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Friedrich Pukelsheim - One of the best experts on this subject based on the ideXlab platform.
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Quota Methods of Apportionment: Divide and Rank
2014Co-Authors: Friedrich PukelsheimAbstract:Quota methods constitute another important family of Apportionment methods. They rely on a fixed divisor of some intrinsic persuasiveness, called quota, and follow the motto “Divide and rank”. The most prominent member of the family, the Hare-quota method with residual fit by greatest remainders, is discussed in the first part of the chapter. The second part addresses various variants of the quota, and various variants of the residual Apportionment step. As a whole, the family of quota methods offers a more eclectic approach to Apportionment problems than the family of divisor methods.
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proportional representation Apportionment methods and their applications
2013Co-Authors: Friedrich Pukelsheim, Andrew DuffAbstract:Exposing Methods: The 2009 European Parliament Elections.- Imposing Constitutionality: The 2009 Bundestag Election.- From Reals to Integers: Rounding Functions, Rounding Rules.- Divisor Methods of Apportionment: Divide and Round.- Quota Methods of Apportionment: Divide and Rank.- Targeting the House Size: Discrepancy Distribution.- Favoring Some at the Expense of Others: Seat Biases.- Preferring Stronger Parties to Weaker Parties: Majorization.- Securing System Consistency: Coherence and Paradoxes.- Appraising Electoral Equality: Goodness-of-Fit Criteria.- Tracing Peculiarities: Vote Thresholds and Majority Clauses.- Truncating Seat Ranges: Minimum-Maximum Restrictions.- Proportionality and Personalization: BWG 2013.- Representing Districts and Parties: Double Proportionality.
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Divisor Methods of Apportionment: Divide and Round
Proportional Representation, 2013Co-Authors: Friedrich PukelsheimAbstract:Apportionment methods are procedures for allocating a total number of seats proportionally to vote counts, census figures, or similar quantities. Apportionment methods must be anonymous, balanced, concordant, decent, and exact. Beyond these organizing principles the central issue is proportionality. This chapter focuses on the family of divisor methods; they follow the motto “Divide and round”. The properties of general divisor methods are elaborated in detail. Five divisor methods are of particular traditional interest: the divisor methods with downward rounding, with standard rounding, with geometric rounding, with harmonic rounding, and with upward rounding.
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The allocation between the EU member states of the seats in the European Parliament Cambridge Compromise
2011Co-Authors: Geoffrey Grimmett, Friedrich Pukelsheim, Jean-françois Laslier, Victoriano Ramirez Gonzalez, Richard Rose, Wojciech Slomczynski, Martin Zachariasen, Karol ŻyczkowskiAbstract:This Note contains the recommendation for a mathematical basis for the Apportionment of the seats in the European Parliament between the Member States of the European Union. This is the unanimous recommendation of the Participants in the Cambridge Apportionment Meeting, held at the instigation of the Committee on Constitutional Affairs at the Centre for Mathematical Sciences, University of Cambridge, on 28-29 January 2011.
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A majorization comparison of Apportionment methods in proportional representation
Social Choice and Welfare, 2002Co-Authors: Albert W. Marshall, Ingram Olkin, Friedrich PukelsheimAbstract:From the inception of the proportional representation movement it has been an issue whether larger parties are favored at the expense of smaller parties in one Apportionment of seats as compared to another Apportionment. A number of methods have been proposed and are used in countries with a proportional representation system. These Apportionment methods exhibit a regularity of order, as discussed in the present paper, that captures the preferential treatment of larger versus smaller parties. This order, namely majorization, permits the comparison of seat allocations in two Apportionments. For divisor methods, we show that one method is majorized by another method if and only if their signpost ratios are increasing. This criterion is satisfied for the divisor methods with power-mean rounding, and for the divisor methods with stationary rounding. Majorization places the five traditional Apportionment methods in the order as they are known to favor larger parties over smaller parties: Adams, Dean, Hill, Webster, and Jefferson.
Charles E. Mclure - One of the best experts on this subject based on the ideXlab platform.
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Does Sales-Only Apportionment Violate International Trade Rules?
2002Co-Authors: Charles E. Mclure, Walter HellersteinAbstract:There has been a pronounced change in the formulas states use to apportion the income of multistate corporations from one that placed equal weight on payroll, profits, and sales to one that places at least half the weight on sales, and eight states base Apportionment solely on sales. This report, which is intended to stimulate further analysis and debate, rather than provide a definitive conclusion, suggests that sales-only Apportionment may violate international trade rules that prohibit export sales.
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Implementing State Corporate Income Taxes in the Digital Age
National Tax Journal, 2000Co-Authors: Charles E. MclureAbstract:This paper reviews issues in application of the state corporate income tax to income from electronic commerce. After examining potential arguments for the tax (benefit principle, ability -to-pay, and entitlement), problems inherent in the tax (complexity and distortions of locational decisions), and the basic structure of the tax (the choice between separate reporting and formula Apportionment, the role of unitary combination, and the choice of Apportionment factors), it discusses two key issues in implementation of corporate income taxes: nexus (jurisdiction to tax) and determination of the income to be taxed by a particular state that invokes nexus.
Marius Zimand - One of the best experts on this subject based on the ideXlab platform.
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Power balance and Apportionment algorithms for the United States Congress
ACM Journal of Experimental Algorithmics, 1998Co-Authors: Lane A. Hemaspaandra, Kulathur S. Rajasethupathy, Prasanna Sethupathy, Marius ZimandAbstract:We measure the performance, in the task of apportioning the Congress of the United States, of an algorithm combining a heuristic-driven (simulated annealing) search with an exact-computation dynamic programming evaluation of the Apportionments visited in the search. We compare this with the actual algorithm currently used in the United States to apportion Congress, and with a number of other algorithms that have been proposed. We conclude that on every set of census data in this country's history, the heuristic-driven Apportionment provably yields far fairer Apportionments than those of any of the other algorithm considered, including the algorithm currently used by the United States for Congressional Apportionment.
