UK election spells the end for the biggest ‘law’ in political science

Every election held under “first past the post” (FPTP) voting in the USA produces perfect two-party outcomes – no party except the Democrats and Republicans gets a look-in. Yet elections held under the same voting system in every other established democracy (such as Britain, Canada and India) have increasingly produced multi-party outcomes.

The UK’s current general election looks certain to put another nail in the coffin of the most famous proposition in political science - Duverger’s Law, first formulated in the 1950s. In its modern testable form (after Gary Cox), the law says that in each local constituency the number of (substantial) parties under FPTP should equal one plus the number of seats being contested (which in this system is 1), so = 2.

A highly nationalised political system, like Britain, should also show two parties dominating nationally, although maybe with smaller regional competitors in some cases – as with small special parties in Scotland, Wales and Northern Ireland. The top two parties should accordingly be able to form single-party majority governments.

Yet with the 2015 UK general election upon us, a five-year coalition Conservative-Liberal Democrat government has just expired. And competition is taking place within party systems that show multiple (big) parties competing in both England and Wales, and Scotland - as my first chart shows.

The different blobs here show where each party stands on a left-right ideology scale. The size of the blob shows how generally significant a party is in UK political terms (including winning seats in the European and Scottish parliaments, or the London Assembly). Finally, the numbers inside each blob show that party’s current level of support, averaged across the six most recent opinion polls.

Chart 1: Two UK party systems, 2015 election

So Britain now is pretty much exactly like every other multi-party system across western Europe.

In England, two old governing parties on the centre-right and centre-left are continuing with flagging support, separated by a small liberal party. The Liberal Democrats’ vote has shrunk dramatically from 23% in 2010, as the cost of supporting a Tory-dominated government.

The UK Independence Party is a pretty standard “anti-foreigner” party, of the kind present in the European right everywhere now. Its appeal is fuelled by scare stories of immigrant influxes and anti-EU rhetoric.

The Greens on the left are still battling to make a mark in the UK, but run third amongst young people.

Turning to Scotland, the Scottish National Party (which has a majority government in the Edinburgh Parliament) is riding high on last year’s referendum wave - when nine out of every 20 people voted to leave the UK. The SNP’s surge has pushed Labour (the traditional hegemon north of the border) to a poor second, and marginalised the other unionist parties. On current form, the SNP might yet win almost every seat in Scotland, unless some Tory and Liberal Democrat voters can bring themselves to back Labour as a tactical vote for unionism.

But the key test of Duverger’s Law comes at the local seats level. My second chart shows the predicted seats outcomes across Great Britain next week.

Each black dot is a single constituency result. On the bottom axis, seats where the Conservatives are leading Labour are shown on the right, and seats where Labour leads the Tories on the left. The vertical axis shows the combined proportion of votes in each locality backing parties running third, fourth or fifth nationally.

Chart 2: The predicted local seats outcomes on May 7

If Duverger’s Law was working perfectly in Britain, all the seats should be piled up on the bottom axis of this chart, and completely within either the red or blue triangles – showing seats where either a Labour or a Conservative MP wins with majority support. (Outcomes exactly like this happen at every election in the USA still.)

Instead, there are no seats close to the bottom axis - almost no UK contests in 2015 will show levels of combined third, fourth and fifth party voting below 20%. There is also a huge upward spread of seats into the “Crown” area shown, which is where parties running third or fourth nationally can potentially win seats (depending on how fragmented this “remainder” vote is). As a result, very few MPs will have more than 50% local support in 2015, and many of these will actually be in Scotland for the SNP.

So the UK’s 2015 general election outcome spells the complete destruction of Duverger’s Law, and in the country which is the classic case for the law.

How voters choose may also soon lead to the UK’s moving further towards a new voting system and a new, fixed constitution. All this now depends on whether Labour’s Ed Miliband can become prime minister, or whether the Conservatives' David Cameron can cling on in 10 Downing Street.

For politics nerds: so, without Duverger’s Law, what is left to explain perfect two-party politics in America? It seems to have nothing to do with first past the post voting per se, but instead to reflect other US-specific features, especially:

• Electing single office-holders (the president, state governorships and big-city mayors) using first past the post - rather than better, modern systems, like the “supplementary vote” system used to choose the London mayor; or the alternative vote used in Australia.

• The largely unregulated way in which majorities inside US state legislatures control congressional and state legislature districting, who can vote and many other features of elections – often now in startling partisan ways.

• The dominance of “big money” campaign finance in US elections.

Patrick Dunleavy receives funding from the Joseph Rowntree Charitable Trust, for the Democratic Audit of teh UK