This question is purely out of curiosity as to how the moderators do their work.

Suppose that someone was suspended for a month, and they decide to remove their account altogether.

After the month has passed, they open a new account (so there is no issue of ban circumvention). But since people can't change who they are, the user is again suspended. And by that time, of course, the moderators already know who the person is behind the user account.

Is the suspension of the new account given as a first offense (i.e., a couple of days), or do the moderators continue from the previous account?

There are two cases to consider, the first is that the suspension is given for something unrelated to the previous suspension; or when the suspension is given for the same reason the original account was suspended for.

I'm looking to understand the possible reasons (e.g., the user is trying to start over, versus the user is fully aware of the severity of the offense) for choosing one punishment over another.

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    $\begingroup$ Do moderators identify suspended users to the IP address level, or just by email account, or...? If email, what if user denies being the same person when using a different email? (I'm just curious about these I think relevant related points) $\endgroup$ – gnometorule Apr 2 '15 at 15:09
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    $\begingroup$ @gnometurtle: Well, good questions, albeit my interest lies in the case the moderators already have sufficient evidence. $\endgroup$ – Asaf Karagila Apr 2 '15 at 15:11
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    $\begingroup$ @gnometorule Moderators suspend accounts. But they have tools (involving IP address information) to find out whether two accounts are likely used by the same person. $\endgroup$ – user147263 Apr 2 '15 at 15:27
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    $\begingroup$ @pizza: Forgive me if this is "off-topic", but I thinks "pizza" is your best moniker to date! Helpful comment, by the way. Cheers! $\endgroup$ – Robert Lewis Apr 4 '15 at 6:02
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    $\begingroup$ @pizza What about shared computers or IP that is shared by many users, like in many universities? As a matter of fact, I'm using a shared IP; IP address information can be unreliable. $\endgroup$ – d80d2729a352b1366139fc119d3345 Apr 6 '15 at 8:15
  • $\begingroup$ @Fermésomme I'm sure they're aware of this fact and have already run into this issue. There's more than just IP that can be used to detect multiple accounts. None of them are perfect (if you really want to bypass it just use tor and close the browser each time you logout), but they can help in some cases. $\endgroup$ – Najib Idrissi Apr 6 '15 at 8:27
  • $\begingroup$ Sometimes many distinct users, with different behaviors on the site, may connect through the same IP (for example, if many users are using a corporate proxy which assigns the same outgoing IP to all). In this case, banning by IP would be very unfair. I just want to support @Fermésomme on this. Please, don't ever ban by IP, you may affect devoted users of this site. $\endgroup$ – becko Apr 13 '15 at 12:56
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    $\begingroup$ @becko The system isn't as simple as "this IP is not allowed". If you're a registered member in good standing, that fact trumps the IP you have. $\endgroup$ – user147263 Apr 13 '15 at 15:15
  • $\begingroup$ @pizza That's reassuring. But what if a new, innocent user, tries to create a new account from an IP that has been banned due to another user sharing the same IP? $\endgroup$ – becko Apr 13 '15 at 15:37
  • $\begingroup$ @becko Then they are probably going to be limited in some way (1 question / week?) until their account is established enough to be trusted. It's the only way bans can be enforced at a place where nobody knows you're a dog... Users suffering from collateral damage sometimes contact SE via contact us form so that things can be sorted out manually. $\endgroup$ – user147263 Apr 13 '15 at 16:52

Is the suspension of the new account given as a first offense (i.e., a couple of days), or do the moderators continue from the previous account?

It depends on the type of offense. Say the user was suspended for being rude on his old account, and had a 7 day and then a 30 day suspension. Then a new account comes, and the user is again rude. This would escalate to a half year or year long suspension. But suppose now the user was creating low quality posts, say. Then it might have to be discussed whether to escalate the suspension or start with a new tally.

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    $\begingroup$ Thanks. That is what I was looking to learn! $\endgroup$ – Asaf Karagila Apr 5 '15 at 7:06

There are no hard rules with suspensions, there are guidelines, but moderators can deviate from them based on the particular situation. The official guideline from SE on suspension lengths is to start with 7 days for the first suspension, 30 days for the second and 365 days for the third suspension. In most cases there are warnings about the behaviour issued before the suspension, either in comments or in a moderator message.

