But the Liberal Democrats - also meeting in Blackpool - probably have the most direct interest in the Tory contest, because as they continue their own inquest into the aftermath of the general election, they must decide where to place themselves in the political spectrum during the course of this Parliament. And the outcome of the Tory leadership could have a significant impact on the future direction of the Liberal Democrats.
In May, the Liberal Democrats made little headway against the Tories in their "decapitation" strategy, when they devoted much energy to trying to unseat Shadow Cabinet members Theresa May, David Davis, Oliver Letwin and Tim Collins. Mr Collins was defeated in Westmoreland; the others held on - with Mr Davis spectacularly increasing his majority over his Liberal Democrat opponent.
If the Tories are to begin their recovery anywhere, it is said, they will have to win the seats now held by the Liberal Democrats. Some Liberal Democrats did indeed have narrow squeaks earlier this year. Six of their MPs beat the Tories with only three-figure majorities. Tactical voting by Labour supporters, in favour of the Liberal Democrats, may have saved the day for them. But the remainder - those that were gained mostly from the Tories in 1997 - have now grown solid Liberal Democrat tap roots.
The longer an individual Liberal Democrat MP is in post, the more difficult it becomes for them to be unseated. So it looks as though, while the Liberal Democrats' further advance against the Tories has finally faltered, they are nevertheless solidly entrenched in enough seats to permanently deny the Tories any chance of an overall majority.
Liberal Democrats have also demonstrated that they are capable of becoming the main alternative to Labour in many of the inner cities. Where, for example, the Tories once held seats in the suburbs of Leeds, Bristol, Birmingham and Manchester, such seats are now held by the Liberal Democrats. And they have not done this by being to the left of Labour. They have collected Tory votes where the Tory infrastructure has collapsed. These new MPs will not allow the party to be "to the left of Labour".
All of this means that if Labour is to be defeated, it will require a combination of, rather than competition between, Tories and Liberal Democrats. It was once unthinkable for Liberal Democrats to consider any kind of pact except with Labour. Next time, however, the Liberal Democrats will need to be perceived as part of the effort to defeat Labour.
But the growing impression left by the aftermath of the recent general election is that the Tories and the Liberal Democrats are now competing for the same agenda and the same votes. A Ken Clarke win for the Tory leadership would presage an overlap of policy on the Iraq war. Whoever leads the Tories is likely to give serious consideration to the growing calls for a universal "flat tax" currently being pioneered across Eastern Europe. And it can only be a matter of time before the Liberal Democrats' review of their own taxation policy leads them also to a similar conclusion.
So is it possible to imagine the Liberal Democrats ever being able to serve alongside the Tories in government? Both parties will deny such a possibility. Mr Clarke's pitch is that he is best placed among the Tory contenders to convert Liberal Democrat voters back to the Tories. Yet the odds of an overall Tory majority under the current electoral system appear as remote next time as they were in May 2005.
However hard the competition between a Clarke Tory party and a Kennedy Liberal Democrat party, the easier it will be possible to imagine the two sitting around the same cabinet table. The Liberal Democrat price would, of course, be proportional representation. Ken will utterly resist such a notion - at least during the next three months of the protracted leadership campaign. But if Mr Clarke can dump the euro with such bravado, could he not do the same over the electoral system? The Tories need PR as much as the Liberal Democrats.
On the face of it, Mr Kennedy should fear a Clarke-led Tory party most, but it could provide him with the route to a share in power. Is it also possible to imagine either David Davis or David Cameron considering a coalition with Mr Kennedy? When the penny finally drops that three party politics are probably here to stay, proportional representation will have to be on the Tories' agenda whoever becomes their leader.Reuse content