If I have a question, and it is marked dupe, the system should check to see if it was offered as a related question when the title was being typed (simply by using the same search feature that the AJAX uses), and if my title doesn't match against the dupe in the related searches, the question should not be closed as dupe. If it's not offered, then one of two things happened. Either, A) the question wasn't close enough to be considered dupe, or B) they were similar but value exists in leaving both up for the differing titles (some people ask similar questions if varying ways and passers by may never find version A in their search but they would have found the "dupe" if it were left alone and answered appropriately).
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There's a problem with this approach:
Duplicate questions can share no words in common, and if not tagged properly, won't show up in the related search column.
The "Related" column depends heavily on the title as well as the tags in the question.
Example 2 (duplicate of Example 1):
Those two will likely not show up in the related search, even though they are duplicates.
Why not? It's still a duplicate.
I think the problem is that some people think that having a question closed as a dupe is some sort of punishment. Closing it is an attempt to concentrate the knowledge present on SO and avoid duplicate (duh?) effort of people writing answers. It's not because something is particularly wrong with the question.
What to do about this?
There seems to be a couple of fundamentally flawed assumptions here. First, that the computer is always right, while a human looking at the same data is wrong. Second, that the person asking the question actually bothered to read what the computer suggested might be duplicates before posting the question. In the first instance, when it comes to math I usually believe the computer is right and recheck my math first. When it comes to subjective interpretation, though, I'm much less trusting of the computer's (the algorithm, in reality) judgement. In the second instance, user's don't read.
This is one of the reasons that Stack Overflow is heavily community moderated.
You mean not close enough to be considered a dupe by the software that does a cursory check for exact duplicates. That doesn't mean it's not the same as another question.
This part is exactly right. We do normally leave duplicate questions that are worded differently on the site. That is, we close them but don't delete them. The reason for this is exactly as you stated, so other people using the same keywords as the second question can find it. Note that a link to the original question is automatically placed at the top of the post whenever a question is closed as a duplicate. This is to ensure that people can find the original, even if they searched using different terms.
When two version of the same question have very dissimilar wording, we have a good candidate for leaving the later case undeleted because that improves the searchability of the site.
But it is still a duplicate, and we still want to have only one canonical version of each question. Accordingly, differently worded duplicates should still be closed.