How can a group of programmers sort their opinions and come to consensus on the best answer?

Our organisation is faced with a difficult problem to solve, where there is no "right" answer. Each solution has many advantages and disadvantages.

I have given a group of programmers a questionnaire and collected their detailed opinions on many different issues related to this problem. They all have very, very different opinions of the possible repercussions of each solution.

Next week we will all meet to put our brains together to settle on one way forward. I will be leading the meeting.

Can anyone suggest a process by which I can put everyone's opinions on the table, and have everyone sort through them and comment/rank/sort answers to help the group come to consensus?