Efficiency of socialised services

Americans get very antsy about socialised anything, with some vague feeling that if the country socialised anything, it would turn into a soviet state1. A common claim is that government run health services are inefficient and have a long waiting time.

However, Queuing theory tells us that as the efficiency of a serving process increases, the queue length increases to infinity. This is easy to understand: inefficiency is due to the server sitting idle having run out of work to do. A poisson distribution (the typical distribution for people turning up to a queue) can have arbitrarily long gaps, with exponentially decreasing probability.

Thus, if we want to make sure that the server has something to do for (100-eps)% of the time we need something like -log(eps) people in the queue. This gets long with high efficiency. So you can have an efficient service, or short queues, but not both. A socialised health system can be efficient, but then you have to live with long wait times with non-urgent care (because you are padding to fill the gaps). Alternatively, we could change the measure of efficiency, perhaps including patient waiting times, but then you would have to do real analysis, and that's too hard.

Anecdotally, my experience with socialised health care is that when I had to have non-urgent surgery I had to wait almost 2 weeks, then had the surgery done for free. My experience with american privatised health on the other hand is that it is expensive and takes a long time for service (even a GP visit can be a multiday affair costing $250).

1Though this does not apply to roads or airports for some reason.