So this is just a general question I have about AskUbuntu. I have seen 2 badges and there are possibly more, in which you have to delete your own question to be able to achieve. However, when I go to delete a question, I am greeted with the warning "Deleting questions may result in a ban from asking questions" or something like that, but that shouldn't be right. If the purpose of deleting questions is to obtain a badge, there should not be the potential risk of getting banned involved!
There are 2 such badges.
Peer Presure: Delete own post with score of -3 or lower.
Disciplined: Delete own post with score of 3 or higher.
None of the badge is specifically for deletion of a question. They can earned either by deleting a question or an answer.
When an off-topic or poorly written question or answer is posted on the site, it generally attracts downvotes. By looking at the downvotes, it can be judged if the post is helpful. Self-deleting such posts would award a badge. While the purpose of earlier said badge is clear, but what about being disciplined. The purpose of being disciplined was asked on Meta Stack Exchange and Super User Meta.
As per Shog9's answer:
Here's a scenario I've been in many times: I post a quick answer to a question. It's accurate and reasonably helpful, and therefore collects several up-votes. Then someone else posts their answer... The extra time they spent on it clearly shows: it's comprehensive, easy to read, links to tangential-related information, includes good code samples...
And so I delete mine and up-vote the new answer. Maybe edit it a bit, to include something from mine that I feel would benefit it.
End result: the question gets a single, solid answer. The other guy is rewarded for the extra effort he put into it. I'm rewarded with... the satisfaction of a job well done.
And maybe a badge...
Now coming to the ban. Getting a ban isn't triggered by merely deleting one post (AFAIK). Your all activities are monitored and it is observed how helpful are your questions or answers. If you try to delete multiple helpful posts you might even get suspended to cool down.
So, I'll advise to delete those posts which you think are very bad to avoid ban and suspensions. :)