It does make sense. A smaller group will have a correspondingly smaller number of people who will end up needing treatment, so the expected value for an individual's cost doesn't actually depend on the number of people in the group, just the probability that any specific person will end up requiring treatment and the cost of the treatment. Maybe you are confused because you chose a specific example wherein the expected number of treatments required is less than one? Are you thinking that because it's not possible to have only a fraction of a person require treatment that we need to round up to 1 person? That's not how probability works and if you simply extend that logic to a group of a single person then your error should become immediately apparent. While it's true that only whole numbers of people can get sick, when you take repeated samples of small groups you will find that occasionally one group member will require treatment, but much more commonly than that, zero group members will require treatment. When you weight each case by its relative probability of occurring, then you get the same expected cost per person that you calculated for the large group.
Your lack of intuition about such a simple linear relationship should be extremely concerning to you. It suggests that you are approaching the question with an emotional attachment to a particular outcome that is blinding you to the extremely simple and intuitive correct answer.
There's a lot more to unpack here, but I don't have time to address it point by point. You are making a lot of assertions that seem much more reflective of left-wing ideology than actual conditions on the ground. You suggest that consumers demanding better is a solution to public systems that don't actually meet consumers needs, but the very nature of public goods ensures that no individual consumer will ever be in a position to make a demand that administrators will have to prioritize over competing demands from producers and public employees. The nature of democracy gives outsized influence public sector unions and interest groups that can then turn around and contribute a share of those benefits back to politicians campaigns. In contrast, a competitive market affords consumers to actually make demands with some weight behind them. A producer has to take a consumers demands into account lest that consumer simply take his business to a competing producer. The weight of the empirical evidence affirming this fundamental difference between public and private systems is completely overwhelming, and your resistance to the idea that capitalism is a far better system than socialism for the vast majority of goods suggests an emotional attachment to an ideology that has very intentionally been sold to the public in such a way as to make uncritical advocacy for that ideology very self-flattering to those very advocates.
I know that I didn't really address the middle part of your argument but let me assure you that those ideas are just as contrary to reality as any of the ideas that I chose to address. I might come back to those in a future post if I find myself with both the time and the inclination to do so.
Your lack of intuition about such a simple linear relationship should be extremely concerning to you. It suggests that you are approaching the question with an emotional attachment to a particular outcome that is blinding you to the extremely simple and intuitive correct answer.
There's a lot more to unpack here, but I don't have time to address it point by point. You are making a lot of assertions that seem much more reflective of left-wing ideology than actual conditions on the ground. You suggest that consumers demanding better is a solution to public systems that don't actually meet consumers needs, but the very nature of public goods ensures that no individual consumer will ever be in a position to make a demand that administrators will have to prioritize over competing demands from producers and public employees. The nature of democracy gives outsized influence public sector unions and interest groups that can then turn around and contribute a share of those benefits back to politicians campaigns. In contrast, a competitive market affords consumers to actually make demands with some weight behind them. A producer has to take a consumers demands into account lest that consumer simply take his business to a competing producer. The weight of the empirical evidence affirming this fundamental difference between public and private systems is completely overwhelming, and your resistance to the idea that capitalism is a far better system than socialism for the vast majority of goods suggests an emotional attachment to an ideology that has very intentionally been sold to the public in such a way as to make uncritical advocacy for that ideology very self-flattering to those very advocates.
I know that I didn't really address the middle part of your argument but let me assure you that those ideas are just as contrary to reality as any of the ideas that I chose to address. I might come back to those in a future post if I find myself with both the time and the inclination to do so.