One error Romney made is that a wager on his part would have been politically more palatable than a bet. The subject matter in question is Romney's own words; he is presumably quite aware of what he said. Therefore, he's proposing what appears to be a sucker bet, which would create a $10K debt for Perry, which seems unfair. Also, gambling is offensive to some voters; Perry's refusal to go there scored points for him at Romney's expense.
Even a wager (where payment would occur only if Perry could prove his case) would carry the risk of Romney being perceived as something of a crackpot, or someone who reneges on a wager, if Perry could make a convincing case.
For those who don't follow politics, Mitt Romney offered to bet Rick Perry $10,000 that Perry had misquoted Romney. (video)
Most political commenters see the move as a gaffe. They claim the bet made Romney look out of touch, because it reminded voters that Romney is rich enough to afford $10,000.
As a believer in prediction markets, I am disappointed in the public's reaction. Romney made a bold move by making his beliefs pay rent. Critics point out that $10,000 is "chump change" for Romney, but Romney still but himself at risk. If he had lost the bet, Perry could have made a production about cashing a $10,000 check from a disgraced Romney. Besides, if money were the issue, Perry could have countered with a non-monetary bet. "Loser has to attend the next debate in a clown suit" or something.
If politicians had to face real consequences every time they made a false statement, they would have a larger incentive to tell the truth. It's a shame Romney's bet probably won't catch on.
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This post is not an endorsement of Mitt Romney or his politics. All I am endorsing is political betting.