Random Apportionment: A Stochastic Solution to the Balinski-Young Impossibility

An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate common sense. For example, The Alabama paradox occurs when the total number of seats increases but decreases the allocated number of a state and the pop...

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Bibliographic Details
Published in:Methodology and computing in applied probability 2023-12, Vol.25 (4), p.91, Article 91
Main Authors: Hong, Jyy-I, Najnudel, Joseph, Rao, Siang-Mao, Yen, Ju-Yi
Format: Article
Language:English
Subjects:
Apportionment
Business and Management
Decision making
Economics
Election results
Electrical Engineering
Expected values
Life Sciences
Mathematics and Statistics
Methods
Paradoxes
Political power
Presidential elections
Quotas
Seats
Statistics
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Summary:An apportionment paradox occurs when the rules for apportionment in a political system or distribution system produce results which seem to violate common sense. For example, The Alabama paradox occurs when the total number of seats increases but decreases the allocated number of a state and the population paradox occurs when the population of a state increases but its allocated number of seats decreases. The Balinski-Young impossibility theorem showed that there is no deterministic apportionment method that can avoid the violation of the quota rule and doesn’t have both the Alabama and the population paradoxes. In this paper, we propose a randomized apportionment method as a stochastic solution to the Balinski-Young impossibility.
ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-023-10070-x