Abstract
In the classical cake-cutting problem, strategy-proofness is a very costly requirement in terms of fairness: for n= 2 it implies a dictatorial allocation, whereas for n≥ 3 it implies that one agent receives no cake. We show that a weaker version of this property recently suggested by Troyan and Morril (J Econ Theory 185:104970, 2019) is compatible with the 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 the literature are obviously manipulable, including the original moving knife mechanism and some other variants of it.
| Original language | English |
|---|---|
| Pages (from-to) | 969-988 |
| Number of pages | 20 |
| Journal | Social Choice and Welfare |
| Volume | 59 |
| Issue number | 4 |
| DOIs | |
| State | Published - Nov 2022 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2022, The Author(s).
Funding
We thank Maria Kyropoulou, Thayer Morril, Hervé Moulin, Alexander Nesterov, Gabriel Ziegler and the anonymous reviewers and Associate Editor of this journal for their helpful comments. We are grateful to Sarah Fox, Jacopo Gambato and Fabian Spühler for proof-reading this paper. Josué is partially supported by the UK Economic and Social Research Council, grant R1379QMs. Erel is supported by the Israeli Science Foundation grant 712/20.
| Funders | Funder number |
|---|---|
| Economic and Social Research Council | |
| Israel Science Foundation | 712/20 |