding $100 in the street and being told by a powerful bystander that they can keep the money if they agree on how to divide it. The $100 is a marginal gain. Let each person take $50 and be on with their day. The rich person would be laughed at if they proposed to keep $99 because their total wealth is so much greater than that of the poor person. If anything, the pauper can make a moral argument to receive more. The same logic applies to pooled invested money. Everyone wins. Even the bigger investor gains more than they would have had they invested alone. Their extra gain is part of the marginal gain.
I have been explicit about the number of pizza slices in the introductory example, but I have treated the investment scenario only conceptually. To drive the point home, consider the numbers used by NB. Adele is the pauper. She has $5K to invest, can get only 1% interest, and expects a gain of $50. Billy can invest $20k at 2% and gain $400. If they pool their money, they can get 3% interest so that $25k yield a total gain of $750. This total gain is the sum of the gains that could be made individually (400 + 50) and the marginal gain, which is the additional gain obtained from pooling the investments (750 – 450). As equal partners, each investor is now marginally better off by $150. Why should Billy, NB ask, pocket 4/5 of the marginal gain just because he came in with 4/5 of the invested capital?
Nalebuff and Brandenburger do not say much about why popular intuition tends to depart from their proposed solution. Perhaps it is the psychologist’s task to speculate. One possibility is greed paired with myopia. People, and MBA students in particular, may automatically assume they would be the bigger investor and be attracted to a decision rule that favors them while retaining an air of fairness. Their myopia would be their failure to see that they might as well find themselves in the role of the lesser investor. Another possibility is the failure to distinguish marginal from total gains. Admittedly, making this distinction requires a bit of cognitive work. Then again, in the pizza scenario, all gains are marginal, and intuition still favors an uneven split.
A third possibility is that people have trouble seeing investments as sunk or inert. They treat it as if it worked like an (human) animal. They view all gains as the result of labor and thus of merit. On this view, the rules of equity, as opposed to equality, apply (Adams, 1963). Equity reasoning cannot, however, explain a preference for preserving unequal proportions in pizza sharing.
My students like to say “Every case is different,” and indeed, multiple psychological factors might be in play, which makes the agreement-seekers’ work difficult. Consider these complexities next time you ponder a fair division of the dinner bill. One heuristic is to plan the next dinner without inviting your myopic friends. Another heuristic is to curb your own greed.
Adams, J. S. (1963). Toward an understanding of inequity. Journal of Abnormal and Social Psychology. 67, 422–436.
Brams, S. J., & Taylor, A. D. (1996). Fair division: from cake-cutting to dispute resolution. Cambridge University Press.
Krueger, J. (2000). Distributive judgments under uncertainty: Paccioli's game revisited. Journal of Experimental Psychology: General, 129, 546-558.
Nalebuff, B., & Brandenburger, A. (2021, November - December). Rethinking negotiation: A smarter way to split the pie. Harvard Business Review, 110-119.
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