Customer Reviews

Fair Representation: Meeting the Ideal of One Man, One Vote

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This book covers in detail the problem of aproportionnement from an historical and a mathematical point of view. The maths are simple and the historical reasearch is complete.

However, it might be to concentrated on the US congress apointement problem. Some international perspective would have been appreciated.

Anyway, it is still the best reference on this topic.

The title of this book is a little misleading. The book is not about proportional representation as generally understood. This book is really about how to decide the number of representatives each state of the USA should have in its House of Representatives. Ideally each state should have the same number of representatives per million people, but this is impossible to achieve exactly. Suppose you set a quota of one representative per 30,000 voters and find that a particular state should then get 1.6 representatives, should the state get 1 or 2? The politicians's answer, it seems, depends on whether or not he or she lives in the state and whether or not his or her political leanings are those of the state. This has led to all kinds of wrangling by the politicians over the years over what seem a relatively minor issue. So what recipe should one use to determine the number? This book describes in detail the recipes that have been advanced and those used over the years.

There are paradoxes. For example, depending on the recipe used, if an extra state is added and extra representatives are added for it, another state may find it has one fewer representative and another state one more. Or, depending on the recipe used, a state could encourage emigration and thereby increase its number of representatives!

It all comes down to what criterion one uses to minimize the inequality. What is fair? In the early 1920s Edward Huntingdon, professor of mechanics and mathematics at Harvard University, showed that depending on how this inequality is measured, exactly five methods result, and no others.

The paradoxes can be avoided by using one of the divisor methods; two more criteria lead to the deduction that the fairest system is that of Webster, known elsewhere as Sainte-Laguë.

But, there is a problem. None of the divisor techniques guarantee that no state's representatives will differ by more than 1 from that calculated using the quota. Fortunately, with Webster's recipe the likelihood of such a difference is so improbable that this can be ignored.

Afficionados of proportional representation will find this book interesting and useful. It is generally clearly written. It is, however, severely limited in scope, as it is limited to the history of distributing representatives to states in the United States.

The term fair representation usually means that the number of representatives elected from a political party is proportional to the number of votes for that party. This is a different problem altogether, although there are some common features, and it is discussed in a final short chapter. This topic is best addressed in the books by David Farrell.

The best system of fair representation, the single transferable vote, is not even mentioned.