I think it would be much easier to abuse than you would like - and correspondingly, the behavior would alter in favor of those more ruthless, not against them. Joe would probably be much better able to send to the other planet, those who object to him, rather than the other way around - which means more people would act like him, and fewer would dare to object.
So, first, you need someone to keep track of what is an exile-worthy offense or not. What those factors are, and how they're portrayed, is going to be very important. There's lots of historical precedence for people judging, with harsh penalties, "moral" values that do no harm (personal preferences like sexuality or religious beliefs) over "practical" values that do a lot of harm (practices like exploitation in the name of business, or socially common abuses). It probably won't take much before people are exiling for "being different" without harm, and leaving be those who cause harm in expected ways.
Next, there will be a really, really clear power differential based on online presence. After all, the trial depends on whatever is being said online about him, and the online doesn't really have a mechanism for being verified as truthful.
Joe, with his lots of money, can fund a big website devoted to his charitable acts (whatever they may be), and populated by his friends, acquaintances, or yes men. He can fund a genuinely useful or popular site, and use it to spread bits of pro-Joe propaganda. He can fund a few online rants, through proxies against some person who's questioning his practices, and make it look like they're persecuting him or others who are successful in business, this person has a grudge, they're being mean.
So, someone who is quiet and minding their own business, will not have a strong online presence to debunk any claims made against them. Anyone who does have a strong online presence, will have people for and against them, people who think the world of them or hate them - its human nature to polarize. A few big, showy, well trafficked pages (something which, unfortunately, money can manipulate) can swing opinion about somebody in a big way - especially in a very large community (all of online-world), where people who actually know the person are very, very few. And, even at the very worst, it can be easy for Joe to swing up enough dirt about whoever is complaining about Joe, to make it look like an argument, opposing viewpoints, and mutual antipathy rather than "Joe is being a real jerk" - which can derail the voting-for-exile process altogether.
What process is there for verifying things attributed to a person are really from them, especially online actions which use screen-names? Joe can deny that the nasty rant posted under a similar screen-name is his, or can fake up a nasty, obviously biased, anti-Joe rant under an opponent's screen-name to undermine their credibility. What process is there for verifying that nominations are made by people with a real or even personal grievance, instead of people who find a ranting webpage, take a side based on the clever portrayal of one-sided or biased information, and bounce over to fill the nomination forms without verifying what's going on?
And, finally, once you have your thousand nominations - who gets to set up the voting process, and what information is given, in what priority? Does the page list the person and grievances against them first, does it have a space for the person's defense, does it show the votes for and against (people tend to vote with the "winning" side - so an early imbalance, even if not based on factual evidence, can influence a swell in public opinion and manipulate the voting). Does it rank these kinds of resources by how much they're verified, how much they're viewed, what kinds of things they directly said or participated in, or what things other people are saying about them? Does it include the context and behavior of the accusers?
Context is key. Context is key. And online presences can be manipulated in a lot of ways, both legitimately or covertly. The voting will not decide whether the person is exiled to another planet or not - the process for deciding what context will be used to show Joe's life and character, and the grievances against him (and the actions and characters of his accusers) will influence the vast majority of people into voting one way or another. The contributions from those who know Joe and are themselves for and against him, and the contributions of those who carefully researched and weighed the evidence and judged him - are both going to be overwhelmed by the huge numbers, the majority of the world's population who haven't met him, and don't really know what's going on, but are influenced by popular opinion and the context in which he is presented.
Just take a look at online witch hunts - proof is a lot less important than how something can be made to seem.