Brian Martin describes a difficult committee meeting he once attended which consisted of one representative from each department. When the meeting ended it left a bitter taste for many who participated. Having learned from this experience, Martin became a chair of the committee and tried a new system that overcame many of the previous problems. The meetings for ranking scholaships and grant applications were shorter, and less contentious. The method is called "ranking by medians", and is currently used at the University of Wollongong for ranking scholarships at the university level. This article provides a discussion of how it works, and why it works. An example is also provided. Technicalities are provided in the appendix.