I don't think it was ever explicitly declared by SE, but my understanding is that the rules apply to a single person, independent of how many accounts that person uses. I don't think it makes sense to interpret it any other way.

Users trying to start over by using a new account are not really handled any different. As long as they don't cause trouble again, they're free to do so and start from a blank slate (even though the moderators might know that they're an old, deleted user). But if they cause trouble, the whole history of the person is taken into account.

There aren't many completely independent suspension reasons, very often there is not a single problematic behaviour but a combination of multiple ones that leads to a suspension. In cases where the new problematic behaviour is entirely different from the behaviour that caused prior suspensions, I'd probably warn the user first, and not suspend immediately. But when I'm at a point where I consider a suspension necessary, I'd take the history of the user into account, and it doesn't matter much if the previous suspension was for a different reason.

This is from the perspective of a moderator a different site, but I don't think the Math.SE mods deviate strongly here from the rough moderator consensus. But suspensions are handled individually, and many factors affect the final outcome. There are no hard rules, and each moderator might make slightly different decisions.

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    $\begingroup$ Thanks for the enlightening answer. I'll wait to hear from our site's moderators. $\endgroup$ – Asaf Karagila Apr 2 '15 at 17:53

Your question brings up a few points that I want to clarify, ranging from philosophical to rather technical. I'll try to keep it as brief as possible.

Suspensions are a tool available to moderators that allow them to resolve disruptions with the least amount of intervention possible. While the system recommends a length at which they might suspend a user, the choice is left to the moderator. The only guidance that we provide is to select the amount of time they deem appropriate to cause the behavior to stop; the length of a suspension in no way needs to be commensurate with the actual infraction it's designed to address.

The ugliest of arguments can, in many cases, be addressed with a 24 hour suspension being issued to all participants. We also make it clear that we're not trying to punish anyone, we just want to ensure that all involved have ample time to cool off.

Lengthier suspensions are common only when multiple suspensions have been issued previously. Even in those cases, the increased length is simply moderators trying to find the right amount of time for you to be away from the site in order for the behavior to stop. When that starts getting longer and longer, and there's no sign that a user will once again sit down to play chess instead of throwing the pieces around the park - it's time for them to leave.

Moderators have a special reason they can select when deleting an account:

This user is no longer welcome to participate on the site

They must also give a reason for this, a short explanation in the same form. Once initiated, our abuse mitigation systems begin tracking things and said systems are quite good at preventing users that have gone so sour that all they want to do is cause disruptions from doing so.

There's also another caveat to suspensions - if you request account deletion during a suspension and return to the site within the period you were supposed to be suspended, the system will re-issue the suspension in a manner that causes you to wait until the original suspension would have lifted. These anti-recidivism measures were put in place precisely to curtail folks that just kept recycling accounts to get around restrictions.

Now, if this is somehow tied to multiple accounts that the system didn't manage to piece together on its own, we can and will merge them all together, if those accounts are continuing to be problematic. That is to say, if you were suspended four times, and then one day showed up and just started contributing valuable things to the site in a way that didn't annoy anyone - I'd say the minimal amount of intervention was whatever it took for that to happen.

In short, in all but the rarest of exceptions, when the behavior stops, so does any grudge we once held against it. If, in the course of causing disruptions, a user did something we just consider categorically unforgivable (you can't really describe it, you just know it when you see it, a death threat would be one example) - then we would just continue to destroy their accounts as we found them and ramp up the abuse mitigation layer on affected sites.

It's hard to give a blanket policy because the only thing mods can do is evaluate each user as a unique case, and do what they feel is the minimum amount necessary. But, the information I gave above is a pretty good insight into how those decisions would be made. Each mod is different as well, and they are (so long as the majority of their community and fellow moderators support them) free to moderate their sites as they see fit. There's also the question of escalation, if we (Stack Exchange) have to get involved, then we also become part of that decision making process.

Wait, I think I remembered saying something about being brief, sorry about that.

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    $\begingroup$ Thank you Tim for that answer. It's quite interesting. $\endgroup$ – Asaf Karagila Apr 6 '15 at 11:10

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