In this week's New Statesman, Richard Reeves, Nick Clegg's former strategy director, calls for a recasting of the Liberal Democrats as a centrist liberal force that divorces itself from the party's social democrat past. Intellectually, the case may be a powerful one. But electorally, there is a huge problem: the strategy ignores the people who support the Lib Dems today.

Even though so many left-leaning voters have deserted the party, few of its loyal supporters are classical liberals of the centre or soft-right. New Fabian Society analysis of YouGov polling from the last 12 months shows that, even after two years of the coalition, the Lib Dems' remaining supporters are much closer to Labour than to Tory voters. Lib Dem and Labour supporters share views on the economy and government and far more Lib Dems would consider voting Labour than Conservative.

First, consider how people identify on a left-right political spectrum. 43% of remaining Lib Dem supporters describe themselves as on the left of politics, compared to 53% of Labour supporters and 1% of Conservatives. By contrast, just 8% of Lib Dem and 6% of Labour voters place themselves on the right of politics, compared to 60% of Conservative supporters.

Labour and Lib Dem supporters also have similar views on the role of government in British life. Consider this statement of the liberal case against the state: "Government should do the bare minimum and stay out of people's way; people are freer when there is less Government". Forty four per cent of Conservative voters say it's a convincing argument, compared to just 24% of Lib Dem and 22% of Labour voters.

It's a similar story on the economy. Forty eight per cent of Conservative voters are sympathetic to cutting red-tape, compared to 13% of current Lib Dems and 9% of Labour supporters. Forty two per cent of Lib Dems and 40% of Labour supporters want an interventionist industrial strategy, compared to 25% of Conservatives.

So how does this translate into the political preferences of Lib Dem supporters? During the summer, YouGov found that 54% of remaining Lib Dem voters would consider voting Labour, while only 36% would consider the Conservatives (defined as a 4 out of 10 chance of voting for the party in question). This finding is so striking because we are talking about current Lib Dem supporters not the defectors.  This pro-Labour bias comes on top of Lib Dem deserters splitting 4-to-1 in Labour's favour.

These new insights into the Lib Dems' remaining supporters should give both parties pause for thought. It suggests, for the Liberal Democrats, that a centrist appeal to classical liberalism will do little to consolidate the party's current support, let alone grow it. It demonstrates that, in the voters' eyes, the Lib Dems should reject 'equidistance' in favour of a pro-Labour bias.

Meanwhile, Labour politicians need to recognise that most remaining Lib Dem supporters continue to have left-leaning views. If the electoral maths demands it, Labour should stand ready to cooperate with a party that speaks for people who share their values and are deeply suspicious of Conservatism.