The People’s Charter of 1848 contained six demands, then considered dangerously radical by both Whig and Tory governments. One of the six was:

EQUAL CONSTITUENCIES, securing the same amount of representation for the same number of electors, instead of allowing small constituencies to swamp the votes of larger ones.

The Chartists might have been surprised to find that it was a Conservative-dominated government which first tried to enact equal representation, in the Parliamentary Voting System and Constituencies Bill 2010 (PVSCB in civil servantese). As I write, the controversial bill has passed the Commons, and is being considered by Their (unelected) Lordships, who have no scruples about amending bills on how to elect another house.  Oh well, that’s politics.

Some political science questions stand out:

• Why have equal districts taken so long?
• What is so difficult about it?
• Although equal districts (One Vote, One Value) are obviously necessary to secure democracy, are they sufficient?

Why so long?

Any electoral reform has to be approved by sitting politicians: the incumbents. But some incumbents will lose their seats under any electoral reform. One of them called himself a “dying swan” in the 1867 Reform Bill debates.  The dying swans prevented electoral equality from even being attempted in any reform bill before 1884. It was only a secondary criterion of the 1884-5 redistribution, and it was undermined because neither that redistribution of seats nor the next in 1918 contained any review mechanism. Population movement ensured that constituencies were extremely unequal when the current system, which does allow for reviews, was created between 1944 and 1947. Even then, electoral equality was subordinated to preserving “local ties” and avoiding “inconveniences”. In plain language, incumbent protection trumped citizen equality.

Why then are the Conservatives now pressing for equality? Perhaps because they are democrats; also, however, because they see a partisan advantage in it. They know that they tend to win in large, and in growing, seats. Labour (and also the Celtic nationalists) tend to win in small, and in declining, seats. The expenses upheaval of 2009 means that many dying swans are already dead, so that the Coalition need worry less about unhappy incumbents than previous governments.

Why so difficult?

But there are other difficulties. Whenever you divide a human cake you have to deal with crumbs. Cake crumbs, like money, can be divided into fractions of any size. Human beings can only be divided into whole (‘integer’) numbers.  If you specify that subnational units – like States in the USA, or the four nations (and, formerly, the counties) of the UK – must each have an integer number of representatives, you face a non-trivial rounding-off problem, called the “apportionment” problem. It is full of twists and turns. For instance the Alabama Paradox. The most intuitive rounding-off rule is to give each unit the integer part of its exact entitlement and allocate the fractions in declining order until you run out of seats to allocate. That rule was used in the USA in 1880. Under it, Alabama would have eight seats in a House of Representative of total size 299, but only seven seats if the house were enlarged to 300.

Luckily, it has been proved that there is a unique best solution. It is called the “Webster rule” in the USA, and the “Sainte-Laguë” rule in Europe.  Until 2010, the UK rules for redistricting not only failed to use the right rule, but they were actually contradictory. A small number of political scientists have been pressing successive UK governments on this. They have succeeded in getting the Sainte-Laguë rule adopted (since 2004) for allocating seats to European Parliament constituencies. The present bill uses it for the first time to allocate Westminster seats to the four countries of the UK. With three co-authors (two of them, including H Peyton Young of the Oxford University Department of Economics, being the solvers of the apportionment problem) I recently wrote a British Academy pamphlet to help guide policy discussion on the bill. Sometimes – not very often – there is a right answer to a question in social science. It is good that lawmakers seem to be listening.

Necessary – and sufficient?

The United States has now got meticulously equal Congressional districts within each State. Has it eliminated gerrymandering? Absolutely not, because in most states it is up to the state legislature to draw district boundaries. The ancient arts of packing and cracking, which Governor Elbridge Gerry understood very well back in 1812, are still alive there. The party that controls the state legislature tries to put the opposite party’s voters into safe seats, and maximize the number of seats that go to its own party. For citizen equality you need both equal districts (as in the current bill) and a non-partisan redistricting procedure (as in the UK’s four Boundary Commissions). Maybe Parliament will get it right this time.

Iain McLean is Professor of Politics at the University of Oxford and author of The Fiscal Crisis of the United Kingdom and What’s Wrong with the British Constitution? He has recently co-authored the Political Studies Association Briefing Paper The Alternative Vote.

Please listen to a podcast representing highlights from the conference entitled ‘Current issues in apportionment and redistricting: international perspectives’, convened by Professor Iain McLean (Department of Politics and International Relations), Dr David Goldey (DPIR), Dr Luc Borot (Maison Française d’Oxford) and Dr Alan Renwick (Reading) on 12-14 May 2011.  Please note that the podcasts are not released under a creative commons licence.

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