Posting this as an intellectual exercise. And calling it intellectual is probably a stretch, as I haven't really thought much about it.
We often say that LLMs answers are average, as in, they will tell you what is the most likely answer among all the data they have been trained on. It usually won't give you the outlier (and even if you prompt specifically for such outliers, you're getting the mean outcome among that outlier field).
A few days ago, someone told me that if you ask your LLM to ask for a random number between 1 and 30, there is a very high probability it'll answer 17 (unless you prompt it to invoke a random number generator, ofc). Regardless of the specific LLM you ask.
My wife has been prompting Gemini a lot these days asking it whether a certain stock will go up or down. It often answers her by giving her a probability that it will go up. I got bothered by how much fait she puts in these numbers, and then, to try to prove a point (yes, silly, I know... happy wife, happy life), I asked her to ask the same question, but in the negative (using a new session). To illustrate that
- What is the probability that SK Hynix's stock goes up? Answer: 20%
- What is the probability that SK Hynix's stock goes down? Answer: 70%
Simplifying by ignoring the case that it stays completely flat, there is a clear mismatch between these two answers. If I could trade against the LLM, there is a 10% arbitrage opportunity here.
Of course, I can't trade against an LLM.
But, putting all the above together, would it be possible to take advantage of the fact that my wife is likely not the only one to ask such questions to their favorite LLM? And retail people using LLMs to ask such questions likely use the mainstream ones, so one could check which probabilities these LLMs converge on.
[Insert plenty of other simplifications (small variations to the above prompts, delays in training, etc) and their impact here]
And maybe, just maybe, one could then figure out how to leverage this retail asymmetry?
Then again, I hate the stock market, and I keep telling my wife that day trading is a losing game, so it'll just remain a silly thought on SN.
I really enjoy the spirit of this idea, especially the connection to random numbers that seem random but aren't. Another example is when people are asked to pick a random number from 1 to 100, 37 comes up more often than it should. 37 has the quality of "randomness" to the human mind where numbers like 1, 50, and 100 do not, despite all being equally likely.
I wonder if there is a more direct way of exploiting this besides the stock market.
In the stock market, the issue is that the LLM bias may be swamped by too many other factors for it to consistently make a profit. Even if it was consistently profitable, once the strategy catches on, shares known to be underpriced by LLMs will get bid up, and shares known to be overpriced will get sold down, to the point where the excess gains disappear.
One thing I like to annoy physicists with is: "Econ is harder than physics, because in physics the behavior of the objects you model doesn't depend on your model of the objects' behavior."
Yes, that. And LLMs just mimic that human behavior.
I had a similar experience when asking classmates in gradschool for random numbers to decide which exercise number I'd tackle next. Out of 20 questions, all theodd numbers came out first.
Yeah, that's the thing with market inefficiencies. They tend to get arbitraged away.
One thing I like to annoy economists with: "You don't contribute anything to society "Economics is remarkably good at explaining why what just happened was inevitable."
Just kidding.
I don't have econ friends.