Some/many users seem to quickly downvote a question once they see that it's been marked as either a duplicate or a possible duplicate; is that the recommended course of action - to downvote a question simply because it's a duplicate question?
While voting is anonymous and users are of course free to vote however they like...
Users are not necessarily encouraged to downvote questions purely because they are duplicates.
Voting up a question or answer signals to the rest of the community that a post is interesting, well-researched, and useful, while voting down a post signals the opposite: that the post contains wrong information, is poorly researched, or fails to communicate information.
Duplicates can be a good thing in a way, so questions do not become 'bad' questions simply because they are duplicates. A question is not necessarily poorly researched just because it's a duplicate, as finding the duplicate before asking can be very tricky due to the different possible wordings of the same question. Once a question is marked as a duplicate, "often they are left as a signpost pointing people towards the canonical answer to that question" (source), so in that way, they help future users search for and find the information they are looking for. For more on why duplicates can be a good thing, see Is it encouraged to delete your own questions if they have possible duplicates? and Rules for a duplicate post deletion
The two most upvoted answers (scores 44 and 19 respectively) from the MSE question Should we downvote duplicates? both indicate that, while still a perfectly acceptable thing to do, downvoting duplicates isn't the most helpful course of action:
I have several times asked a question that the "similar questions" search did not identify that I later found to be a duplicate of an existing question when someone pointed it out. I think, then, in the general case that a downvote is probably not appropriate because it is entirely possible that the user did search and did not find a question like their own in the list. The best solution is merely to close it with the reference to the existing question unless the question is bad in some other respect.
Downvotes are not meant to be used as punishment. That being said, they are your votes, and you should use them as you see fit. (Leaving a comment telling the user to search harder next time will probably be more helpful than a downvote.)
- You're free to vote how you choose
- Leaving a comment is much more helpful than downvoting a duplicate
To clarify: Obviously users are free to vote how they please, I am simply trying to make a helpful recommendation on voting on duplicates that is clear and accessible. The site recommends/encourages users to downvote non-useful things and to +1 useful things, and as the site's consensus is that dupes can be useful, they might not deserve a downvote just for being a dupe. Of course, it's up to each user to decide how they want to vote.
There are two ways to answer this question:
Users Should Downvote However They Want
Downvoting on Stack Exchange is anonymous for a reason. As long as a user is not abusively downvoting (that is, they are targeting a specific user, and not the questions themselves), SE has always quite openly asserted that users can downvote whatever and whenever and why ever they want.
The Help Center gives reasons why you might want to downvote, or why most people downvote, or what downvotes were invented for. But those are always just that: guidelines. (If we're going to start demanding everyone follow the guidelines to the letter, I have some scope and tagging discussions we can revisit...)
In the end, trying to tell users how to downvote is always wrong.
Duplicate Questions Are Usually Downvote Worthy
The bigger issue is that you're basically arguing against a strawman here. You somehow claim to know, for a fact, that users are downvoting a duplicate questions because they think they're supposed to. To repeat a previous point: downvotes are anonymous. You have no idea why someone's doing it. Even if they leave an explicit comment, they could be lying.
The vast majority of the time, duplicate questions deserve downvotes. The fact that the question has been asked and answered before by definition means that the answer could have been found with sufficient research. It's merely a matter of each user's personal judgement if they feel the level of research was justified or not.
A duplicate question that is 1) well written and 2) asked in a new, original, or unique way can stand on it's own as a decent question. Most dupes are not that. Most can be found in a trivial amount of time... most of them can be found by the software which suggests them when you vote to close.
People are 100% within their right to downvote those duplicates if they think the original question was "easy enough" to find. And they are 100% within their rights to define "easy enough" however they want.