Another serious question: if a stock has no voting rights and no dividends, why would it be worth anything at all? That is, what makes it different from a piece of paper with the company's name on it? If there are voting rights, then there's value because someone potentially could buy enough shares to meaningfully exert those rights, but if not, then what value do the shares have to anyone?
That's an interesting question. To oversimplify it, the value of a stock of essentially a wild-ass guess about how much cash one might be able to pull out of a company eventually per share times the number of shares.
If I a company isn't paying dividends or buying back stock, and we (the shareholders) can't coerce said company into doing so at some point, it's essentially an indestructible piggy bank in which money evaporates while you helplessly watch.
If the company is successful, they will pay a dividend or do a buyback later. For example, Facebook raised $16B in its IPO, and recently bought back $6B worth of shares at about 4 times the IPO price. The IPO was a great deal for common shareholders, despite their lack of control. Perversely, the comparison to Facebook might bias people to pay more for Snapchat shares with no voting power.
It's value is that you can sell it to someone else.
One of the big risks that Snap is taking in this IPO is that their common stock has no practical value.
As you said, stock generally has two ways of being worth something: partial control and/or profit sharing.
Snap common stock has neither. It's only value is its ability to be sold to someone else. It's basically a currency? Is $Snap the new BTC? I have no idea.
But that just pushes the question one layer of abstraction deeper. Why would that person be willing to buy Snap shares from you at any price?
On a long enough timeline, you have to believe that Snap will either disburse dividends, be acquired by another company or find some other way to convert ownership into actual cash.
They would buy because they believe they can sell it later at a higher price, based on the belief that other people want to buy $SNAP and will drive the price up.
I'm not avoiding your question—I agree that it should be based on underlying value—but that seems to be the only reason to buy $SNAP