A comparison between the methods of apportionment using power indices: the case of the U.S. presidential elections

In this paper, we compare five well-known methods of apportionment, the ones by Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index and the populations are the ones of the different States of the U.S. We first explain under which conditions this comparison makes sense. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.Banzhaf index, methods of apportionment, distances, balance population-power.

A note on apportionment methods

This paper investigates the suitability of apportionment methods based on the idea of preserving the coalition function of the simple game represented by the populations of the states. The results show that an apportionment method which satisfies desirable properties such as population monotonicity, house monotonicity, etc., does not exist. A classification of simple voting games via winning coalitions is also given.apportionment methods, simple games, winning coalitions

A comparison between the methods of apportionment using power indices: the case of the U.S. presidential election

In this paper, we compare the five more famous methods of apportionment, the methods of Adams, Dean, Hill, Webster and Jefferson. The criteria used for this comparison is the minimization of a distance between a power vector and a population vector. The power is measured with the well-known Banzhaf power index. The populations are the ones of the different States of the U.S. We then compare the apportionment methods in terms of their ability to bring closer the power of the States to their relative population: this ensures that every citizen in the country gets the same power. The U.S. presidential election by Electors is studied through 22 censuses since 1790. Our analysis is largely based on the book written by Balinski and Young (2001). The empirical findings are linked with theoretical results.Banzhaf index, methods of apportionment, distances, balance population-power.

U.S Presidential Elections and the Referendum Paradox*

In the United States, the president is elected by the Electoral Col- lege (EC) and not directly by individual voters. This can give rise to a so-called referendum paradox in which one candidate receives more popular votes than any other, but this candidate is not elected. The 2000 election is an example of this phenomenon. Can the EC be reformed so that a referendum paradox never arises? We consider vary- ing three natural parameters. First, we consider changing the method of apportioning seats in the House of Representatives to states. Sec- ond, we consider changing the total number of seats in the House. Intuition suggests that as the number of seats approaches the number

The Impact of ICT on Profit Allocation within Multinational Groups: Arm's Length Pricing or Formula Apportionment?

The use of information and communication technologies (ICT) within multinational groups leads to a rising number of intragroup cross-border transactions. At the same time, transactions and the organisational structures of affiliated groups become more and more specific and, thus, less comparable. The importance of human capital and of mobile factors of production, such as intangible assets, increases. The objective of this paper is to give an insight into the principal issues of profit allocation within multinational groups resulting from these economic changes. It is examined whether the traditional transaction methods based on the arm?s length principle can be upheld and to what extent the alternative method of formula apportionment is more suitable. The tax principles of inter-nation equity and feasibility are used to evaluate the different methods of profit allocation. We conclude that, in the light of the two demanded principles, formula apportionment is more appropriate than the arm?s length principle as regards the changed economic structures by use of ICT. As formula apportionment constitutes a suitable alternative especially in the European Union, the proposals made by the European Commission are considered to be a good starting point. --International Company Taxation,Profit Allocation,Transfer Pricing,Arm?s Length Principle,Formula Apportionment,Inter-Nation Equity