There have been a number of ideas to allow a Brainstormer to dispute the ranking of an idea as being a duplicate.

But not many of these ideas for "having the function" of disputing a duplicate, include some ideas or suggestions as to "how" this might be done.

So here are some possibilities;

1) Where the duplicates are listed in the idea, there is the duplicate report link;
" [Report a duplicate and merge its votes to this idea]
"
When this is clicked on, a box appears for you to type in the number of the idea that you think is a duplicate (Note there is no option to choose Which of the two ideas is a duplicate of the other).
Just as simply as this, and using slightly amended code for this feature, there could be another link (below) for;
" [Dispute a duplicate and separate its votes from this idea]
"

2) Now the admins are probably keen to make sure that nothing happens without consulting them (even though the Brainstormer never got consulted before their idea got marked as a duplicate, by another Brainstormer who usually doesn't consult them either - but may leave a comment afterwards).
So allowing for reasonable courtesies, the admins could receive the same form of notification of a "disputed dup" as they currently do for a "reported dup" (using similar code).
They could then email/message/comment the Brainstormer and ask for them to explain, or tune up their idea description to make differences and similarities to the dup(s) clearer.

3) The "report a dup" process could do with a small tweak, that Does consult the Brainstormer Before marking the idea as dup. Such as sending them a message, and requesting a timely response.

4) The definition (or broad understanding) of what constitutes a "duplicate" could be explained in a very necessary "help" section on the menu.
But ideas for "different solutions" to same problems, should not be considered a duplicate, any more than the answering of a question with a "yes" is a duplicate of an answer with a "no" (purely on account of they were answers to the "same" question).

5) When a dup is reported, the details of the reporter should be noted. These may or may not (according as what may seem appropriate) be publicly viewable.
But this information would enable admins to detect overly zealous dup reporters, and be able to contact them if needed.
Plus if dup reporters are found to be far less accurate in their reporting of dups, then they may be offered temporary restriction of duping privileges. These may be learners, who just need a bit of time to learn that refereeing is probably not the realm for the new players.
Also, accurate and fair dup reporters, could be invited by admins to help with "moderating" the dup and dispute process.

Note:
Ifr you know of similar or related (non-duplicate) ideas, then join them to the "idea group" called GGG0000002-dispute by adding that GGG# name to the tags for idea. Then all related ideas in that group can be found by a tags search for that tag.

view (and Vote) Idea ;
Idea #11885: Method to "associate" "related ideas" & to form "idea group"s -will work for now.
http://brainstorm.ubuntu.com/idea/11885/