There is value in clarifying which definition is being used. That is, I hope, what I've been doing here, in opposition to the notion that there is only one sense that can be used and so any clarification is nonsense.
And while strong arbitrage is nice in having 0 risk as opposed 0.1 risk or 0.11 risk, we experience no trouble in real life because some words can be made to overlap despite their average & typical uses. Expected profits or edges don't necessarily cover the same mental ground; if I buy and hold indexes for 50 years, I might expect a profit, but few would call that arbitrage.
"The sense of a sentence - one would like to say - may, of course, leave this or that open, but the sentence must nevertheless have a definite sense. An indefinite sense - that would really not be a sense at all. - This is like: An indefinite boundary is not really a boundary at all. Here one thinks perhaps: if I say 'I have locked the man up fast in the room - there is only one door left open' - then I simply haven't locked him in at all; his being locked in is a sham. One would be inclined to say here: 'You haven't done anything at all'. An enclosure with a hole in it is as good as none. - But is that true?"
--Wittgenstein, Philosophical Investigations, 99
What you're doing is purposefully diluting the word. "Arbitrage" as a word exists to talk about riskless profit. You're trying to introduce risk to it, to what end?
I've noticed something very curious on Intrade markets for 2012 Republican Presidential Nominee - Ron Paul gets 3.5% of getting a nomination - a value that's clearly (and spare me EMH here) wishful thinking of Ron Paul supporters more than any genuine estimate.
And this brings me to a question - if prediction markets overestimate chance of winning of some rare case, how can I profit from that? Naively if I know true chance is 1%, I win $3.5 99% of the time, and lose $97.5 1% of the time, for expected payoff of $2.5. But my maximum loss is 39x higher than my expected profit, and I won't be getting any money out of it for three more years.
I'd need to bet significant amount to earn any money out of it, and that would require accepting 39x as high maximum loss. No reasonably prediction market would accept this kind of leverage without some collateral, nor could I get any reasonable loan for it at rates that would make this arbitrage profitable.
The only way I can think of would be convincing someone with plenty of money that I'm right, and have him provide me with collateral for some (probably very high) portion of the payoff. But if results depend on my ability to convince rich people, that's not prediction market! None of this is a problem for people trying to artificially pump estimates for Ron Paul - they'll just take the loss, and write it off as marketing expense.
None of these problems occur if some position is vastly overestimated, like 60% estimate if I know true value to be 40% - this would be a cheap bet - maximum loss of $40 for expected profit of $20, and people who want to pump it need to take about as much risk as people who want to bring it back to the true value, not a lot more.
I'm confused. Is there some nice way to arbitrage this, or is this an inherent weakness of prediction markets and we should only trust positions they pick as leaders, not chances of their long tail?