About the relation between the Relative Fairness Bound (RFB) measure and the apportionment problem

2008 ◽  
Author(s):  
Joanna Jozefowska ◽  
Lukasz Jozefowski ◽  
Wieslaw Kubiak
Keyword(s):  
Apportionment Problem

scholarly journals Solving the generalized apportionment problem through the optimization of discrepancy functions

2001 ◽  
Vol 131 (3) ◽  
pp. 676-684 ◽  
Author(s):  
Joaquı́n Bautista ◽  
Ramon Companys ◽  
Albert Corominas
Keyword(s):  
Apportionment Problem

scholarly journals A New Quota Approach to Electoral Disproportionality

Economies ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 17 ◽  
Author(s):  
Miguel Martínez-Panero ◽  
Verónica Arredondo ◽  
Teresa Peña ◽  
Victoriano Ramírez
Keyword(s):  
Empirical Approach ◽  
Apportionment Problem

In this paper electoral disproportionality is split into two types: (1) Forced or unavoidable, due to the very nature of the apportionment problem; and (2) non-forced. While disproportionality indexes proposed in the literature do not distinguish between such components, we design an index, called “quota index”, just measuring avoidable disproportionality. Unlike the previous indexes, the new one can be zero in real situations. Furthermore, this index presents an interesting interpretation concerning transfers of seats. Properties of the quota index and relationships with some usual disproportionality indexes are analyzed. Finally, an empirical approach is undertaken for different countries and elections.

scholarly journals Last Words on the Apportionment Problem

1952 ◽  
Vol 17 (2) ◽  
pp. 290 ◽  
Author(s):  
Walter F. Willcox
Keyword(s):  
Apportionment Problem

The Apportionment Problem

Science ◽  
1982 ◽  
Vol 217 (4558) ◽  
pp. 437-438 ◽  
Author(s):  
S. J. BRAMS ◽  
P. D. STRAFFIN
Keyword(s):  
Apportionment Problem

scholarly journals A Comparative Study on Objective Functions of Product Rate Variation and Discrete Apportionment Problems

2015 ◽  
Vol 19 (1) ◽  
pp. 69-74
Author(s):  
Gyan Bahadur Thapa
Keyword(s):  
Decision Making ◽  
Mathematical Programming ◽  
Comparative Study ◽  
Mathematical Models ◽  
Efficient Frontier ◽  
Rate Variation ◽  
Objective Functions ◽  
Inequality Measures ◽  
Mathematical Programming Problems ◽  
Apportionment Problem

Setting the proper objective functions to optimize the decision making situations is prevalent in most of the mathematical programming problems. In this paper, we formulate the mathematical models of product rate variation and discrete apportionment problems. Furthermore, a brief comparative study of the objective functions to both the problems is reported in terms of inequality measures, precisely indicating the equitably efficient frontier for production rate variation problem via discrete apportionment. The largest reminder algorithm and rank-index algorithm for the apportionment problem are discussed briefly.Journal of Institute of Science and Technology, 2014, 19(1): 69-74

scholarly journals Approval-Based Apportionment

2020 ◽  
Vol 34 (02) ◽  
pp. 1854-1861
Author(s):  
Markus Brill ◽  
Paul Gölz ◽  
Dominik Peters ◽  
Ulrike Schmidt-Kraepelin ◽  
Kai Wilker
Keyword(s):  
Polynomial Time ◽  
General Setting ◽  
Fixed Number ◽  
Natural Restriction ◽  
Apportionment Problem

In the apportionment problem, a fixed number of seats must be distributed among parties in proportion to the number of voters supporting each party. We study a generalization of this setting, in which voters cast approval ballots over parties, such that each voter can support multiple parties. This approval-based apportionment setting generalizes traditional apportionment and is a natural restriction of approval-based multiwinner elections, where approval ballots range over individual candidates. Using techniques from both apportionment and multiwinner elections, we are able to provide representation guarantees that are currently out of reach in the general setting of multiwinner elections: First, we show that core-stable committees are guaranteed to exist and can be found in polynomial time. Second, we demonstrate that extended justified representation is compatible with committee monotonicity.

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