This is touched on in some of the other posts, so I won't belabor the point, but the issue with only positive feedback is that there isn't a way to identify items that are popular but also controversial.
For example, an Airbnb venue with 5,000 likes would be considered 'better' than one with 500. But add in negative feedback, and consider if the same venue with 5,000 likes also had 4,500 dislikes, while the venue with 500 likes only had 50 dislikes.
Negative feedback helps us discern between if something is 'better' or simply 'popular' -- the latter can be gamed with marketing, while the former is much harder.
That is a great point. At $work, we're about to revamp how we do ratings. The idea was to only consider positive feedback, but maybe we should figure out how to include negative feedback too. But that brings up the question of how to avoid the spammers, scammers and idiots that inevitably popup?
For example, an Airbnb venue with 5,000 likes would be considered 'better' than one with 500. But add in negative feedback, and consider if the same venue with 5,000 likes also had 4,500 dislikes, while the venue with 500 likes only had 50 dislikes.
Negative feedback helps us discern between if something is 'better' or simply 'popular' -- the latter can be gamed with marketing, while the former is much harder.