All voting systems are unfair to part of the electorate. But are some more unfair than others?

A man knocked on the door the other day and asked: “Do you want to save money on your electricity bill?”  The idea that I might answer ‘No’ was clearly not in the script he had prepared.

On the face of it that’s the same with the question: do we want a better voting system? Support for reform of the way we elect MPs to Westminster is for many people the default. Now that Colin Firth and Helena Bonham Carter are backing the vote for change it looks like the cool option will be to vote Yes at the May 5^th referendum on voting reform – especially now they have done so well at the Oscars.

Reform doesn’t just mean change, it means change for the better, the removal of abuse or the rectifying of something faulty. In classical political theory reform meant change that was gradual, as distinct from revolution which was sudden. But modern politicians have recoined the word – rather as they have co-opted the word ‘modernise’ – to mean any changes of which they approve.

The automatic assumption in the ‘modern’ world that all change is good. Certainly opposition to change has been the lament of old men throughout the ages. “In this uncertain life… nothing is secure, nothing keeps,” bemoaned Euripides. But since Darwin’s insight that it is not the strongest of the species that survive, nor the most intelligent, but the one most responsive to change, our culture has been seized with the notion that we must change in order to survive. To live is to change and to be perfect is to have changed often, as John Henry Newman had it.

Anyone who rejects change is the architect of decay: the only human institution which rejects progress is the cemetery, said the modernists of the 1960s. More recently the self-help gurus of the New Age warn us that we cannot manage change, only be ahead of it. If we can’t accept change we can at least change the way we think about it.

Yet we all know that some ‘reform’ is bad, or at the very least ambiguous, or euphemistic. Mao Tse Tung used to speak of “reform through labour” which meant dissidents were made to work as part of their political re-education. We all know what that meant. Nor are we necessarily enamoured of the constant reshaping of our public services by politicians of all colours. The entire 1970s were plagued by seemingly ceaseless reorganisations of local government. The 1990s saw the same constant reconfiguration of how things were done in Britain’s schools. The same process is now at work ‘modernising’ the National Health Service.

Some change on healthcare is inevitable. Diseases of old age are set to rise by 30 per cent over the next eight years. The NHS drugs bill has been growing by £600 million a year. And advances in medical technology burden the public purse even as they liberate the individual patient. But many of the changes have been ideological to-ing and fro-ing between opposing visions one of which sees the best interests of the NHS in competition and the other wants integration and co-operation.

In recent years we have had the Health Act 1999, Care Standards Act 2000, NHS Reform & Health Care Professions Act 2002, Health & Social Care Act 2003, Human Tissue Act 2004, Human Protection Agency Act 2004, Health Act 2006, NHS Redress Act 2006, The Local Government and Public Involvement in Health Act 2007, Health and Social Care Act 2008, Health Act 2009, Personal Care at Home Act 2010 and now the Health and Social Care Bill 2011. None of these have been repealed, merely piled one on top of the other in a polity which has undermined stability. Small wonder that senior and junior doctors constantly warn that patient care could suffer as a result of NHS ‘reforms’. Our headteachers tell a similar story.

There is, at the very least, a paradox in the idea that we should devolve healthcare down to the lowest level feasible – GPs surgeries as part of the Big Society – but then simultaneously suggesting that hospital purchasing on A4 paper, medical gloves and cannulas must be done by the central government. That sounds suspiciously like the Big State. Perhaps the BBC, which has banned its reporters from using the word reform when discussing the May referendum, needs also to revise its language on the ‘reforms’ Michael Gove is introducing in schools or Andrew Lansley in the NHS.

So it may also worth scrutinising the received wisdom on changes to our voting system.

There is no doubting that the existing first-past-the-post system is flawed. At the last election Labour won five times as many seats as the Liberal Democrats despite winning only five per cent more of the vote than the smaller party. With  23 per cent of the vote the Lib Dems won only 8 per cent of the seats. It took around 33,000 votes to win a Conservative seat where 100,000 were needed to win a Liberal Democrat one.

It was as if every Tory voter went into the polling booth with three votes where those supporting Nick Clegg’s party had just one vote. The constituencies that Labour held generally contained fewer voters than those the Tories won. Too many votes are effectively wasted in seats where one party has a large majority; for no matter how many votes a party accrues in a single seat, it still only gets one member of parliament.

The May 5 referendum will ask if we want henceforth to elect or MPs by the Alternative Vote (AV) system in which we would be asked to rank candidates in order of preference –  1,2,3 rather than with a single cross. Then if one candidate gets more than half the votes they win outright; if not, the candidate with least votes is eliminated, and their votes are redistributed to whoever we put as our second preference. The process is repeated till someone gets more than 50 per cent of the votes.

