Suppose we define the generosity as the ratio of the gift to each entity’s overall net worth and we see that Jeff Bezos’ donation is the smallest fraction of his net worth. Is that really all we need to know to draw that conclusion or are there other factors to consider? This may not be Bezos’ only charitable donation. Suppose we learn that he has made 18 other charitable donations within the last quarter that when added together, exceed any of the other entity’s donation ratios. Is this question intended to cast a judgement about the values and character of each entity or merely a problem about ratios wrapped in a timely context?

I think one takeaway for the students is to think more deeply about numbers rather than just taking each of them at face value. But we also want to caution against making a judgement when we think we have all the information (comparing each donation relative to the means of each entity) when there might still be unknown unknowns lurking (failing to consider other donations/contributions the entities have made). As the famous quote says, “it’s not what we don’t know that hurts us the most, it’s what we think we know for sure that just ain’t so.”

Are we asking who is most “deserving recognition” or “deserving praise” or “how much they value the well-being of others vs themselves” or “likely to be charitable in the future” or “having the biggest positive impact with their donation” “having the biggest net-positive impact” )

If this step is missing and it’s left as a vague “who do I like most” type question, I don’t expect it to be a very useful discussion.

To put it another way, I think it’s important to consider *why* we might care about generosity. Which donation(s) should we write a newspaper article about? Which type of donor should we be marketing charities to? Which donor(s) should we preferentially patronize* due to their donation? Which one deserves the biggest tax write-off? What effect on the world would praising or criticizing each donor have?

*Buying their oil over competitors. Watching their movies. Using their site. Buying their homemade crafts. Joining their Patreon. Etc.

One argument for proportional model: If rich people/entities donate a small percentage of their wealth, that means the world is worse off with so much wealth concentrated among these “less generous” entities. Whatever group gives the highest percentage is the group we want to have more money.
Example: Suppose non-CEOs give 5% of their money to charity, and CEOs give 2% of their money to charity. A world where non-CEOs have 90% of the wealth is more charitable than a world where CEOs have 90% of the wealth.

One argument for the simple model: Having one more large donor does much more good than having one extra small donor. Thus we should praise/reward large donors when they donate, to encourage them to donate more. Praising poorer donors is perhaps a waste of time.

Throw up an annoyingly vague question, then let the room straighten it out and tell you what they “should” be answering

Btw. I think this answers the question that has been stewing about modeling and defining “real world” vs. “non-real world”
Obviously in the pure world of mathematics all models are perfect! It isn’t until we try and apply them to the “real world” that they become broken.

Great post.