Does order matter when distributing resources?

Imagine that you are a government official responsible for deciding how state money is spent on different medical treatments. Your budget is limited so you cannot afford to offer treatment to everyone who might benefit. Right now, you must choose to spend money on one of two treatments.

  • Treatment A treats a life threatening illness. It saves patients' lives and returns them to perfect health after treatment
  • Treatment B treats a different life threatening illness. It saves patients' lives but is not entirely effective and leaves them with paraplegia after treatment. These patients are entirely normal before their illness but after treatment will have paraplegia.

Suppose the state has enough money to offer Treatment A to 100 patients. How many patients would have to offered Treatment B so that you would have difficulty choosing which treatment to offer?