# Weitzman’s The Noah’s Ark Problem

“The “Noah’s Ark Problem” is intended to be an allegory or parable that renders a vivid image of the core problem of maximizing diversity under a budget constraint. What is treated here is actually not the most general form of the underlying mathematical problem. Some slight generalizations are possible, but they would come at the expense of diluting a crisp version of the basic paradigm. Noah knows that a flood is coming. There are n existing species/libraries, indexed i = 1, 2,… , n. Using the same notation as before, the set of all n species/libraries is denoted S. An Ark is available to help save some species/libraries. In a world of unlimited resources, the entire set S might be saved. Unfortunately, Noah’s Ark has a limited capacity of B. In the Bible, B is given as 300 x 50 x 30 = 450,000 cubits. More generally, B stands for the total size of the budget available for biodiversity preservation. In either case, Noah, or society, must face the central problem of choice. A basic choice question must be answered. Which species/libraries are to be afforded more protection-and which less-when there are not enough resources around to fully protect everything? I present here the simplest way that I know to model the analytical essence of this choice problem. ” The ‘Noah’s Ark Problem’ is a parable intended to be a kind of canonical form of the simplest possible way of representing how best to preserve biodiversity under a limited budget constraint…

…The solution of the Noah’s Ark Problem is always “extreme” in the following sense. Noah, or the conservation authorities that he symbolizes, should be concentrating all their resources on maximal protection of some selected species/libraries, even at the expense of exposing all remaining species/libraries to minimal protection…

…The ranking formula (29) encourages the conservation authorities to focus on four fundamental ingredients when choosing priorities: Di = distinctiveness of i = how unique or different is i; Ui = direct utility of i = how much we like or value i per se; APi = by how much can the survivability of i actually be improved; Ci = how much does it cost to improve the survivability of i. I am not intending here to argue that it is easy in practice to quantify the above four variables and combine them routinely into the ranking formula (29) that defines Ri. The real world is more than a match for any model. The essential worth of this kind of research is to suggest a framework or way of thinking about biodiversity preservation, and to indicate how it might be backed by a rigorous underlying formulation.

-Martin L. Weitzman, “The Noah’s Ark Problem.” Econometrica, Vol. 66, No. 6 (November, 1998), 1279-1298.

RIP, Martin Weitzman. I cannot remember another paper with this much math in it that was still accessible to a lay reader like me. Also, it strikes me that this theoretical model could be applied in other areas of life, such as friendships.