If you participate in an IPO, you specify how many shares you're willing to buy and the maximum price you're willing to pay. All the investors who are actually sold the shares get them at the same price, and the entity managing the IPO will generally try to sell the shares for the highest price they can get. Whether or not you actually get the shares is a function of how many your broker gets and how your broker distributes them - which can be completely arbitrary if your broker feels like it.
The price that the market is willing to pay afterward is usually a little higher. To a certain extent, this is by design: a good deal for the shares is an incentive for the big (million/billion-dollar) financiers who will take on a good bit of risk buying very large positions in the company (which they can't flip at the higher price, because they'd flood the market with their shares and send the price down).
If the stock soars 100% and sticks around that level, though, the underwriting bank isn't doing its job very well: Investors were willing to give the company a lot more money. It's not "stealing", but it's definitely giving the original owners of the company a raw deal. (Just to be clear: it's the existing company's owners who suffer, not any third party.)
Of course, LinkedIn was estimated to IPO at $30 before they hiked it to $45, and plenty of people were skeptical about it pricing so high even then, so it's not like they didn't try. And there's a variety of analysis out there about why it soared so much on the first day - fewer shares offered, wild speculative bubbles, no one could get a hold of it to short-sell, et cetera. They probably could have IPO'd for more, but it's unlikely there was, say, $120/share financing available: just because one sucker will pay the price doesn't mean you can move all 7.84 million IPO shares for it.