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Fair cake-cutting algorithms with real land-value data

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Abstract

Fair division of land is an important practical problem that is commonly handled either by hiring assessors or by selling and dividing the proceeds. A third way to divide land fairly is via algorithms for fair cake-cutting. Such un-intermediated methods are not only cheaper than an assessor but also theoretically fairer since they guarantee each agent a fair share according to his/her value function. However, the current theory of fair cake-cutting is not yet ready to optimally share a plot of land, and such algorithms are seldom used in practical land division. We attempt to narrow the gap between theory and practice by presenting several heuristic adaptations of famous algorithms for one-dimensional cake-cutting to two-dimensional land-division. The heuristics are evaluated using extensive simulations on real land-value data maps from three different data sets and a fourth (control) map of random values. The simulations compare the performance of cake-cutting algorithms to sale and assessor division in various performance metrics, such as utilitarian welfare, egalitarian welfare, Nash social welfare, envy, and geometric shape. The cake-cutting algorithms perform better in most metrics. However, their performance is greatly influenced by technical implementation details and heuristics that are often overlooked by theorists. We also propose a new protocol for practical cake-cutting using a dynamic programming approach and discuss its run-time complexity versus performance trade-off. Our new protocol performs better than the examined classic cake-cutting algorithms on most metrics. Experiments to assess the amount that a strategic agent can gain from reporting false preferences are also presented. The results show that the problem of strategic manipulation is much less severe than the worst-case predicted by theory.

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Notes

  1. The face-ratio is not incorporated into the agents’ value functions, since this would make the value functions non-additive, while most cake-cutting algorithms require additive valuations.

  2. In Sect. 7 we discuss more algorithms we plan to experiment with in future work.

  3. Note that even this exhaustive search does not yield the maximum possible utilitarian value overall due to the parallel cuts assumption.

  4. It has been proven that even for 1-dimensional cake, neither Even-Paz nor Last-Diminisher yield the maximum utilitarian value; finding an allocation that maximizes the utilitarian value is NP-hard. The same is true for egalitarian value [3]. However, since the focus of the present work is the adaptation of one-dimensional algorithms to a two-dimensional cake, we consider the maximum utilitarian value attained by one of the \(2^{n-1}\) possible cut-direction sequences as “optimal”.

  5. Since LE computation depends on the relations between all pairs of agents, no such function exists for this metric.

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Acknowledgements

We are grateful to the team of Madlan (https://www.madlan.co.il) for the permission to use land-value data from their website for research purposes. We are grateful to the referees for their helpful comments. Erel is supported by the Israel Science Foundation (Grant 712/20).

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Authors and Affiliations

  1. The Open University of Israel, Ra’anana, Israel

    Itay Shtechman & Rica Gonen

  2. Ariel University, 40700, Ariel, Israel

    Erel Segal-HaLevi

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  1. Itay Shtechman
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Correspondence to Itay Shtechman.

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Shtechman, I., Gonen, R. & Segal-HaLevi, E. Fair cake-cutting algorithms with real land-value data. Auton Agent Multi-Agent Syst 35, 39 (2021). https://doi.org/10.1007/s10458-021-09524-8

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