Fair Cake-Cutting in Practice

Abstract

Using a lab experiment, we investigate the real-life performance of envy-free and proportional cake-cutting procedures with respect to fairness and preference manipulation. We find that envy-free procedures, in particular Selfridge-Conway, are fairer and also are perceived as fairer than their proportional counterparts, despite the fact that agents very often manipulate them. Our results support the practical use of the celebrated Selfridge-Conway procedure, and more generally, of envy-free cake-cutting mechanisms. We also find that subjects learn their opponents' preferences after repeated interaction and use this knowledge to improve their allocated share of the cake. Learning reduces truth-telling behavior, but also reduces envy.

Fair cake-cutting algorithms with real land-value data

“…between fairness and efficiency [24,26,31]. Some experiments check whether participants choose to play strategically, and how their manipulations affect the fairness of the final outcome [21,32,35,42].…”

“…In lab experiments, due to practical reasons, the division instances are small (e.g. [35] report a cake-cutting experiment with at most 4 participants per instance). In contrast, in our simulation experiments we could compare division procedures on much larger instances.…”

“…It is known that most existing cake-cutting algorithms are not strategyproof, which means that agents may gain by strategically reporting false preferences [11,40]. In theory, the gain from such manipulation can be very high: there are instances in which a truthful agent receives only 1/n of the total value, while a strategic agent receives 100% of the value [35]. However, such instances are highly artificial.…”

“…On one hand, a worst-case analysis would require us to assume that the strategic agent knows the value functions of all other agents, and uses a globally-optimal strategy. On the other hand, recent evidence from a laboratory experiment [35] shows that humans are far from optimal in manipulating cake-cutting algorithms. Even in simple algorithms like cut-and-choose on a 1-dimensional cake, they often make obvious mistakes such as cutting the cake to the right of their actual half-point when they know that their partner will choose the leftmost piece.…”

Fairness and efficiency in cake-cutting with single-peaked preferences

“…Agent 2 is assigned the interval (c ′ll 1 , c ′ll 2 ] and so on, until the last agent who receives the interval (c ′ll n−1 , 1]. Leftmost leaves generates a Pareto optimal allocation, guaranteeing all agents at least a utility of 1/n (Kyropoulou et al, 2019;Ortega and Segal-Halevi, 2019), in contrast with the Wang-Wu mechanism which guarantees exactly a 1/n utility to all agents; thus leftmost leaves Pareto dominates the Wang-Wu mechanism. However, leftmost leaves can generate envy.…”