An eBay member's feedback profile. Click to enlarge.
When we have a channel to express our anger at a business transaction, we're less likely to demand our money back or proactively injury the company's reputation. This is why most companies employ a team of customer service representatives to endure customer flack all day.
A brief background on the ultimatum game: Subject A is given $20 and told to split it between himself and a Subject B. Subject A can keep $16 for himself and give $4 to Subject B, or give $10 to each player, etc. Subject B sees the offer and can then choose to accept it (the money is split according to A's decision) or reject it (neither subject gets anything). In theory, a penny is better than nothing, so the B's should accept any offer above zero. In practice, many of the offers in which the B's get less than 50% are rejected. Many people see these rejections as a way for the B's to signal their disdain for the A's greediness and punish the A's accordingly.
However, in Xiao and Houser's version, each Subject B was allowed to write a message back to the Subject A, along with his decision on whether to accept the offer. Xiao and Houser found that rejection rates plummeted for low offers, when many of the B's were allowed to write unfavorable messages.
The rejection rates are much lower when the B's can send the A's a message along with their decision (from Xiao and Houser 2005).
This is the brilliance of letting customers sound off on their feelings, even if it's just typing them into a form that few people will ever read.
EBay would be decidedly less successful if there were no way to leave feedback. The signaling aspect of the feedback is obvious and well-documented: a seller who has not delivered on previous orders will earn a poor reputation, resulting in fewer future sales or a ban from eBay. More subtly, many angry customers, especially for the cheapest items, will be satisfied with registering their disdain and won't bother to file for a refund.