We establish a link between multiwinner elections and apportionment problems by showing how approval-based multiwinner election rules can be interpreted as methods of apportionment. We consider several multiwinner rules and observe that they induce apportionment methods that are well-established in the literature on proportional representation. For instance, we show that Proportional Approval V...

Apportionment is the problem of translating an election outcome to a number of seats in fixed-size political house. Mathematically, the problem consists of translating a sequence of reals to a sequence of integers, while ensuring that the sum of the sequence sums to a pre-determined number. The problem arises because seats are indivisible, whereas an election outcome generally gives rise to fra...

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I propose apportioning the United States House of Representatives so as to equalize, to the extent possible, the voting power of the individual voter. Surprisingly such an apportionment falls squarely within the traditional apportionment paradigm and is, in a very precise sense, midway between the Hill method and the Webster method of apportionment.

Using a general multi-country equilibrium model with a multinational enterprise, this paper investigates the efficiency properties of separate accounting and formula apportionment. If governments are large, i.e. take into account the effect of their statutory tax rate on the interest rate, and maximize tax revenues, tax rates under separate accounting may be inefficiently high while tax rates u...

Heating, Ventilation, and Air Conditioning (HVAC) systems account for a significant portion of power consumption in commercial buildings all over the world [1, 4, 5, 6]. Since HVAC systems are designed for centralized cooling supplies, power consumption in each room is inestimable. Therefore, administrators are motivated to apportion the electricity payment for actual users. The even apportionm...

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 discus...

Developing effective strategies for reducing the atmospheric pollutant concentrations below regulatory threshold levels requires identifying the main origins/sources of air pollution. This can be achieved by implementing so called source apportionment methods in atmospheric dispersion models. This study presents the results of a source apportionment module implemented in the SIRANE urban air-qu...

A classifier system is used to learn control and profit optimization of a batch chemical reaction. Ability to learn different market conditions and changes to reaction parameters is demonstrated. The profit sharing algorithm is used for apportionment of credit. The greater effectiveness of the use of the genetic algorithm over apportionment of credit alone or the random replacement of low stren...