You have the unenviable job of chairing this meeting of the IAU `New Facilities' committee. You have to get this fractious bunch of ego-maniacs to come to a consensus on which new facilities should be funded, to advance our knowledge of galaxy formation and evolution. You are a group of astronomers from various small institutions in Europe, Asia and South America.
Everybody here will have a pet instrument or telescope they want to promote. They will also have some particular science questions that appeal to them, and some special expertise in particular areas of high redshift research.
Your job is to get them to focus on the science: get them to think not purely about getting their own instrument or facility funded, but about what we, the human race, want to know about the early universe, and how we can best use our limited resources to learn these things.
You have to get this group to come up with a ranked shortlist of the five best proposals. If you just take a vote at first, everyone will probably vote for their own ideas: every proposal will get one vote, and the whole meeting will collapse in acrimonious failure. You will have to think of how best to manage the process of getting a consensus. You could let people vote at the end, but not for their own project. You might try and force the different groups to join in consortia to propose particular shortlists. You might try a preferential voting system, or simply try and steer the discussion with assertive chairing. Perhaps you should assemble sub-groups made up of representatives from the different institutions to discuss separate issues (eg. infra-red vs. optical, or ground vs. space).
In the final session, you may with to get representatives from each group to stand up and make brief presentations, before calling for some sort of decision. This might be dangerous, however, as it could lead to a hardening of negotiating positions, and make finding a compromise acceptable to all impossible.
You should talk to all the various groups repeatedly as they work on their proposals, and keep tabs on any consensus that might emerge. Hopefully you can spot fights before they start and pour oil on the troubled waters.