In Birmingham, Liberal Democrat MPs and senior advisers were nodding to journalists that legalising same-sex marriages was a Lib Dem victory against archaic Tories. But it's very important for the Conservatives to claim ownership of this welcome policy, for philosophical and political reasons.

Growing cultural liberalism has certainly helped bring this about, but the logic for extending marriage to same-sex couples is not in fact liberal.

Liberals believe in the autonomy of individuals to conduct their lives free from external constraint so long as they do not undermine the rights of others. So the state should be morally neutral. When it comes to marriage, therefore, liberals argue that the state is not being neutral when it only grants the title of marriage, and the benefits that come with it, to heterosexual couples.

But this new policy is not extending those privileges to everyone. Consensual polygamous partnerships, for instance, are not being allowed to marry. A truly liberal position would be that the state does not sanction marriage at all as the benefits from it discriminate against those who do not marry.

The real reason why marriage is being extended to gay couples is because government - shaped by the changing attitudes of the public - now believes same-sex couples are worthy, that they fulfil the purpose of marriage and deserve marriage's associated benefits. This is Aristotelian, not liberal, logic.

This is why the policy is more conservative than liberal. First, Conservatives more strongly believe that justice depends on what individuals deserve. Many liberals, notably John Rawls, believe that moral desert cannot be the grounds for determining the just allocation of titles and resources.

Second, Conservatives, unlike liberals, are sceptical of introducing new rights based on abstract arguments: they prefer to grant rights and implement change based on the evolution of public opinion, to ensure support for and the stability of government, which is what this policy amounts to. So it's time for the Conservatives to say the decision to legalise same-sex marriage is motivated by conservative thinking.

This is important politically too. Recent analysis showed that the Conservatives failed to secure a majority at the last election because they did not convince floater voters the party shared their values. An increasingly liberal-minded electorate need reassurance that the party is in touch with modern Britain, not reluctantly dragged into the twenty-first century by Liberal Democrats.

Cameron, of course, knows this. Hence why Downing Street told the press, despite the Liberal Democrat Equalities Minister formally announcing it, that the PM had "personally intervened" to introduce the policy consultation. Expect more noises from Cameron on this in the weeks ahead, especially to counterbalance more traditional message he is likely to trumpet at the forthcoming Conservative Party Conference.

Ryan Shorthouse is a spokesman for Bright Blue