Do people down vote questions simply because the question is a
duplicate of another question?
I do sometimes, but only if I believe the question is a definite dupe, and it showed absolutely no research effort at all.
If the dupe could easily be found, such as when typing the question title the "Questions that may already have your answer" shows the dupe clearly.
Or their title is so similar that they just haven't tried to search.
All that said, it is rare I downvote "only because dupe", because how do I know they aren't just terrible at searching, and I don't feel it right to penalise people for that, not on a "help" site.
it can be difficult if the title is phrased differently.
I do have sympathy for this, and sometimes have missed a previously asked question myself, even after searching for 20 mins with various keywords.
But, that's fine really. Someone good at searching or remembers a question will flag it and community will close as dupe, downvote, and we all move on.
No-one has been hurt, or lost any real money, etc.
I think that it is a problem that (if) this is happening because it
leads the asker to delete their question, which in turn makes it
difficult to find the original question with the answer, leading to
more duplicate questions.
But this works ok, because if it's a popular problem which would benefit from different question titles and keywords, then other users will also raise a dupe, and not everyone will delete their question, so eventually there will be a searchable dupe, or dupes.
Also there's not much you can do about this. You're not - you're absolutely never ever - going to change why people downvote, and (eg) some will downvote because it's a dupe, and that's their prerogative as it is yours to not downvote.
We all downvote for very personal reasons, and some most certainly will downvote because they're annoyed at something and see a dupe and presume lack of research - They woke up to find their cat prefers their work shoes to the litter tray...