The first and most obvious question is "what is Labour's Deputy Leadership for?". Nobody imagines that John Prescott has been the number two figure in the government for the past ten years. Most people believe that has been Gordon Brown. A few make the case that it has been Tony Blair.
In a Brown-led government it is not at all clear who will be number two, or if such a position will exist at all. According to James Naghtie, in his excellent book The Rivals, Brown gives no-one in the cabinet any respect, looking down and writing notes the whole time that any of his peers is speaking. He puts down his pen and sullenly pretends to listen only for Blair. The message is clear: Blair is, perhaps, his equal; no-one else is of any consequence. If this is how the man behaves as Chancellor, we can assume there is little likelihood that anybody but Brown will matter after June 27th. Certainly, anyone elected Deputy Leader without his blessing would be excluded from all real influence. An entirely nominal position, with no actual responsibility at all, would be most likely. No change there, then.
According to Guido Fawkes, however, the purpose of the Labour Deputy Leadership has been discovered. It is to make a little on a crafty bet.
Guido suggests, rightly, that the bookmakers are wise to have Alan Johnson as the favourite, but that they may have underestimated Harriet Harman. Certainly, if Gordon Brown had his way, then Harman would win. But he may not get his way. Indeed, after he steamrollered all opposition in his own election, some people will want to give him a bit of a slap just to make a point. The Deputy Leadership election might be their opportunity.
There are two factions who want to make a bit of a protest: the left and the Blairites. The hard left will start off supporting Cruddas, shift to Hain, and would choose Benn ahead of Johnson or Harman if Benn goes into the final vote.
This is, of course, the difficulty with exhaustive ballots. We don't know who will make it to the final two. Given a choice between the Brownite, Harman and the Blairite, Johnson, the left would probably be split. Facing an urgent need to protest against both Gordon and Tony, they would not know how to vote between a proxy for each of them.
The Blairites will start by supporting Blears and shift to Johnson. If neither of those makes it to the final two, they may panic a bit. Presumably they would prefer Harman to Hain or Benn, but may feel obliged to poke Gordon in the eye, just for old times' sake.
If you want my guess as to the candidate that Betfair has most underestimated, it is probably Peter Hain.