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Now, say that you somehow knew that this coin wasn't a fair coin, and instead was weighted 55% to fall on heads, 45% tails. Then, you would be happy buying these contracts for 50 cents -- given the contract pays out $1 if the coin lands on heads, and you know there's a 55% chance of heads, the expected price for the contract is 55 cents, and you make 5 cents in expectancy.
So, if you had information about the "fair value" of this contract, telling you that the price should be 55 cents, you'd be incentivized to buy the contract at prices below 55 cents. If the contract was trading at any price other than 55 cents, then, from your perspective, the price would be incorrect. And if the price is incorrect, then you'd be able to make money trading: buying for prices below 55 cents and selling at prices above 55 cents. And finally, as a result of your trading, you'd provide one-sided demand to the market, pushing the price closer to the actual correct price.
From this simple mechanism, wherein everyone who has information is incentivized to make money on their information by trading, prices start getting pushed to accurately reflect the aggregate of the information that everyone possesses! So in markets, there is a profit incentive to provide information, and this makes prices more accurate.
Finally, I think a common misconception is that prediction markets are sometimes wrong, as events priced at low probabilities sometimes happen. For example, in the 2024 election, Trump was trading at probabilities below 50%, but he still won! However, this is conflating present information about the future with future results. Given the earlier example about the biased 55% coin -- before we flip the coin, the best thing we can possibly say about the future really just is that there's a 55% chance of heads and 45% chance of tails. If we then flip the coin and it lands on tails, that doesn't mean we were incorrect -- it was just the best statement about the future that we could have possibly made.
Prediction markets -- or really any price system -- aggregate the best available information about the future. If you can confidently state that they are wrong -- that their best available information about the future is inaccurate -- then you should be trading and making money.
Does that clear things up a bit for you? It's a longer response, but I think it might address some of the confusion that you (or anyone else) might have regarding what people actually mean when they say that these prices predict the future.
So the data/copyright issue that you might be worried about is actually completely solved already! Anthropic is just paying a settlement here for the illegal pirating that they did way in the past. Anthropic is allowed to train on books that they legally acquire.
And sure, Chinese AI companies could probably scrape from LibGen just like Anthropic did without getting in hot water, and potentially access a bit more data that way for cheap, but it doesn't really seem like the buying/scanning process really costs that much in the grand scheme of things. And Anthropic likely already has legally acquired most of the useful texts on LibGen and scanned them into its internal library anyways.
(Furthermore, the scanning setup might actually give Anthropic an advantage, as they're able to digitize more niche texts that might be hard to find outside of print form)
> When each LLM was put into a public-facing version of Claude, it was complemented by other software that filtered user inputs to the LLM and filtered outputs from the LLM back to the user. As a result, Authors do not allege that any infringing copy of their works was or would ever be provided to users by the Claude service.
(from Bartz v. Anthropic in the Northern District of California)
The difference is that in these private rooms, liquidity providers are often able to understand their customer more. For example, big passive index funds aren't buying and selling due to some adverse knowledge of future price movement. Instead, they are merely following the index. If market makers are able to distinguish between the passive indexers and the smart sophisticated hedge funds, they will then be able to provide to the passive indexers at a better price.
In this example, these "lower-than-optimal" prices weren't passed on to the end consumers in the first place–instead, arbitrageurs like the author's friend would take advantage of them to gain a profit. The end prices that the average, uninformed buyer would see would therefore be inflated, with traders like the author's friend taking their cut.
Sure, the rise of more efficient, algorithmic players decreased the profitability of less sophisticated middlemen like the author's friend. But, since these algorithmic players were more efficient, they were able to take less of a cut, leading to lower prices (and overall benefit) for the average buyer.