In Public Markets, No. Another Investor is not very likely to have access to information unavailable to you, and their investment will move the price of the security and be "priced in" by the time you get to invest. Public Markets clear in Series.
In Private Markets, Yes. Another Investor is very likely to have access to information unavailable to you, since the private nature of the company makes it harder to get standardized information. Furthermore, their investment will not move the price of the security very quickly, since private investments tend to get done in discrete rounds. Therefore, each additional Investor is likely bringing some additional information to the table. Since the price doesn't move very quickly, it is rational to take this additional information, and therefore Social Proof, into account. Private Markets clear in parallel.
This makes two assumptions:
- You don't rely purely on Social Proof. It is an input into the decision process, along with Team, Traction, Market, Product, Competition, Price, etc..
- The Investors you're factoring in aren't relying purely on Social Proof either (although as rational actors, they are factoring it in). Markets in which followers rely almost completely on Social Proof are cumulative advantage markets, and function differently as the value of the product / investment increases along with increased consumption of the product. I.e., I'm more likely to listen to band that my friends listen to, because then we can listen to it and talk about it together. Their listening to the band has increased its actual value to me.
An aside - Investors who say they do not factor in Social Proof at all are not being completely honest with themselves. Consider the case in which they are going to participate in a private investment but the other investors drop out. Or previous, deep-pocketed investors refuse to commit their pro-rata contribution into the new round. The negative Social Proof would almost definitely kill the financing. The decision to invest or not invest carries information, and in private investments, information is scarce.