TL;DR
This paper identifies errors in established theorems on cake-cutting fairness and Pareto-optimality, emphasizing the need for additional hypotheses for correctness.
Contribution
It critically revises existing theorems in cake-cutting literature, highlighting inaccuracies without supplementary assumptions.
Findings
Proposition 7.1 in Brams and Taylor's book is false without extra hypotheses.
Several Pareto-optimality theorems in Brams, Jones, and Klamler's 2006 paper are incorrect.
The paper underscores the importance of additional conditions for valid cake-cutting theorems.
Abstract
Without additional hypotheses, Proposition 7.1 in Brams and Taylor's book "Fair Division" (Cambridge University Press, 1996) is false, as are several related Pareto-optimality theorems of Brams, Jones and Klamler in their 2006 cake-cutting paper.
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Taxonomy
TopicsMerger and Competition Analysis · Game Theory and Voting Systems