First of all, there are two broad categories of suspension: site suspension and chat suspension. I will address each of the separately.
Chat suspension
This is a suspension that is applied to your chat user. It doesn't block you from using any SE site and, in fact, it isn't even linked to any SE site. The SE chat system is shared across all sites in the SE network. With the exception of Stack Overflow and Meta Stack Exchange, who host their chats on http://chat.stackoverflow.com and http://chat.meta.stackexchange.com, all the rooms of the various sites are hosted on http://chat.stackexchange.com. This also means that all moderators of the SE network are chat moderators and any one of them can apply chat suspensions to any user from any site.
A chat suspension means that a user cannot participate in chat until the suspension is over. The user can still use the main sites normally, they just can't chat. Since these suspensions only affect chat, they are not treated with the same gravitas as site suspensions. For example, they can be issued automatically when multiple users flag something in chat as offensive. Then, the system will give a half-hour suspension to the offending chat user.
Alternatively, any moderator on the network can choose to suspend a user from chat if they feel they are being disruptive or if they are behaving in a way that breaks the Code of Conduct.
There are no clear cut rules about these suspensions since it's not really possible to have rules covering all eventualities. The details are left up to individual mods' discretion. However, it usually just comes down to "be nice" and "don't be disruptive".
Site suspension
These are the serious ones. When your user is suspended from the site, you cannot ask or answer questions. This sort of suspension can only be given by the site's mod team and by SE employees. Site suspensions are always accompanied by an email (and also a site inbox notification) from the mod team that will give the reason for the suspension. The suspended user can respond to the email to defend themselves if they feel the suspension was unfair. It isn't even possible to suspend a user without an email, the SE mod interface doesn't allow it. The only way we can suspend is by sending an email explaining the suspension.
As for when we suspend, the rules are relatively simple: if you break the code of conduct or other rules of the site. The most common reasons for suspending users (in no particular order) are:
- Sock puppet shenanigans. A user has created multiple accounts and is using them to upvote their main account. Or, more generally, a user has multiple accounts and is using them to do things that would be impossible with a single account (down/upvoting posts multiple times, getting around a question ban or suspension, generally trying to game the system).
Vote shenanigans. A user keeps voting for another user. This can be upvotes or downvotes. While moderators cannot see who voted for whom, we do have access to general voting trends and tools that alert us when something looks fishy. Voting based on who posted instead of what was posted is against the spirit of SE and if a user insists on doing so, they may be suspended.
Rudeness. If a user is consistently rude or aggressive towards other users, the mods can choose to suspend them. Again, this is down to the discretion of individual mods. There is no way to define a clear threshold of rudeness after which a suspension will be applied. So we need the judgement of a human.
- Defacing the site. A user who defaces posts (bad edits, hate speech, spam, even excessive deletion of your own content) can be suspended if they ignore moderator warnings and continue in their destructive behavior.
- Anything else that is harming the site. Users who are being disruptive can be suspended to protect the site. This includes spammers, trolls, people who consistently post poor quality content etc.
In all of these cases, unless what you are doing is just blatantly bad, the mods will give a warning first. Our first recourse is always telling the user they're doing something wrong and we'll only suspend if they ignore that warning and persist in doing whatever it is they're doing. Of course, if a user is doing something really bad, we may go straight to a suspension, but those are the cases where the user knows exactly what they're doing wrong.
As for the length of suspension, this is the guidance the SE interface gives mods:
- First (serious) offense: you get a 7-day suspension.
- Second (serious) offense: 30 day suspension.
- Third (serious) offense: 365 day suspension.
Also, for the first not so serious offense, the usual reaction is just a mod message letting you know you crossed a line and no suspension.
Now, the details will always vary. Mods are humans and able to apply their own judgement. This is actually precisely why we're here: as human exception handlers, and suspending users is very much an exception. This means we can choose to give a shorter or longer suspension as we feel is merited. There are no strict rules about this sort of thing and there can't be since the details will always be important. Someone who posts a comment using racial slurs and threatening physical harm will be dealt with much more heavily than someone who posts a comment calling another user a jerk. But, obviously, you cannot have a set of rules that says something like "jerk=1day, asshole=4days" etc. There will always be judgment calls.
In conclusion, there are no published suspension policies for the same reason there are no set sentences for crimes in real life. Just like you need a judge to make the call for how long to send someone to jail for, or a school principal to decide how long to suspend a student for, you need a human to make the call for how long to suspend for. And, just like in real life, there are guidelines that help make this decision, but these are not set in stone and cannot be 100% specific and unchanging.