Paradox of Choice
I've been again pondering The Paradox of Choice and how to model it mathematically.
Yes, I've done this before. This time though I used a different model for the estimated benefit. Before, I used a very simple model and said that the new best option could be 1 better than the old best option. Here, I attempt to model the values of all items with a Gaussian distribution, then calculate the estimated value of the best item. Even though I used the erf function to calculate the probability that we'd see a large value, the graph ended up looking just like my previous one, which used ln as the characteristic function.
Intuitively, as you add more and more choices, the odds are that the best choice won't be much better than when you had just a few choices. However, the cost of evaluating them has gone up. That's the paradox of choice. Our culture puts a great value on choices, shown by the green line going up as choices go up, and that means more choices are more valuable, but eventually the cost of evaluating them all, shown by the red line, overtakes them, and more choices are just not worth the cost of evaluating them.