Various experiments have been made to evaluate various procedures for fair division, the problem of dividing resources among several people.
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.
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.
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.
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.
Cooperative game theory studies the question of how this surplus should be allocated, taking into account the various coalitional options of the players.
They test the fairness and welfare of their algorithms on electricity usage data from Texas, which they adapt to the situation in Nigeria.
Shtechman, Gonen and Segal-Halevi[12] simulated two famous cake-cutting algorithms - Even–Paz and Last diminisher - on real land-value data from New Zealand and Israel.
Cavallo[13] developed an improvement of the Vickrey–Clarke–Groves mechanism in which money is redistributed in order to increase social welfare.
Dickerson, Goldman, Karp and Procaccia[14] use simulations to check under what conditions an envy-free assignment of discrete items is likely to exist.
Segal-Halevi, Aziz and Hassidim[15] 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.
Several experiments were conducted with people, in order to find out what is the relative importance of several desiderata in choosing an allocation.
James Konow[16] 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 (vignettes) to people and asking them whether the outcome is fair or unfair.
The experiments revolved around four aspects of justice: Sometimes, there are only two possible allocations: one is fair (e.g. envy-free division) but inefficient, while the other is efficient (e.g. Pareto-optimal) but unfair.
One experiment[17] found that the most important factors were Pareto-efficiency and Rawlsian motive for helping the poor (maximin principle).
However, a later experiment found that these conclusions only hold for students of economics and business, who train to acknowledge the importance of efficiency.
This experiment also revealed a recurring process which was used during the negotiation: subjects first find the most equitable division of the goods.
Several pairs of players had to divide among them 3 indivisible goods (a ballpoint pen, a lighter and a mug) and some money.
Then, they let them play the procedure in two modes: binding (strict adherence to the protocol rules) and non-binding (possible renegotiation afterwards).
Their conclusions are: (a) The sophisticated mechanisms are advantageous only in the binding case; when renegotiation is possible, their performance drops to the baseline level of DC.
Before the procedure, each participant was shown all the 64 possible allocations, and was asked to grade the satisfaction and fairness of each of them between 0 (bad) and 100 (good).
In the lab, information-advantaged players aggressively exploited asymmetric information, and drastically misrepresented their true valuation through strategic bidding.
Adjusted Winner (AW): a procedure that allocates divisible objects in order to maximize the total utility.
In condition (2), while players dramatically misrepresent their true valuation for objects, both efficiency and envy-freeness approach maximum levels.
In all cases, the structured AW procedure was quite successful in attaining a win-win solution - about 3/2 times more than unstructured negotiation.
Conflict-resolution algorithm: Hortala-Vallve and lorente-Saguer describe a simple mechanism for solving several issues simultaneously (analogous to Adjusted Winner).