Vital, yet unrepresentative. That’s democracy for you

1st May, 2010

If a week is a long time in politics, you are reading these words a long time after I wrote them. It may be that the outcome of this week’s general election is now a foregone conclusion, but if not, the oddities of the British electoral system are to blame.

John Curtice of the University of Strathclyde, an expert on the electoral system, offered my colleagues on the BBC’s More or Less the following scenario: if the Liberal Democrats won the same number of seats as at the last election, and if any swing from Labour to the Conservatives was uniformly distributed, then the Conservatives would need an 11-point lead in the share of the vote to win an overall majority. Labour could get an overall majority with a dead heat. If the Lib Dem vote were to be squeezed a bit, Labour could even win an overall majority while earning fewer votes than the Conservatives.

The Tories haven’t always been disadvantaged in this way. In 1951, Churchill’s Conservatives won an overall majority despite attracting fewer votes than Atlee’s Labour party. Then, Labour won its heartland seats with huge majorities and huge turnouts. But no matter how many votes you secure in a single seat, you still only get one member of parliament.

The current Conservative disadvantage is partly because people have been moving from urban (Labour) seats to rural or suburban (Tory) seats. The Boundary Commission struggles to keep up, so Tory seats are larger – more votes, still just a single MP. The Labour party has also tended to win the marginal, low-turnout seats. That may be the luck of the way the voters are distributed, or it may be the result of superior grass-roots organisation from Labour and tactical voting by Liberal Democrat supporters. Neither factor is guaranteed this week.

The confusion deepened after Nick Clegg’s performance in the first televised debate caused a surge in reported support for the Liberal Democrats. One remarkable piece of analysis in the middle of April suggested that an opinion poll putting Labour in third place would nevertheless give them more seats than either opponent; the Liberal Democrats would have almost one-third as many seats despite a greater share of the vote.

Electoral reform might seem to be the answer, and certainly (there are devils in the details, though) it could prevent a party losing the popular vote but winning the election.

Yet, I am reminded of Kenneth Arrow – the youngest and perhaps most brilliant of all the Nobel laureate economists – and his “general possibility theorem”. Arrow’s theorem – more popularly known as the impossibility theorem – explores how individual preferences could be lumped together to express the preferences of society.

To get a rough idea of the proof, first let’s agree that if A is unanimously preferred to B, society must be assumed to prefer A to B. We can then prove (I won’t – but it can be done) that we can shrink the size of this decisive group regarding A and B from “everyone” to a single decision-maker. In other words, “society’s preference” between A and B ends up depending on some particular individual. Finally, it can be proved that if an individual is decisive as far as A and B are concerned, she ends up being decisive over all possible outcomes. In short, the only “social preference” is the whim of a dictator.

Arrow’s theorem is often interpreted as meaning that no voting system can ever reliably reflect society’s real preferences. It actually means something much more profound: that it is nonsense to even speak of society’s real preferences. In an election week, this puts democracy in its proper place: it is indispensable, but let’s keep a sense of perspective, shall we?

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