To be honest the request makes no sense whatsoever for either candidate.
David Cobb wasn't even on the ballot and received 186 write-in votes, 11,721 less than the next placed candidate (Michael Peroutka, the Constitution Party candidate). He only got 72 votes more than Joe Schriner, a local independent. So for the Green candidate the only outcome that could change is that instead of finishing 5th, he could finish 6th.
For Michael Badnarik there is even less sense. As the Libertarian Party candidate, he might be expected to turn down a chance to waste taxpayers' money. Instead he demands a recount. As the LP candidate scored 14,695 votes in Ohio, or 2,725,357 fewer than John Kerry (Democrat), it does not seem plausible that Badnarik thinks he could finish second. On the contrary, the LP only finished 2,717 votes ahead of his nearest rival (Peroutka). So again there is only one plausible change, Badnarik could finish 4th instead of 3rd.
If there was any chance the result might give the minor parties automatic registration on the ballot next time, I could approve of the attempt.
Of course the real reason for the sudden enthusiasm of Libertarians and Greens for a full recount has more to do with the perception that if a recount lead to a Kerry win in Ohio, which overturned the presidential election, then both the Green and Libertarian parties could proclaim that they had achieved a massive impact.
However, unlike Florida in 2000, the gap between the Republican and Democrat candidates is greater than the total number of minor party votes combined (119,775). At 2.12%, the lead President Bush enjoyed over Senator Kerry was more than 230 times greater than that of Florida in 2000.
UPDATE: I found this news release from the Libertarian Party. It claims that the purpose of the recount is to "expose irregularities" in the election process.
More revealing of Michael Badnarik's agenda is the following quote:
In addition to other perceived fraud -- or at least irregularities -- in Ohio's presidential election, Badnarik pointed to the "disturbing" fact that exit polls in many states showed Kerry winning the race.
"The phenomenon that is most damaging, in my point of view, is that for 20 years now, the media have been doing exit polls and using that information to project who was going to win that election," he said. "And because people leaving the polling places are typically very candid, the exit polls have historically been within 1 percent of the actual vote totals.
"Now, all of a sudden in this election, the exit polls and the vote totals differ by a significant amount -- and the talking heads on television are looking at it and wondering why the exit polls were wrong in this election. From what I can see, there's no reason to believe the exit polls were wrong, and fairly good reasons to believe that it was the election process that was faulty."
So there we have it. Badnarik wants the John Kerry to win the presidency. And he is willing to waste $1.5 million of Ohio's taxpayers' money to try to achieve this aim. No amount of spin can dress this up as a vehicle for advancing Libertarian ideas.