Coherence (fairness)

Coherence,^[1] also called uniformity^[2]^: Thm.8.3 or consistency, is a criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but also for each sub-problem. Every part of a fair division should be fair.^[2]

The coherence requirement was first studied in the context of apportionment. In this context, failure to satisfy coherence is called the new states paradox: when a new state enters the union, and the house size is enlarged to accommodate the number of seats allocated to this new state, some other unrelated states are affected. Coherence is also relevant to other fair division problems, such as bankruptcy problems.

^ Balinski, Michel (2005-06-01). "What Is Just?". The American Mathematical Monthly. 112 (6): 502–511. doi:10.1080/00029890.2005.11920221. ISSN 0002-9890. S2CID 32125041.
^ ^a ^b Balinski, Michel L.; Young, H. Peyton (2001) [1982]. Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.

[:2-1] Balinski, Michel (2005-06-01). "What Is Just?". The American Mathematical Monthly. 112 (6): 502–511. doi:10.1080/00029890.2005.11920221. ISSN 0002-9890. S2CID 32125041.

[:0-2] Balinski, Michel L.; Young, H. Peyton (2001) [1982]. Fair Representation: Meeting the Ideal of One Man, One Vote. New Haven: Yale University Press. ISBN 0-300-02724-9.

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