When some site, like for example DP forums, shares revenue with its users, how can they prevent that dishonest users invite their friends, dogs and family to click on these links? I don"t want to use this business model, just because i'm afraid of possible abuse of the system. It feels liking giving away control on your site, which can hurt it's reputation. Is this correct or am i missing something that makes this safe?
No, you're not missing anything - it is a potential problem. In the case of DP the tens of thousands of threads mean it's pretty likely that there will be many, many genuine clicks to every fraudulent one - so many that the fraudulent clicks practically won't count.