With the melodrama of the primary season behind us, the next big game in US politics will be “Pick the Veep” — and it will really all be about one Veep in particular: Obama’s.

While the benefits a VP can bring to the ticket are relatively small compared to the damage they can inflict if the choice is a bad one (Thomas Eagleton anyone?), good VP choices attempt to add something to the ticket – a few votes from a particular State or region where the VP originates, some particular demographic block like women or working class males, and sometimes even a policy strength that the Presidential candidate may be perceived to have as a weakness (although this carries the risk of the theory working in reverse where the Veeps’ strengths end up highlighting the Presidential candidates’ weaknesses rather than complementing them).

Yet the overriding need for all Veep candidates is that they fit with the general vibe of campaign. It’s no use running on a meta-theme of ‘change politics’ if you then appoint some Washington old boy who has more frequent flyer points on his K-Street card than Tom DeLay.

The Intrade markets for the Democrat Vice Presidential Nominee have thrown up a few interesting possibilities in this regard, particularly the alternative Intrade market which has a broader selection of candidates.

Clinton and Virginia Senator Jim Webb are riding high as the favourites for the nominee, with both hovering around the high teens to low twenties as an implied probability of clinching the Veep spot. While Clinton’s chances are pretty self-explanatory, Webb’s come from him ticking all the right boxes – he burst on to the scene by knocking out Republican Jim “Macaca” Allen in the Senate race for Virginia at the last mid-terms, he combines a strong anti-war position with the military experience of being Secretary of the Navy under Reagan. He’s a popular Senator in a swing State that has strong appeal to working class males and he brings with him high levels of support and regard from military families – an important demographic for any election campaign with a large focus on Iraq.

After Clinton and Webb, the next bunch of contenders hovering around the high single figures to low teens as implied probabilities, are a mix of the usual suspects and some out of left field possibilities.

Everyone has, or no doubt will, in the very near future read about the chances of Joe Biden, Mark Warner, General Wesley Clarke, Michael Bloomberg, Claire McCaskill, Ed Rendell and Kathleen Sebelius.

Even Bill Richardson is often invoked, particularly as a way to bring the Hispanic vote on board for the Dems – but that risks having two minorities on the same ticket which would be a stretch, and there’s the permanent rumour windmill that hangs around Richardson of the type that Glenn Milne would be talking about were he an Australian politician.

But there are three intriguing possibilities at the moment that aren’t the usual suspects.

Firstly, the Republican Senator from Nebraska Chuck Hagel. This guy has been smacking the Bush administration around over the Iraq war for years, has sided with the recent Democrat anti-war push in the Senate, is retiring this term and is currently running at 9% odds for getting the VP nomination. An Obama/Hagel ticket would send shockwaves through the US political system – but his biggest drawback is the obvious, he’s a Republican and many Democrats would go ballistic at the mere thought of a cross-party ticket.

Secondly, one of the most popular Governors in the country, Brian Schweitzer from Montana, has rocketed into 10% odds from nowhere over the last week. Schweitzer is the leading Democrat Prairie Populist in the country and has shown the Democrats that they can win over even the strongest of Republican electorates if they frame their political language right. He’s the master of the one liner – “I believe in gun control; you control your gun and I’ll control mine” — he speaks fluent Arabic, is a soil scientist by trade, is big on energy reform and would add to the ticket in unusual places if Obama is really pursuing a 50 State strategy – particularly the Dakotas and Colorado. His one liners would create mischief for McCain in the news cycle and he’d bring good down ticket support in Senate and Congressional races across the normally Republican leaning areas of the US.

Finally, there’s the Ohio Governor Ted Strickland who is currently running a 10% probability in the Intrade markets. What makes Strickland interesting is that nearly all Republican roads to the White House go through Ohio. If the Democrats take Ohio it would be almost impossible for McCain to become President. Strickland is highly popular (61% approval rating currently), has very broad support in the electorate and would bring a conservative flavour to balance out the Obama ticket. He might even drag a few percentage points of the vote in a really critical State along with him. Strickland has repeatedly stated that he would not accept a VP nomination which throws a spanner in the works – but looking at the Intrade odds, no-one seems to believe him.