Fair division experiments
Various experiments have been made to evaluate various procedures for fair division, the problem of dividing resources among several people. These include case studies, computerized simulations, and lab experiments.
Case studies
Allocating indivisible heirlooms
Flood describes a division of a gift containing 5 parcels: whiskey, prunes, eggs, suitcase, etc. The division was done using the Knaster auction. The resulting division was fair, but in retrospect it was found that coalitions could gain from manipulation.When Mary Anna Lee Paine Winsor died at the age of 93, her estate included two trunks of silver, that had to be divided among her 8 grandchildren. It was divided using a decentralized, fair and efficient allocation procedure, which combined market equilibrium and a Vickrey auction. Although most participants did not fully understand the algorithm or the preference information desired, it handled the major considerations well and was regarded as equitable.
Allocating unused classrooms
In California, the law says that public school classrooms should be shared fairly among all public school pupils, including those in charter schools. Schools have dichotomous preferences: each school demands a certain number of classes, it is happy if it got all of them and unhappy otherwise. A new algorithm allocates classrooms to schools using a non-trivial implementation of the randomized leximin mechanism. Unfortunately it was not deployed in practice, but it was tested using computer simulations based on real school data. While the problem is computationally-hard, simulations show that the implementation scales gracefully in terms of running time: even when there are 300 charter schools, it terminates in a few minutes on average. Moreover, while theoretically the algorithm guarantees only 1/4 of the maximum number of allocated classrooms, in the simulations it satisfies on average at least 98% of the maximum number of charter schools that can possibly be satisfied, and allocates on average at least 98% of the maximum number of classrooms that can possibly be allocated.The partial collaboration with the school district lead to several practical desiderata in deploying fair division solutions in practice. First, the simplicity of the mechanism, and the intuitiveness of the properties of proportionality, envy-freeness, Pareto optimality, and strategyproofness, have made the approach more likely to be adopted. On the other hand, the use of randomization, though absolutely necessary in order to guarantee fairness in allocating indivisible goods such as classrooms, has been a somewhat harder sell: the term "lottery" raised negative connotations and legal objections.
Resolving international conflicts
The adjusted winner procedure is a protocol for simultaneously resolving several issues under conflict, such that the agreement is envy-free, equitable, and Pareto efficient. While there are no account of it actually being used to resolve disputes, there are several counterfactual studies checking what would have been the results of using this procedure to solve international disputes:- For the Camp David Accords, the authors construct approximate numeric valuation functions for Israel and Egypt, based on the relative importance of each issue for each country. They then run the AW protocol. The theoretical results are very similar to the actual agreement, which leads the authors to conclude that the agreement is as fair as it could be.
- For the Israeli-Palestinian conflict, the author constructs the valuation functions based on a survey of expert opinions, and describes the agreement that would result from running the AW protocol with these valuations.
- For the Spratly Islands dispute, the authors construct a two-phase procedure for settling the dispute, and present its outcome.
Allocating rooms and rent
Sharing cooperation surplus
When different agents cooperate, there is an economic surplus in welfare. Cooperative game theory studies the question of how this surplus should be allocated, taking into account the various coalitional options of the players. Several cases of such cooperation has been studied, in light of concepts such as the Shapley value.Fair Bargaining
Flood analyzed several cases of bargaining between a buyer and a seller on the price of purchasing a good. He found that the "split-the-difference" principle was acceptable by both participants. The same cooperative principle was found in more abstract non-cooperative games. However, in some cases, bidders in an auction did not find a cooperative solution.Fair Load-Shedding
Olabambo et al develop heuristic algorithms for fair allocation of electricity disconnections in developing countries. They test the fairness and welfare of their algorithms on electricity usage data from Texas, which they adapt to the situation in Nigeria.Computerized simulations
Fair cake-cutting
Walsh developed several algorithms for online fair cake-cutting. He tested them using a computerized simulation: valuation functions for each agent were generated by dividing the cake into random segments, and assigning a random value to each segment, normalizing the total value of the cake. The egalitarian welfare and the utilitarian welfare of various algorithms were compared.Shtechman, Gonen and Segal-Halevi simulated two famous cake-cutting algorithms - Even–Paz and Last diminisher - on real land-value data from New Zealand and Israel. The agents' valuations were generated by taking the market value of each land-cell and adding a random "noise" based on two different noise models: uniform noise and hot-spot noise. They showed the algorithms perform better than two alternative processes for dividing land, namely selling the land and dividing the proceeds, and hiring a real-estate assessor.
Welfare redistribution mechanism
Cavallo developed an improvement of the Vickrey–Clarke–Groves mechanism in which money is redistributed in order to increase social welfare. He tested his mechanism using simulations. He generated piecewise-constant valuation functions, whose constants were selected at random from the uniform distribution. He also tried Gaussian distributions and got similar results.Fair item assignment
Dickerson, Goldman, Karp and Procaccia use simulations to check under what conditions an envy-free assignment of discrete items is likely to exist. They generate instances by sampling the value of each item to each agent from two probability distributions: uniform and correlated. In the correlated sampling, they first sample an intrinsic value for each good, and then assign a random value to each agent drawn from a truncated nonnegative normal distribution around that intrinsic value. Their simulations show that, when the number of goods is larger than the number of agents by a logarithmic factor, envy-free allocations exist with high probability.Segal-Halevi, Aziz and Hassidim use simulations from similar distributions to show that, in many cases, there exist allocations that are necessarily fair based on a certain convexity assumption on the agents' preferences.
Laboratory experiments
Several experiments were conducted with people, in order to find out what is the relative importance of several desiderata in choosing an allocation.Important concepts
James Konow reviewed hundreds of experiments, done by phone interviews or written surveys, aimed at eliciting people's preferences and ideas regarding "what is fair?". Most experiments were done by presenting short stories to people and asking them whether the outcome is fair or unfair. The experiments revolved around four aspects of justice:- Equality and Need: egalitarianism, Rawls' theory and the Social contract and Marxism. Konow claims that there is little evidence for these as a general fairness principle, except when considering the basic needs. He calls it the Principle of Need: just allocations provide for basic needs equally across individuals.
- Utilitarian and Welfare economics: utilitarianism, Pareto efficiency, envy-freeness. There is evidence that people want to maximize total surplus, even when it comes at a personal cost to them. This leads to the Principle of Efficiency: aiming to maximize the sum of derived values.
- Equity and moral Desert: Nozick's theory of choice, Buchanan's theory of moral desert, and the theory of equity, which says that the rewards should be proportional to the contributions. He defines the Principle of Equity, which generalizes the equity formula to the entitlement formula: the entitlement of each agent is based on his inputs, outputs, endowments and costs. His allocation should be proportional to the variables he controls, but not to exogeneous variables of which he has no control.
- Context: experiments show that the weighing of the above three principles depends on context. Aspects of context include past transactions. The endowment effect affects fairness: reducing someone's endowment is considered unfair. There are also information and framing effects: subjects may respond differently depending on what kind of information they are given on the situation. Theories of local justice say that people solve each instance of fair division locally, based on fairness principles relevant for that instance, emphasizing procedural fairness. Experiments find effects of scope, that is, determining the set of agents and the set of allocations to compare. There are differences between countries and cultures in the relative weight they assign to different fairness principles, as well as to related principles such as self-interest, love, altruism, and reciprocity.