I would not. Many times duplicates are created because:
Title of question is not well formed so the person that created the duplicate could not find it easily or quickly (Reason why he/she ended up creating a duplicate).
The OP did not take the time to look in all first 100 questions that might have been similar. Only on the first 10 and none of those first 10 solved the problem. But guess what, question number 42 was the answer.
Op did not take the time to even see that the first question that appeared as duplicate while typing the title was the actual solution (This are the ones that do not even take the time to use the search box but can wait 5 days for the answer to their question).
So as you can see, an OP could fall in any of this options (There are more am guessing) so marking them with a downvote (Which I also consider it should be used only in some cases and not in a happy down vote everybody way) without knowing how much time the user took to make the question, if he/she did a search first or just basically how much effort it was put on the question is wrong.
I would first see the question, see if it is easy to find a duplicate, which tells me that the OP did not even take the time to search for it. I would also read the information about the question to not jump into the conclusion that it is a duplicate of another when it just so happens it was not.
As you can see there are several points that could argue not to do the downvote in the first place. Are there questions that deserve a downvote? Yes. Are all duplicates in need of a downvote? No. We need to first study the case before downvoting like it was something easy to do.
In case it was not pointed, downvoting also implies that you are completely against the question/answer, how it was made (Spam, Negatively, Not an actual question/answer, Etc..), not just that you disagree with it.
If you simply disagree with the question or answer at hand, you would use the comments for that, not only to correct the user, but to help improve the situation. Downvoting simply jumps to "I do no agree in any way to what has been written here" and does not add any helpful feedback for the user.
Again, the main point is knowing what question/answer should be downvoted and why. Important part is why. In my case I personally avoid downvoting, I rather help the person, point them to the right direction. If the question is a duplicate and is obvious it is, then yeah, I would simply mark it as duplicate and be done with that (No need to downvote). If the question needs more information or a better format I tell the OP about it (No need to downvote).
Will of all that said, I think you get my idea of how I view the use of votes and how one can approach other users to help.
Example of a question that could have a downvote - Install drivers
But can also get some assistance (And a kick into FAQ land)