Blog: Expanded Universe

A naïve utilitarian contemplates upvotes

We might model how good a post overall is by drawing a bar chart, one bar for each reader, reflecting how good they think the post is (how much utility they get out of it). Then the goodness of the post is the area under the curve.

readers utility

We might also model that a reader upvotes a post if its subjective goodness crosses some threshold, so, the number of upvotes a post gets is just the number of bars passing the threshold:

upvote threshold number of upvotes readers utility

The post depicted above would receive the same number of upvotes as the following "much better" post:

upvote threshold number of upvotes readers utility And as the following "much worse" one: upvote threshold number of upvotes readers utility

The number of upvotes only gives a weak lower bound (the shaded blue rectangle) on the total utility of the post.


Let's additionally make up a rule that there's an upper bound on the total utility a post can have (the idea being, I think it's hard to write a post with both broad and deep appeal).

Then, we see that any individual reader's absolute favorite posts won't have as many upvotes as the most-upvoted posts, because total utility "spent" on making a post good for specifically them trades off against it being "spent" on reaching the upvote threshold for more readers.

? upvote threshold ? number of upvotes readers utility

One more made-up rule. Now, every reader has a marginal post that they would have read instead of this one if it didn't exist, and that other post would have provided that reader some positive utility. Then the marginal utility created by a post is only the blue area above that line:

upvote threshold margin number of upvotes readers utility

Under this rule and the previous, "spending" the total utility of your post to acquire more and more upvoting readers is a less efficient way to create more marginal utility than "spending" it on readers who already love your post.