Error minimization methods in biproportional apportionment

Ricca, Federica; Scozzari, Andrea; Serafini, Paolo; Simeone, Bruno

doi:10.1007/s11750-012-0252-x

Cited by 6 publications

(6 citation statements)

References 14 publications

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“…If the number of atomic voters is small then the corresponding inverse problem is exactly of the type investigated here. electoral systems, as discussed in Grilli di Cortona, Manzi, Pennisi, Ricca, and Simeone (1999), Pennisi, Ricca, Serafini, and Simeone (2007) or Ricca, Scozzari, Serafini, and Simeone (2012).…”

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confidence: 99%

Heuristic and exact solutions to the inverse power index problem for small voting bodies

Kurz

Napel

2013

Ann Oper Res

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Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse images, i.e., to determine a voting system which induces a power distribution as close as possible to a desired one. The paper considers approximations to this inverse problem for the Penrose-Banzhaf index by hill-climbing algorithms and exact solutions which are obtained by enumeration and integer linear programming techniques. They are compared to the results of three simple solution heuristics. The heuristics perform well in absolute terms but can be improved upon very considerably in relative terms. The findings complement known asymptotic results for large voting bodies and may improve termination criteria for local search algorithms.

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confidence: 99%

Heuristic and exact solutions to the inverse power index problem for small voting bodies

Kurz

Napel

2013

Ann Oper Res

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“…Our approach is obviously limited and the problem is open to several alternative approaches that deserve extra work. A particular one that deserves mention is the error minimization approach that has yielded a class of methods to solve biproportional apportionment problems (Ricca et al (2012) and Serafini and Simeone (2012)). These methods take a fractional matrix as the target (fair share table in our case) and solve a constrained optimization problem where the objective corresponds to a measure of the error between the solution and the target matrix.…”

Section: Discussionmentioning

confidence: 99%

Affirmative Action in Two Dimensions: A Multi-Period Apportionment Problem

Evren¹,

Khanna²

2021

Preprint

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In many settings affirmative action policies apply at two levels simultaneously, for instance, at university as well as at its departments. We show that commonly used methods in reserving positions for beneficiaries of affirmative action are often inadequate in such settings. We present a comprehensive evaluation of existing procedures to formally document their shortcomings. We propose a new solution with appealing theoretical properties and quantify the benefits of adopting it using recruitment advertisement data from India.

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“…One approach is based on characterizing proportionality via a set of axioms and finding the unique apportionment that satisfies them [1,2,14,8,5,6]. Another approach is based on finding an apportionment that minimizes a measure of deviation from given quotas [4,[15][16][17].…”

Section: Problem Statementmentioning

confidence: 99%

“…In the Controlled rounding procedure [4,16] the apportionment x ij must satisfy x ij ∈ { q ij , q ij }. Hence the problem may be rephrased by saying that one has to compute a binary matrix y ij ∈ {0, 1} that must satisfy the constraints…”

Section: A Certificate For the Controlled Rounding Apportionmentmentioning

confidence: 99%

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Certificates of optimality for minimum norm biproportional apportionments

Serafini

2014

Soc Choice Welf

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Abstract. Computing a biproportional apportionment that satisfies some given properties may require a high degree of mathematical expertise, that very few voters can share. It seems therefore that the voters have to accept the electoral outcome without any possibility of checking the validity of the stated properties. However, it is possible in some cases to attach to the computed apportionment a certificate which can guarantee the voters of the validity of the apportionment. This type of investigation has been first proposed in [18]. In this paper we pursue the same line of approach and show that a certificate can be produced and easily checked by a layman for apportionments that minimize either an L1-or an L2-norm deviation from given quotas.

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Error minimization methods in biproportional apportionment

Cited by 6 publications

References 14 publications

Heuristic and exact solutions to the inverse power index problem for small voting bodies

Heuristic and exact solutions to the inverse power index problem for small voting bodies

Affirmative Action in Two Dimensions: A Multi-Period Apportionment Problem

Certificates of optimality for minimum norm biproportional apportionments

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