Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fair Allocation based on Diminishing Differences   Ranking alternatives is a natural way for humans to explain their
preferences. It is being used in many settings, such as school choice, course
allocations and residency matches. In some cases, several `items' are given to
each participant. Without having any information on the underlying cardinal
utilities, arguing about fairness of allocation requires extending the ordinal
item ranking to ordinal bundle ranking. The most commonly used such extension
is stochastic dominance (SD), where a bundle X is preferred over a bundle Y if
its score is better according to all additive score functions. SD is a very
conservative extension, by which few allocations are necessarily fair while
many allocations are possibly fair. We propose to make a natural assumption on
the underlying cardinal utilities of the players, namely that the difference
between two items at the top is larger than the difference between two items at
the bottom. This assumption implies a preference extension which we call
diminishing differences (DD), where X is preferred over Y if its score is
better according to all additive score functions satisfying the DD assumption.
We give a full characterization of allocations that are
necessarily-proportional or possibly-proportional according to this assumption.
Based on this characterization, we present a polynomial-time algorithm for
finding a necessarily-DD-proportional allocation if it exists. Using
simulations, we show that with high probability, a necessarily-proportional
allocation does not exist but a necessarily-DD-proportional allocation exists,
and moreover, that allocation is proportional according to the underlying
cardinal utilities. We also consider chore allocation under the analogous
condition --- increasing-differences.

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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: comp-gas