My opinion on the matter is that there should be absolutely no player-to-player influence on beacons that can occur unless there is a prior relationship established. Examples of prior relationships would be shared beacon control, guild relations, and being on friend's lists. I am not saying that these three relationships should automatically grant influence/control over one another's beacons! They are just examples of the only acceptable relations if there were to be any voting system established. Personally, I think any voting system is a terrible idea because there's too many chances for groups of people to influence the people that want to be alone. Guilds and such will already have inherent benefits, they don't need another power to exert on noobs.
In addition to the previous thought, I'm surprised that people are even considering the beacon system as a means of controlling griefers. People who are honestly griefing, just like in any other successful MMO, should simply be able to be reported and dealt with immediately. Trying to make a system where all of the rules are known and must be followed by everybody the same gives the developers an impossible task of thinking and anticipating EVERY way that one may grief other players. The status quo is what it is for MMOs because of this exact point. People are creative, and they'll find ways to mess with the system no matter what. We just have to count on good communities and a simple system of reports. If anything, I guess this is a type of "vote". When one player is caught griefing and gets reported for the same thing enough times, they're punished.
Why the last system? Because of my current situation. I don't have time to get on and play like I want to right now. But, I know that in about 5 weeks I'll be able to play a lot. I can get on and find some fuel to keep my creations active, but I couldn't get on and create social ties that would ensure the people around me didn't vote my beacons away. It's just not fair to the people who are in these situations if their beacons can be influenced in any way by others.
Another example that serves the same point is that I have found areas that I want to build specific builds on. I want those builds made out of specific materials, and it takes time to gather those materials. Sometimes, I want to claim an area for the sake of claiming it until I can find the right mats. If others were able to vote away my beacon because I didn't have anything there for a time, then what's the point of having beacons to claim land in the first place?
I'll just restate my main point here for the devs: PLEASE do not give players any control over other player's beacons. I honestly think that any control, or "votes", you give to others will cause more problems than it fixes.
If people didn't like a player's beacon, then let them send a message (in limited quantities) asking them to move it. But don't institute a system in which the player who owns the beacon can lose his beacon or stuff without his lack of attention.