The biproportional apportionment problem (BAP) must be faced in many proportional electoral systems where seats must be allocated to parties within regions. BAP is a non-trivial optimization problem, and only sophisticated algorithms are currently available for solving it. The issue is: are they “writable” as an actual law? Citizens rightly demand simple, easy to understand, voting systems. The alternative, though, seems to have simple, but unsound electoral laws. We propose the following way out of this dilemma: leave to a mathematically sophisticated algorithm the task of producing an optimal apportionment, but attach to it a “certificate of optimality”, that is, describe a simple procedure whereby anybody can check, through some elementary operations, that the seat allocation output by the algorithm is indeed an optimal apportionment. We discuss one such certificate, based on the Max flow- min cut Theorem, relative to a parametric max flow method of ours for BAP.
Certificates of optimality: the third way to biproportional apportionment
true
2012-02-01
research_article
247-268
en
https://scigraph.springernature.com/explorer/license/
articles
2012-02
2019-04-10T20:39
http://link.springer.com/10.1007/s00355-010-0528-8
University of Udine
Department of Mathematics and Computer Science, University of Udine, Udine, Italy
pub.1008592628
dimensions_id
Numerical and Computational Mathematics
doi
10.1007/s00355-010-0528-8
Serafini
Paolo
Simeone
Bruno
38
0176-1714
1432-217X
Social Choice and Welfare
readcube_id
28f000fc95018e139e7e2ad40cfd131549a95e9484819e6a8754ac59e737248b
2
Mathematical Sciences
Department of Statistics, University La Sapienza, Rome, Italy
Sapienza University of Rome
Springer Nature - SN SciGraph project