If your data suggest that the stock is trading at a discount due to irrationality, then you have a perfect opportunity to buy lots of an underpriced stock.

I think the point OP was trying to make is that, that irrationality may not be easy to capture with automated systems, therefore the value of data is limited by your trading system/algorithm's ability to detect/predict irrational human behaviour. Or atleast that's what I read of it.

Yes, the grandparent comment makes a good point. You can have plenty of solid data and still make a losing trade.

But, given enough data-informed trades that would otherwise be proditable, the law of large numbers suggests that an overall strategy will still be sound. You can afford to have the market be irrational here and there if you really are correctly forecasting earnings in advance most of the time.

The market can stay irrational longer than you can stay solvent. Keynes.

"Trump tweets a company name and the stock price decreases" is a signal. If you think about trading strategies as collections of consistent signals you can execute on, rather than assumptions that require market rationality, it doesn't really matter that a rogue event can cause an unpredictable response. The law of large numbers will generally protect you, given a consistent strategy and enough capital.

As an example, a hedge fund that consumes data capable of accurately forecasting earnings in advance can also diversify by consuming social media data. Matt Levine has written about profitable trading strategies developed with sentiment analysis on Trump's tweets. Instead of a hedge fund betting on the stock going up and getting blindsided by a random Trump tweet (or other irrational thing), it will use that as a signal if it can.

You don't think ever hedgefund is actively consuming social media data? How do you think the price of these stocks are affected so quickly?