Suppose you were tasked with deciding the best way to invest $8 Billion Dollars in infrastructure projects in your city. Being the responsible, welfare maximizing decision-maker you are — you hire your best team of planners, engineers, and economists to go away and dream up a list of projects with their associated benefits and costs. Your dream team succeeds and comes back to you with 6 winning projects that should make the lives of all your citizens better. There’s only one slight problem — the total cost of your projects comes out to $27 Billion.
Still, it doesn’t seem like a big deal. Your team has kindly calculated benefit cost ratios for all your projects, so you know which projects perform the best. Evidently, the first thing to do is pick the best performing option – project number 4 – with benefits of $22B, costs of $6B, and $2B leftover to spend. Notice the next best performing option within your remaining budget is project number 3 — which just happens to cost $2B, netting you $5B in benefits. Overall you’ve generated a BCR of 3.375, and provided a boon to your citizen. Satisfied with a hard day’s work, and knowing that you performed your job as a responsible, welfare maximizing decision-maker, you go home and rest. Just as you’re about to go to bed it dawns on you, by choosing projects 6 and 2 you get total benefits of $28B for a cost of $8B, with a BCR of 3.5 – you question how a sure-fire method such as prioritization and ranking could have failed you so completely, depriving your citizens of $1B worth of value.
In maths this problem is called the knapsack problem, and prioritization is called the greedy algorithm for solving it. It is a problem of discrete optimization (combinatorics – the study of combining things), which is generally solved by a method of dynamic programming, which is a method for systematically breaking down big problems into smaller problems. Despite the known failures of the greedy algorithm for solving these problems, prioritization and ranking frameworks still dominate public policy. It might not seem like such a big deal in the above problem, where the optimal solution is readily apparent, but as the options increase the complexity of the problem increases dramatically.
In my opinion, the biggest culprits for why there isn’t staunch opposition to prioritization and ranking frameworks lies at the feet of economics. Economics doesn’t teach its’ students about combinatorics, because economics assumes that goods are infinitely divisible, and as such they are not discrete optimization problems. While these assumptions are largely okay for understanding the issues of economics and resource allocation, it needs to be explained that these assumptions are used to make relatively simple analytical solutions possible. In a world where you have to make choices between discrete options – economists simply aren’t equipped to handle these problems and drive the public policy framework towards more suitable methods.
For the curious: