But you've ignored adverse selection. Many of the people commenting here have no insurance coverage, because they're 22 and it is irrational for them to pay for coverage they're not mandated to have.
I see that if people were i.i.d., the difference between BCBS's risk pool and Medicare's risk pool would be irrelevant. But they aren't.
Lumping in seniors with 22 year olds does not reduce the variance any more than lumping in 22 year olds with more 22 year olds does.
Statistical variance is not a major contributor to the cost of health insurance. You are simply wrong on this point.
Additionally, adverse selection has nothing to do with a variable risk pool. Adverse selection is a problem caused by asymmetrical information: if you know you are sick, you might lie to your insurance company about preexisting conditions to gain insurance. Adverse selection also has nothing to do with a variable risk pool.
You sure are better with math than I am. But you're not helping me understand how, given the fact that the majority of the uninsured in the US are below the age of 35, and the fact that people under the age of 35 have less reason to pay into the system than people over 35, and the fact that people under the age of 35 are similarly much less likely to incur costs, mandated guaranteed issue or government single-payer doesn't improve the risk pool.
You've clearly demonstrated that the problem with the current insurance scheme isn't a trivial stats 101 observation, but I feel like you're dodging the point because I've given you an excuse to do so by making that point clumsily.
I'm not sure what point you were making. You originally suggested that there were economies of scale due to the reduced variance of a national risk pool, which is true but so minor as to be irrelevant.
Regarding the lower average cost of people under 35, this is true. However, this is not an economy of scale - the cost to insure 1 million people aged 20-35 is very close to 100 times the cost to insure 10,000 people aged 20-35. No economy of scale there.
Adding cheaper people to the market will lower the average cost of the broader health insurance market. Millions of new netbook buyers lower the cost of laptops, since the average price of 1 million netbooks and 1 million macbooks is lower than the average price of 1 million macbooks. This isn't an economy of scale, it's simply a change in market composition. A change in market composition (in vacuo) doesn't lower costs to any individual. Millions of new netbook buyers didn't make my macbook cost any less.
It will also raise prices in any individual market segment due to increased demand: if demand for netbooks/health insurance for 20-35 year olds goes up, prices will too.
But you've ignored adverse selection. Many of the people commenting here have no insurance coverage, because they're 22 and it is irrational for them to pay for coverage they're not mandated to have.
I see that if people were i.i.d., the difference between BCBS's risk pool and Medicare's risk pool would be irrelevant. But they aren't.