Quotatone Apportionment Methods

It has recently been pointed out that there exists more than one house monotone apportionment method satisfying quota. This paper gives a simple characterization of all such methods as an immediate consequence of the Quota method's existence. Further, a manner of exposition is formulated which unites several key house monotone apportionment methods, thus clearly showing their connections

Proportional Consistency of Apportionment Methods

We analyze a little-known property of apportionment methods that captures how allocations scale with the size of the house: specifically, if, for a fixed population distribution, the house size and allocation can be scaled down within the set of integers, then the apportionment should be correspondingly scaled down. Balinski and Young (2001) include this property among the minimal requirements for a "reasonable" apportionment method. We argue that this property is better understood as a consistency requirement since quota-based apportionments that are "less proportional" meet this requirement while others that are "more proportional" do not. We also show that the family of quotatone methods based on stationary divisors (including the quota method) do not satisfy this property

Cost Allocation in Water Resources Development - A Case Study of Sweden

Methods for allocating the joint costs of a water supply facility among the different users are systematically compared using basic principles from game theory and fair division. The analysis shows that some of the more widely used methods, including the separable costs-remaining-benefits methods, seem less satisfactory than a lesser-known game theory method based on the idea of the "core". The methods are applied to the cost sharing problem of a group of municipalities developing a joint municipal water supply

System and Decision Sciences at IIASA 1973-1980

This report contains a brief history of the past achievements of the System and Decision Sciences Area at IIASA, and a summary of its current and future research directions. There is a comprehensive list of the scientific staff of the Area since 1973, together with a list of their publications; abstracts of the most recent reports and biographies of the scholars working in the Area in 1980 are also included

The Webster Method of Apportionment

Several results concerning the problem of U.S. Congressional apportionment are given which together indicate that a method first proposed by Daniel Webster (also known as "Major Fractions") is fairest judged on the basis of common sense, Constitutional requirement, and precedent

Az Imperiali és Macau politikai választókörzet-kiosztási módszerek empirikus vizsgálata

Dolgozatomban bemutatom az Imperiali és Macau körzetkiosztási módszereket és megvizsgálom, hogy egy alapvető arányossági kritériumnak, az ún. Hare-kvóta tulajdonságnak mennyire felelnek meg. Emellett arra a kérdésre keresem a választ, hogy a két módszer valóban kedvez-e a vidéki megyéknek, azaz több körzetet osztanak-e ki kis megyéknek, mint amennyi a Hare-kvóta szerinti illetné őket. Ismertetem a körzetkiosztás alapvető tulajdonságait, illetve – mivel az Imperiali és a Macau módszer a jól ismert Jefferson/D’Hondt körzetkiosztási módszerek némileg módosított, átalakított változatai –, egy rövid történeti áttekintés keretében ez utóbbiakat is bemutatom. Az elemzés módszertanát részben a körzetkiosztási probléma matematikai eszköztára adja: az eljárásokat ház-monotonitás, népesség-monotonitás, illetve a kvóta tulajdonság alapján elemzem; emellett a módszertan másik részét a saját szerkesztésű, C++ nyelven írt számítógépes program képezi, amely adott népességi adatok és parlament-méretek esetén meghatározza az Imperiali és Macau módszerek szerinti körzetkiosztásokat

The Theory of Apportionment

A key problem area at IIASA is the study of how goods and resources -- as well as "bads" such as costs, pollution, and risks -- can or should be shared among different nations, groups, or individuals. This raises the question of what is meant by a fair division -- and, if this question can be answered at all, how fair divisions can be achieved. One of the situations studied in the System and Decision Sciences Area was how to allocate or "apportion" discrete entities in proportion to predetermined claims, a problem which encompasses many situations including for example the apportionment of political representation among different regions and constituencies. The result of this study was the development of a general theory to deal with such problems, together with concrete criteria of fairness which will hopefully prove useful to analyzing larger classes of problems

Stability, Coalitions, and Schisms in Proportional Representation Systems

Methods to allocate seats in proportional representation systems are investigated in terms of underlying common-sense properties. Important among these are concepts of stability, coalition encouragement, and schism encouragement. In addition, a new concept of uniformity is introduced which seems inherent in the very idea of the word "method", and it is shown that this concept is essentially equivalent to a previously investigated property called consistency. These and other criteria are shown to uniquely determine certain methods. In particular, the Jefferson method (incorrectly credited to d'Hondt) and the Quota method are given characterizations which commend them as the principal candidates for use in proportional representation systems

IIASA Reports, Water Resources and Climate, 2(1):281-564 (July-September 1980)

This issue of IIASA REPORTS is devoted to water-resource management and global climatic change. The three papers that appear represent an important -- but nontheless limited -- segment of the range of IIASA's research activities in these areas. The papers appearing are: -- H.P. Young, N. Okada, and T. Hashimoto, "Cost Allocation in Water Resources Development - A Case Study of Sweden; -- I.V. Gouevsky, D.R. Maidment, and W. Sikorski, "Agricultural Water Demands in the Silistra Region;" and -- H. Flohn, "Possible Climatic Consequences of a Man-made Global Warming." The issue also includes a report on a Task Force Meeting on Decision Support Systems

Quotatone Apportionment Methods

The problem of apportionment is that of allocating an integer number of seats “proportionally” among a set of states or regions as a fraction of their populations. An apportionment method satisfies quota if it accords to each state the exactly proportional (rational) number of seats due it rounded up or rounded down. A method is house monotone if no state’s allocation goes down when the total number of seats to be distributed goes up. This paper gives a simple characterization of all house monotone methods satisfying quota. Further, a manner of exposition is formulated which unites several key house monotone apportionment methods, thus showing clearly their connections