ah! fair enough actually. No idea how I missed that. But to be fair, I don’t know how much others would care about this when suspecting him, so it may be moot anyway.
But I think if there’s a risk reward graph of risking insider trading at X amount vs at Y amount, it’s not 10 times more suspicious to trade 10 times as much, so therefore he would be acting irrationally.
But yeah, it’s a fair argument that maybe he is acting irrationally precisely to avoid such suspicions.
Warning: more for imho beautiful geeky abstract high-level interpretation than really resolving with certainty the case at hand.
:-)
I purposely didn’t try to add any conclusive interpretation of it in my complaint about the bite-its-tail logic mistake.
But now that we’re here :-):
It’s great you did the ‘classical’ (even if not named as such) mistake so explicitly, as even if you hadn’t made it, somehow the two ideas would have easily swung along with it in many of us half consciously without being fully resolved, pbly in head too.
Much can be said about ’10x times as suspicious’; the funny thing being that as long as you conclude what you now just iterated, it again defeats a bit the argument: as you just prove that with his ‘low’ bet we may—all things considered—here simply let him go, while otherwise… Leaving open all the other arguments around this particular case, I’m reminded of the following that I think is the pertinent—even if bit disappointing as probabilistic fuzzy—way to think about it. And it will make sense of some of us finding it more intuitive that he’d surely gone for 800k instead of 80k (let’s ascribe this to your intuition so far), and others the other way round (maybe we’re allowed to call that the 2nd-sentence-of-Dana position), while some are more agnostic—and in a basic sense ‘correct’:
I think Game Theory calls what we end in a “trembling hand” equilibrium (I might be misusing the terminology as I rmbr more the term than the theory; either way the equil mechanism here then I’d still wager makes sense at a high level of abstraction): A state where if it was clear that 800k would have made more sense for the insider, then he could choose 80k to be totally save from suspicion, and we’d in that world see many ’80k-size’ type of such frauds, as anyone could pull them off w/o creating any suspicion—well and greedy people with some occasions will always exist. And in the world where instead we assume it was clear that 80k was already perfectly suspect, he would have zero reason to not go all out for the 800k if at all he tries… In the end, we end up with: It’s just a bit ambiguous which exact scale increases the suspicious-ness how much, or, put more precisely: it is just such that the increase of suspicious-ness vaguely offsets the increase in payoff in many cases. I.e. it all becomes somewhat probabilistic. We’re left with some of the insider thieves sometimes going for the high, sometimes for the low amount, and (i) potentially with many of us fighting about what that particular choice now means as fraud-indicator—while, more importantly, trembling-hand-understanders, or actually maybe many other a bit more calm natures, actually see how little we can learn from the amount chosen, as in equilibrium, it’s systematically fuzzy along that dimension. If we’d be facing one single player consistently being insider a gazillion times, he might adopt a probabilistic amount-strategy; in the real world we’re facing the one-time or so random insider who has incentives to play high or low amount which may be more explained by nuanced subtleties rather than a simple high-level view on it all—as that high-level-only view merely spits out: probabilistic high or low; or in a single case a ‘might roughly just as well play high amount as low amount’.
I don’t really claim there cannot be anything much more detailed/specific said here that puts this general approach into perspective in this particular case, but from the little we have here in OP and the comments so far, I think that would reasonably apply.
I think a 10x larger bet would be more than 10x as suspicious. There are more than 10x as many people who would bet 80k on low-medium conviction bets than 800k.
Also liquidity would dry up, quickly, once liquidity providers see the obvious insider, so the reward would be much less than 10x.
Also I see the disutility from suspicion as closer to a step function: you really do not want your suspicion to rise to a level that would warrant a serious investigation. Which is kind of binary, closely-related to the risk of traders framing you as an insider beforehand, and I would think 80k is already pretty close to this threshold (but I’m not familiar with how liquid this market was).
Note the contradiction in your argumentation:
You write (I add the bracket but that’s obviously rather exactly what’s meant in your line of argument)
and two sentences later
ah! fair enough actually. No idea how I missed that. But to be fair, I don’t know how much others would care about this when suspecting him, so it may be moot anyway.
