Kenneth Arrow’s impossibility theorem, which earned him the Nobel Prize in Economic Science in 1972, proved that no voting system can satisfy a limited set of rational and reasonable conditions. That’s sad, but, still, several methods to vote exist, flawed though they may be.
One is the preference intensity method, also known as proportional voting. If each of six in-house lawyers who are evaluating the proposals of firms for a panel can allocate up to six votes to a firm, that is proportional voting.
Another group of methods, collectively referred to as rank-order voting, has at least five variations to determine the winner. (1) Most first place votes; (2) runoff between the top-two first-place vote getters; (3) survivors, where you drop the firm with the fewest first place votes and then reexamine and reallocate the votes to the remaining firms. A vote for a dropped firm goes to the next choice of that voter; (4) numerical total, where for example each voter’s first place firm gets 5 points, second place gets 4 points and so on and you add up each firm’s points; and (5) head-to-head matchups, where each firm goes against each other firm and the one with the most victories is the winner.
Law departments should be aware of these ways to reach a decision based on one person, one vote. More on these methods can be found in James Stein, How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics (HarperCollins 2008) at 207-220.