Insurance, in law and economics, is a form of risk management primarily used to hedge against the risk of a contingent loss. Insurance is defined as the equitable transfer of the risk of a loss, from one entity to another, in exchange for a premium, and can be thought of as a guaranteed small loss to prevent a large, possibly devastating loss. (emphasis mine)In today's health care debate there is a lot of talk about lowering the cost of insurance so I thought we should first understand what insurance is. Let's say there is a 1 in a 1000 chance of something bad happening and it will cost you $1000 dollars if it happens. Today, what does that cost you? Well today it hasn't happened so it shouldn't cost you anything, right? Wrong! In economic terms the cost to you is $1. This is obtained by multiplying the cost of something bad ($1000) and the chance of it happening (.001).
We have a problem. Clearly the odds of the event happening are very small and if it doesn't happen, you are out a dollar for nothing in return. If it does happen then your dollar is also pretty useless. How is this problem solved? Insurance! As stated in Wikipedia, you pay a small amount in order to have peace of mind in case the bad event happens. This works because in aggregate the likelihood of the event nears 100% and the total costs can be accurately predicted. So if we have 1000 people then it is almost guaranteed that 1 person will have to pay $1000 dollars and the rest will not. This means that for an insurance company to break even it must charge $1 dollar to every person.
There are few caveats. First, insurance cannot be used for events that have already happened. If we have 1001 people, 1000 of which have not had the bad event happen and 1 that has, then what is the expected cost? $2000 ($1000 for everyone else and $1000 for that 1 person). We could solve this problem two ways: deny insurance to the unfortunate person or raise the premium on everyone else. The first case is difficult in that it seems very cruel and it is. However it is nature that is cruel and not us. The second case will inevitably make insurance unaffordable because the unfortunate person is being subsidized by everyone else. Remember, the economic cost to everyone else is really only $1, so the extra dollar does not have value for them. If everyone waited until they had a problem and then wanted insurance, they are really asking society to subsidize known costs (i.e. after the event happens we know you will have to pay $1000). This is a public policy question, not an insurance question.
The second caveat is that insurance should only be used for large costs. The value you principally derive is due to the fact that you don't have a million bucks lying around to replace your house. You probably have access to a few hundred dollars so there is significantly less value as the potential losses decline. At some point the overhead of the insurance company outweighs the potential benefits.
Hopefully this clears some things up.