If I post a question after searching and determining it hasn't been asked. And later find out, on my own or by a fellow user that the question is a possible duplicate. Is it encouraged to delete the questions, or should I wait for the consensus of users that vote to close it ?
DO NOT DO THIS
I'm sorry for shouting, but I've wanted to say this to a few people recently; I got a bit excited.
There are a couple of reasons you shouldn't do this:
Your question may not end up getting closed. For a recent example, see In Star Wars: "The Force Awakens," how could this lightsaber have turned up where it did? and How did Maz Kanata acquire Luke's lightsaber? (but don't if you're avoiding The Force Awakens spoilers). There was a bit of a debacle around these, but there was a time when each had close votes pointing to the other. Obviously only one of them got closed (and then re-opened and the other closed, but that's a different story). Either JMFB or RedCaio could have deleted their questions upon getting close votes, but they shouldn't have, because nobody knew which would end up getting closed.
Admittedly, this is probably more true for questions where the dupe and the original were posted at similar times. Still, its worth noting that we don't necessarily close the newer question in all cases.
There are also a number of cases where duplicate close votes are disputed by the rest of community. To coin a phrase, a single close vote does not a duplicate make.
By far the biggest reason is that having the duplicate question up makes it easier to find the original. Obviously the original wasn't terribly easy to find, since you weren't successful in your search. With your closed question, there's now a whole new collection of searchable terms floating around the Internet, with a great big neon sign pointing to the original question (and answer).
In other words, you just made the question (and its answer) much easier to find. This is a good thing.
Closed questions aren't counted terribly harshly against you when determining a question ban. However, deleted questions definitely count against you, especially if they make up a large proportion of your total answers; quoting that FAQ I linked to (links in the quote are preserved from the source):
It's not a problem to have deleted posts. But if a large percentage of your posts are deleted by yourself or the community, then apparently they are not suitable for the site. Posting them consumes time from users who read them, edit them, or respond to them. Therefore deleted posts have an effect on the filter, among many other factors
As far as I can tell, there are two reasons why a user would feel pressure to delete a question that has close votes (or has already been closed):
The view that closure is a censure. To users who aren't excessively familiar with the SE network (and even to some who are), a close vote feels like a rejection. It can feel like the question is undesireable, when in fact it is not. I suspect that many users see a "Possible duplicate of X" comment as implying:
What the hell is wrong with you? This has already been asked, why are you asking it again?
So the natural desire is to delete it; the question has already been asked, so what benefit can it possibly be adding to the site?
Of course that's a false assumption, which is the point I made earlier in this answer. There's probably some room for user training on the benefit of having duplicate questions, but that's a different issue.
The view that closed = bad. This is problem both for askers and for voters. For askers, the issue is similar to the above:
Oh, I asked a bad question. I should delete it.
Relatedly, there may be the expectation that a duplicate question is going to be downvoted. This is probably not such a critical issue in practice; while there may be many duplicate questions that have attracted some downvotes, according to this SEDE query (inspired by phantom42 doing something similar in comments), only 130 of our duplicate questions have a negative score.