Thanks for sharing that really interesting idea!
It reminds me a bit of Canonizer, but for solving problems rather than quantifying opinions on specific questions, and with a slightly different approach.
In any case, the weighting algorithm seems to be the core piece of this software. With the quality of that algorithm the idea will be a success or a failure. So, let's see how the algorithm has to be designed.
I see one major problem: I assume that at least some people tend to favour certain solutions for ideological reasons or reasons that don't have to do with any of the proposed arguments. These "solution fans" will vote every argument in favour of the proposed solution up, no matter whether it's good or not.
An attempt for a possible solution to this problem is to make the algorithm so that changing your vote for the arguments doesn't impact your vote on the solution. Each solution would have a "solution score" and an "argument score". But it wouldn't really solve the problem, because the solution fans would still skew the argument score by still upvoting all arguments in favour of the solution!
Another attempt to resolve this issue: For every proposed solution you have a fixed quota of votes which you can allocate to the different arguments. So, you would want to use your votes on the very best or worst arguments. Alternatively, you have a normalized vote power of 1 for each solution (or else, depending on your reputation) and this vote power gets distributed over all your votes. So, if you do 7 upvotes and 3 downvotes, each of those votes will have a power of 0.1 (perhaps the power is also dependent on the depth of the tree, not sure whether that's a good idea). So, every time you use another vote, it will reduce the power of the votes you've already used.
The software should be used to inform decision-making, not to automatize it.
After all of these considerations the idea still looks promising. Of course, it needs a good name. Perhaps something like
- Crowd solver
- Decision forest (well, it's made out of trees)
- Swarm solutions