IT will be one of the strangest political contests in British history. The battle between David Cameron and David Davis in front of a Question Time audience on Thursday night has no exact parallel.

Ken Clarke and Iain Duncan Smith did appear together with a modest group of Conservative members on Newsnight four years ago but that was more like a simultaneous set of interviews than a proper contest and the cynics suggested that the programme was in any case transmitted a little too late for the bedtime preferences of the more elderly sections of the party. The Cameron-Davis showdown, by contrast, should attract a much more substantial number of viewers. It is the closest thing that we have had to an American-style presidential debate.

Except that it is far more unpredictable. The US debates started as free-flowing, if cordial and regulated, encounters but have become, many critics charge, little more than highly scripted joint press conferences. In this instance, the questions will be drawn from the studio audience and the candidates will be encouraged to quiz each other. It is a voyage into the unknown. In boxing terms, it is like agreeing to a fight without being certain whether or not the Marquess of Queensbury rules apply.

It is almost impossible to prepare for. Should the two men be using their spare time swotting up on every aspect of public policy or instead rehearsing a few key soundbites that they want to be remembered afterwards?

Might Mr Cameron concentrate on projecting a John Kennedy-esque image of charisma or will Mr Davis hope for a moment when his young rival refers to Margaret Thatcher and reply (in the spirit of Senator Lloyd Bentsen’s gibe at Dan Quayle in 1988): “I know Lady Thatcher. Lady Thatcher is a friend of mine. Mr Cameron. You’re no Lady Thatcher.”? This is, in that sense, an easier exercise to plan for Mr Davis than his opponent. He is the underdog and this is probably his best (perhaps only) chance to completely reverse the dynamics of this leadership battle. He can afford to be assertive but must stop just short of being aggressive.

He has to be “Mr Substance”, offering lots of policy initiatives that he has reason to think most Tories will approve of. He needs to take Mr Cameron’s reported remark that he regards himself as “Blair’s heir” and ask Conservatives whether that is what they want for their party.

The challenge for Mr Cameron is different. He needs to look and to sound good while saying as little as possible. If he set out what the modernisation of the Tories would mean in any detail there is a chance his party would not buy it. He has to survive these 60 minutes. He has little to gain from them. Make no mistakes will be his maxim. As a result, only one man seated on the stage on Thursday will truly enjoy the occasion. He is the third David — David Dimbleby.

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