Asymmetric information is the main justification for mandates, as well as for Medicare. These arguments have been hashed out already many times. The patient knows more about their health than the insurance company. In a voluntary insurance market, the pool of participants will be disproportionately unhealthy. This will raise health insurance costs compared to what they would otherwise be. In extreme cases, higher costs in turn will lead more people, again the relatively healthy, to drop out. And so on and so on, until only the "lemons" (the sickest) are left. Then the insurance companies go bankrupt.
This is referred to as the Lemon problem, first articulated by George Akerlof in 1970, and it is Business 101.
This is one of the problems. But not the only one. There is the expert problem: the doctor knows more than either the patient, or the insurer, and he is also the medical service provider. And there is the moral hazard problem - if everyone is insured they might be using the services more than they'd want to (and then would be optimal) if they are not insured (whether because of more risky behavior, or for whatever other reason). This is a humongous bundle of asymmetric information problems. Each of which is orders of magnitude more important that whatever had been previously mentioned in this thread.