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Power Balance and Congressional Apportionment Algorithms
1996Co-Authors: Lane A. Hemaspaandra, Kulathur S. Rajasethupathy, Prasanna Sethupathy, Marius ZimandAbstract:We measure the performance, in the task of apportioning the Congress of the United States, of an algorithm combining a simulated-annealing-driven search with an exact-computation dynamic programming evaluation of the Apportionments visited in the search. We compare this with the actual algorithm currently used in the United States to apportion Congress, and with a number of other algorithms that have been proposed. We conclude that on every set of census data in this countryUs history, the simulated-annealing Apportionment provably yields far fairer Apportionments than those of any other algorithm considered, including the algorithm currently used for Congressional Apportionment.
Balázs Sziklai - One of the best experts on this subject based on the ideXlab platform.
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Apportionment and districting by Sum of Ranking Differences.
PloS one, 2020Co-Authors: Balázs Sziklai, Karoly HebergerAbstract:Sum of Ranking Differences is an innovative statistical method that ranks competing solutions based on a reference point. The latter might arise naturally, or can be aggregated from the data. We provide two case studies to feature both possibilities. Apportionment and districting are two critical issues that emerge in relation to democratic elections. Theoreticians invented clever heuristics to measure malApportionment and the compactness of the shape of the constituencies, yet, there is no unique best method in either cases. Using data from Norway and the US we rank the standard methods both for the Apportionment and for the districting problem. In case of Apportionment, we find that all the classical methods perform reasonably well, with subtle but significant differences. By a small margin the Leximin method emerges as a winner, but -- somewhat unexpectedly -- the nonregular Imperiali method ties for first place. In districting, the Lee-Sallee index and a novel parametric method the so-called Mo ent Invariant performs the best, although the latter is sensitive to the function's chosen parameter.
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Fair Apportionment in the view of the Venice Commission’s recommendation
Mathematical Social Sciences, 2015Co-Authors: Péter Biró, László Á. Kóczy, Balázs SziklaiAbstract:Abstract The Venice Commission in its Code of Good Practice in Electoral Matters specifies that (single-seat) constituencies should be drawn so that the size difference of a constituency’s size from the average should not exceed a fixed limit while its borders must not cross the borders of administrative regions, such as states or counties. Assuming that constituencies are of equal size within each of the administrative regions, the problem is equivalent to the Apportionment problem, that is, the proportional allocation of voting districts among the administrative regions. We show that the principle of maximum admissible departure is incompatible with common Apportionment properties, such as monotonicity and Hare-quota. When multiple Apportionments satisfy the smallest maximum admissible departure property we find a unique Apportionment by the repeated application of the property. The allotment such that the differences from the average district size are lexicographically minimized can be found using an efficient algorithm. This Apportionment rule is a well-defined allocation mechanism compatible with and derived from the recommendation of the Venice Commission. Finally, we compare this Apportionment rule with mainstream mechanisms using data from Hungary, Germany and the United States
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Fair Apportionment in the View of the Venice Commission's Recommendation
SSRN Electronic Journal, 2013Co-Authors: Péter Biró, László Á. Kóczy, Balázs SziklaiAbstract:In this paper we analyze the consequences of the fairness recommendation of the Venice Commission in allocating voting districts among larger administrative regions. This recommendation requires the size of any constituency not to differ from the average constituency size by more than a fixed limit. We show that this minimum difference constraint, while attractive per definition, is not compatible with monotonicity and Hare-quota properties, two standard requirements of Apportionment rules. We present an algorithm that efficiently finds an allotment such that the differences from the average district size are lexicographically minimized. This Apportionment rule is a well-defined allocation mechanism compatible with and derived from the recommendation of the Venice Commission. Finally, we compare this Apportionment rule with mainstream mechanisms using real data from Hungary and the United States.
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Fair Apportionment of voting districts in Hungary
2012Co-Authors: László Á. Kóczy, Péter Biró, Balázs SziklaiAbstract:One of the aims of the new electoral law of Hungary has been to define a fairer Apportionment into voting districts. This is ensured by a set of rules slightly more premissive than those laid out in the Code of Good Practice in Electoral Matters of the Venice Commission. These rules fix the average size of the voting districts, require voting districts not to split smaller towns and villages and not to cross county borders. We show that such an Apportionment is mathematically impossible. We make suggestions both to the theoretical approach to resolve this problem, study the properties of our approach and using our efficient algorithm and the data of the 2010 national elections we determine the optimal Apportionment. We also study the expected effect of demographic changes and formulate recommendations to adhere to the rules over the long term: increase the number of voting districts to about 130, allow the number of voting districts to change flexibly at each revision of the districts and base the districts on regions rather than counties.
Edward L Maydew - One of the best experts on this subject based on the ideXlab platform.
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coveting thy neighbor s manufacturing the dilemma of state income Apportionment
Journal of Public Economics, 2000Co-Authors: Austan Goolsbee, Edward L MaydewAbstract:Abstract This paper investigates the economic impact of the Apportionment formulae used to divide corporate income taxes among the states. Most Apportionment formulae, by including payroll, turn the state corporate income tax at least partially into a payroll tax. Using panel data from 1978–1994, the results show that this distortion has an important effect on state-level employment. For the average state, reducing the payroll weight from one-third to one-quarter increases manufacturing employment around 1.1%, concentrated in durable goods manufacturing and with larger effects in the long-run. The results also suggest that Apportionment changes have important negative externalities on other states. On average, the aggregate effects of Apportionment formula changes are close to zero.