Obvious Manipulations in Cake-Cutting

Abstract

In cake-cutting, strategy-proofness is a very costly requirement in terms of fairness: for n = 2 it implies a dictatorial allocation, whereas for n ≥ 3 it requires that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril, called not-obvious manipulability, is compatible with the strong fairness property of proportionality, which guarantees that each agent receives 1/n of the cake. Both properties are satisfied by the leftmost leaves mechanism, an adaptation of the Dubins -Spanier moving knife procedure. Most other classical proportional mechanisms in literature are obviously manipulable, including the original moving knife mechanism. Not-obvious manipulability explains why leftmost leaves is manipulated less often in practice than other proportional mechanisms.

Obvious Manipulability of Voting Rules

“…As a new concept, NOM has currently been examined only for a handful of settings. It will be interesting to consider it when analyzing the strategic behaviour of agents in other settings such as fair division (see, e.g., [15]).…”

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.…”