You're shown the type of rule violation (with definition of the rule) claimed and a copy of the potentially offending post with no names attached. Sometimes you'll see a string of three or four posts along with the one that's been alerted. You read the post and mark if you think the rule was violated. If you're unsure, you can opt out before entering your vote and someone else will be called hpon. You never know who the other judges are and vice versa and you don't even know how the vote turned out. If a majority think the specific rule was violated, the post is removed.

Usually takes a minute or two total.

after a post has been alerted. First, the time commitment is very brief. You will be given the post that has been alerted as well as the immediately preceding posts for context. It generally takes only a few minutes to read this and make a decision whether the alerted post should be hidden or left standing. Jury service is anonymous so no will know that you served or how you voted.

After you have read the posts, you will again have the ability to opt out if you are uncomfortable judging the posts. Serving on a jury is an opportunity to serve our community by keeping our posts within the TOS policies as well as insuring that our discussion are welcoming to all posters.

Each "jury service" is only for the post that was alerted and for which you got the invitation. Once you've completed jury service (by either rendering your vote on whether not the alerted post violated the given rule, or by opting out), you're done. It should be noted, however, that as a DU member apparently in good standing, if you do jury service once I think the chances of being invited again will increase. Which isn't a bad thing. It's a small way to give back.

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If you choose not to participate and do not wish to be asked in the future you can so designate on your profile and you will not be asked.

And that you have over 18,000 posts.

Is this the first time in 20 years you were asked to serve on a jury?

Well now you have a good idea from the responses what it entails.
Have you made a decision about participating on a jury in the future?