Suppose you rule a kingdom.
Or, let's dream smaller for a moment: suppose you're the bursar of a college. Your job is to distribute gold to potential students according to whatever metrics you deem fit.
You have 50 gold, and each year of schooling costs 10 gold.
You could:
- Give 5 students 10 gold each, completely paying for their education.
- Give 50 students 1 gold each.
- Spread the gold out so that as many students are able to attend.
- Give gold to students in according to their need. Some bright, poor students might get 10 gold, wealthy students might get 0, and people in the middle might get 2, 5, or 8 gold depending on their needs.
Let's dig in.
- This approach is great for those 5 students, but it only helps 5 people. If you have any wealthy students who can afford it on their own (or especially if you have not-wealthy students who can barely afford it on their own), they may resent the 5 for getting handouts.
- This approach seems to benefit the most people, but not really: if a potential student only has one gold, they can't go to college. This mostly serves to help the students who can only scrounge up 9 coins, and it gives a bit of cushion to those with 10 coins, who likely don't need it. (see note 1)
- Realistically, this looks a lot like the approach above, except you try to find students who are only a gold or two short to attend. This won't help the students who have no coins, because giving one person 10 coins could mean that as many as 9 other students can't attend.
- This seems like the way to do the most good for the most amount of people. Some poor students might get 10 coins, while others who are only short a coin or two can get all of them. You still might have to balance between helping one student a lot and helping three students a little, but you aren't forced to optimize for it in a way that assumes the 0-coin student can never get anything. Add in some metrics (see note 2) or randomization to make it more fair.
Note 1: For the sake of this exercise, assume the gold coins aren't fungible. Giving a poor student a coin doesn't make their life easier in some other way, like making groceries more affordable. Or, if you'd like, assume that you only get the coin if you go to college, so unless you can procure the other 9, you won't get it.
Note 2: Yes, standardized testing is flawed, especially as a screener for education. If you know everything on the test, should we focus on you to learn more and specialize? Or do we prefer the curious student who knows little?