But the result is still not proportional to the overall number of votes cast. So many reformers insist that AV does not go far enough. The Jenkins Commission, set up by the Labour government following the 1997 election, recommended Alternative Vote plus (AV+) which also adds additional candidates from a ‘top up’ party list.

The Electoral Reform Society prefers the Single Transferable Vote – as did, for years, the Liberal Democrats. STV is even more proportional but it requires transferring some of the votes of winning candidates too. It also requires much larger constituencies.

Then there is the Borda system which allocates points to candidates; if there are four candidates the voter gives 4 points to their first preference, 3 to their next choice, and so on. The candidate with the most points wins. Then there are additional-member systems, mixed-member systems, the loser-delegation method, the D’Hondt system and many more…. into which only electoral anoraks need proceed.

The problem is that all voting systems are biased in some way. Martin Rosenbaum from the BBC’s politics department did an interesting thought-experiment in 2009 taking 100 voters and asking them to put four systems in order of preference – first-past the post (FPTP), Alternative Vote (AV), Single Transferable Vote (STV) and the Borda system. This was the result:

The interesting bit comes when you process those preferences using the four different systems. If FPTP is used to count the result, it wins; if AV is used, it wins; if STV is used, it wins; and if Borda is used, it wins.

So fairness does not lie in the fundamental mathematics of the voting systems but in something else. Tim Harford, author of the best-selling book The Undercover Economist, did a similar experiment asking people to rank milk, beer and wine in order of preference. It showed similar biases to Rosenbaum’s. But it also threw up interesting additional questions.

How would the system cope with voter’s expression of more subtle preferences – if, say, beer and milk were brought together as preferences for thirst-quenching drinks, or beer and wine as preferences for alcohol?  In political terms the equivalent might be that candidates should not merely be chosen to reflect the proportional support of  political parties but also, say, the gender balance of the population – so that half of all MPs were women. And after that what about race, or religion?

Small wonder that according to the General Possibility Theorem of Kenneth Arrow – the youngest man ever to win the Nobel Prize for Economics – no voting system can ever reliably reflect society’s real preferences.

Things get even more complex because votes don’t equal electoral power. There is no straightforward link between the number of MPs a party has and its influence, says Tim Harford. He ran the results of the last election through something called the Banzhaf power index which shows there is no simple correlation between the number of MPs and the voting power they command in practice.  Ten per cent of the votes in parliament does not mean 10 per cent of the voting power.

A small party can be as powerful as a much larger one, or utterly powerless, depending on how the coalitions fit together. According to another index, the Shapley-Shubik calculator (which you can find on the website of Professor Dennis Leech, a voting expert from the University of Warwick) Labour and the Liberal Democrats each had 23 per cent of the voting power – but only one was able to exercise it. The Liberal Democrats may have got fewer seats than Labour but they got more power because they joined the government. Lib Dem voters got some power; Labour voters got none.

Democracy has many virtues, but giving equal influence to individual voters, says Harford, is not one of them.

And that is still not all. Thinking on electoral reform cannot restrict itself to just how well outcomes reflect voters preferences. Other issues must be considered. How well does a system reflect the interests of a local area? How stable a government will it produce? And might some systems give undue and disproportionate influence to minority groups and extremist parties?

The systems in some countries, like Italy, are so proportional that they lead to almost annual reconfigurations of impotent or constrained coalition governments. Israel has a different problem: mainstream leaders are constantly in thrall to the demands of small extremist groups who they need to recruit to secure a coalition with a majority. Had the 2010 UK election been run on proportional lines then UKIP would have had 20 MPs and the BNP 12 MPs. The thought of those two parties having the balance of power in a coalition government will not enamour many who might otherwise be enthusiasts for electoral change.

The hard fact is that when it comes to electoral ‘reform’ most politicians decide which system will most benefit their party and then come up with post facto rationalisations to enable them to claim that the system they want is the fairest.

Some will say, with the 18th century poet and philanthropist Hannah More, that reform is “a fine name for ruin”.  Others, with the ex-slave and American social reformer Frederick Douglass, that “if there is no struggle, there is no progress”.

It may be that Edmund Burke offers a more helpful insight. “Reform is a direct application of a remedy to the grievance complained of,” the founding father of Conservatism wrote. The hard thing is working out which grievance is the most serious, and whether the cure might be worse than the original ailment. 

Is the Alternative Vote the answer? It is not even the right question.

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