But I think if there’s a risk reward graph of risking insider trading at X amount vs at Y amount, it’s not 10 times more suspicious to trade 10 times as much, so therefore he would be acting irrationally.
But yeah, it’s a fair argument that maybe he is acting irrationally precisely to avoid such suspicions.
Warning: more for imho beautiful geeky abstract high-level interpretation than really resolving with certainty the case at hand.
:-)
I purposely didn’t try to add any conclusive interpretation of it in my complaint about the bite-its-tail logic mistake.
But now that we’re here :-):
It’s great you did the ‘classical’ (even if not named as such) mistake so explicitly, as even if you hadn’t made it, somehow the two ideas would have easily swung along with it in many of us half consciously without being fully resolved, pbly in head too.
Much can be said about ’10x times as suspicious’; the funny thing being that as long as you conclude what you now just iterated, it again defeats a bit the argument: as you just prove that with his ‘low’ bet we may—all things considered—here simply let him go, while otherwise… Leaving open all the other arguments around this particular case, I’m reminded of the following that I think is the pertinent—even if bit disappointing as probabilistic fuzzy—way to think about it. And it will make sense of some of us finding it more intuitive that he’d surely gone for 800k instead of 80k (let’s ascribe this to your intuition so far), and others the other way round (maybe we’re allowed to call that the 2nd-sentence-of-Dana position), while some are more agnostic—and in a basic sense ‘correct’:
I think Game Theory calls what we end in a “trembling hand” equilibrium (I might be misusing the terminology as I rmbr more the term than the theory; either way the equil mechanism here then I’d still wager makes sense at a high level of abstraction): A state where if it was clear that 800k would have made more sense for the insider, then he could choose 80k to be totally save from suspicion, and we’d in that world see many ’80k-size’ type of such frauds, as anyone could pull them off w/o creating any suspicion—well and greedy people with some occasions will always exist. And in the world where instead we assume it was clear that 80k was already perfectly suspect, he would have zero reason to not go all out for the 800k if at all he tries… In the end, we end up with: It’s just a bit ambiguous which exact scale increases the suspicious-ness how much, or, put more precisely: it is just such that the increase of suspicious-ness vaguely offsets the increase in payoff in many cases. I.e. it all becomes somewhat probabilistic. We’re left with some of the insider thieves sometimes going for the high, sometimes for the low amount, and (i) potentially with many of us fighting about what that particular choice now means as fraud-indicator—while, more importantly, trembling-hand-understanders, or actually maybe many other a bit more calm natures, actually see how little we can learn from the amount chosen, as in equilibrium, it’s systematically fuzzy along that dimension. If we’d be facing one single player consistently being insider a gazillion times, he might adopt a probabilistic amount-strategy; in the real world we’re facing the one-time or so random insider who has incentives to play high or low amount which may be more explained by nuanced subtleties rather than a simple high-level view on it all—as that high-level-only view merely spits out: probabilistic high or low; or in a single case a ‘might roughly just as well play high amount as low amount’.
I don’t really claim there cannot be anything much more detailed/specific said here that puts this general approach into perspective in this particular case, but from the little we have here in OP and the comments so far, I think that would reasonably apply.
Thank you so much for this reply. Makes perfect sense.
Turns out LW obsession with game theory matters in the real world after all :)
I don’t share that intuition, from a few angles.
I think a 10x larger bet would be more than 10x as suspicious. There are more than 10x as many people who would bet 80k on low-medium conviction bets than 800k.
Also liquidity would dry up, quickly, once liquidity providers see the obvious insider, so the reward would be much less than 10x.
Also I see the disutility from suspicion as closer to a step function: you really do not want your suspicion to rise to a level that would warrant a serious investigation. Which is kind of binary, closely-related to the risk of traders framing you as an insider beforehand, and I would think 80k is already pretty close to this threshold (but I’m not familiar with how liquid this market was).