## Tuesday, July 2, 2019

### Socialized Medicine Is the Most Efficient Outcome

In Mutual Aid, Peter Kropotkin describes how non-capitalist societies managed disasters:

As to the social characters of the mediæval guild, any guild-statute may illustrate them. Taking, for instance, the skraa of some early Danish guild, we read in it, first, a statemet of the general brotherly feelings which must reign in the guild; next come the regulations relative to self-jurisdiction in cases of quarrels arising between two brothers, or a brother and a stranger; and then, the social duties of the brethren are enumerated. If a brother's house is burned, or he has lost his ship, or has suffered on a pilgrim's voyage, all brethren must come to his aid. If a brother falls dangerously ill, two brethren must keep watch by his bed till he is out of danger, and if he dies, the brethren must bury him–a great affair in those times of pestilences–and follow him to the church and the grave. After his death they must provide for his children, if necessary; very often the widow becomes a sister to the guild. (141, Dover Books edition, emphasis added)
As we can see, non-capitalist societies had very different ways of managing disasters. Here, Kropotkin describes five, perhaps six, different events that capitalism would handle with insurance. Fire insurance, boat insurance, health insurance, and life insurance would be the capitalist alternative to the duties described here.

Like insurance, these medieval duties spread the cost of a disaster to all those who bought in. Unlike insurance, the incentive to abide these duties was that they were part of the general social agreement that formed the medieval system of distribution. Rather than directly from markets, guild members got their goods through the guild, which in turn dealt with other guilds and merchant delivering goods from foreign lands.

Capitalism spreads risk from disasters through insurance. Insurance companies take great pains to calculate the risk of any one of their clients encountering a disaster to arrive at a premium that spreads the cost of a disaster relatively evenly among insurance customers.

In the simplest model of insurance, we assume all insurance customers have the same probability of encountering a disaster. We'll call this probability p. The cost of the insurance we'll call X. Thus, for any customer, the expected value of their share of the total expected cost: $$\mathrm{E}(C) = \sum_n\frac{pC}{n}$$ Thus, if the distribution of expected costs is distributed fairly (evenly), the individual's premium would be: $$\frac{pC}{n}$$ The percentage of the total cost of a disaster for the individual is the probability of a disaster p divided by the total number of people n on the insurance plan.

We can of course extend the model to accommodate a spectrum of risks in which the risk probabilities would need to be averaged to calculate the expected value of the cost over a given period of time. $$\frac{p_i{}C}{n}$$ Other means of distributing costs are obviously possible, and perhaps preferable. Ultimately, the total value of premiums collected over a given period of time has to be equal to the overall expected value of the cost of disasters.

What's crucial to note here is how the function varies with the number of customers. As you can see, the number of customers n is in the denominator meaning the cost of premiums decreases as the number of customers in an insurance pool increases. What this implies is that putting as many people as possible into one insurance pool is the most efficient distribution of insurance.

So the question remains, do we want socialized medicine from a government nominally accountable to its people or privatized medicine from one corporation accountable to only itself?