Justifying the unjustifiable….

I kept myself amused today my pondering the following thought experiment….

For the sake of argument let us say that the sole source of morality is the good of the most possible people. Let us say that the definition of people includes those who are not yet born for the same reasons that we worry about global warming and other such things. (You can discount those unborn people to a degree if you want, but you can not make their value be 0.)

Again, for the sake of argument, let us also say that the only possible good for people is years of life. Let us therefore say that the end result of all we do should be geared to increasing human longevity by as much as possible for as many as people as possible.

Let us say that health care costs necessary to keep a person alive double for every year of extra life that the available health technology is able to provide for that individual. The idea being that the more you extend a person’s life the bigger the problems get. For the sake of this thought experiment we will say that this process can go on forever as long as you have the money.

I don’t know how to write out exponents with HTML, but what I mean is it cost N to give one person an extra year of life, 2N to give them another year of life, 4N to give them another year of life, 8N to give them another year of life, and so on for as long as you got the cash.

Let us say that more health care technology advances, the cheaper N is. In other words, the exponential growth of cost remains the same, but the starting point gets cheaper and cheaper.

Let us also say that the more years you add on to an individual’s life by paying for health care, the more those dollars help advance health care technology in the same exponential way in which costs increase. The idea being that the further you extend a person’s life, the more new problems that you run into and so you learn more. Now I lack the skills to express that properly but what I mean is this….

As I said above, let N be the cost of a year that you are adding to an individual’s life and let x be the corresponding value of technological knowledge gained by spending the necessary money to get the individual to live N long. So if you spent the necessary money to get someone to live an extra year, you would advance your health care technology by x. But if you spent the money necessary to add another year on to that person’s life (2N) you would get 4x worth of advancement in health care technology.

This is because in this thought experiment every dollar you spend towards getting the second year is worth twice the research value as spending a dollar towards getting the first year. Since you have to spend twice the money for the second year you are getting 4 times the research value.

Let us say that the extra years we purchase for an individual have an economic value. In other words, the more years a person lives, the more money they contribute towards the fund that pays for the health care costs. Let us call this money Y. Let us say that this value is not exponential. In other words, each year of extra life only adds Y amount of money to the fund no matter what.

Let us also say that not all individuals have the same economic value. In other words, a laborer would contribute 1/100 of Y per year to the fund where as a surgeon might contribute 100Y.

Let us assume that all of these statements will always hold true. In other words, let us also assume that there will be no end to time in this thought experiment.

Now, what is best way to spend the health care dollars that we have, keeping in mind that our goal is to bring the most benefit to the most people?

The answer I came up with while thinking on this today is that we would spend the most money buying health care for the economically valuable and the least for the less valuable. If we should somehow have enough money to pay to extend each person’s life up to the point where the cost started to overtake the value of each person’s individual Y value, then we would focus all of our money on extending the life of most economically valuable person around.

Now this result might seem a little counter intuitive given that we said that we wanted to do the most possible good for the most possible people. Why then should we favor the most economically valuable person and why should we pay to let the economically valuable live longer?

The key to understanding this seeming paradox is to understand that this thought experiment the overwhelming imperative would be the maximizing of the research efficacy of your health care dollars. This is because in order to help the most possible people we must always put the needs of the unborn above all else.

Why do we need to help the unborn above all else? Well, we are assuming that time does not end and we are saying that we can not assign 0 values to any potential person. Thus, the value of the unborn to us is infinite times a non zero. Infinite times a non zero will always outweigh the finite present. Therefore, the guiding principle under this system must always be that which benefits the unborn the most.

The only way to help out the unborn is to lower the cost of N as much as possible as fast as possible. The lower we can make the cost of N, the more years of life the unborn will be able to buy. Since that benefit extends to an infinite number of people who come after us, lowering the cost of N is the best way to help the most people.

Paradoxically, this means that we would want to help one person live for as long as possible rather then help many people live longer, all other things being equal. Granted, that would be inefficient at helping the living present, because it is exponentially expensive to extend that one person’s life. But it would be the most efficient way of helping the infinite unborn because it is the best way of lowering the cost of N. As we have already said, the needs of the unborn are more important in our value system than the needs of the present.

Of course, it is not quite this simple. We have to come up with the money to pay for all of this. Thus, we want to maximize the money that we have now so that we can spend as much as possible on lowering the cost of N. This means that we will want to spend money extending the lives of people currently living as long as it is profitable to do so.

In other words, once the cost of paying to extend someone’s life exceeded the value of Y that they were contributing, we would stop paying to extend their life. We are seeking to lower the cost of N the most efficient way possible, after all. The end result is that we would be willing to pay to enable the most economically valuable people to live longer than poor people even though in the abstract we are valuing them all the same.

If we could afford to pay for everyone until the cost of extending their lives overwhelmed the benefits they were providing, we would then pick one person whose economic value was the greatest and spend all the rest of money extending that person’s life, even though we would spend past the payback point.

Why would pick the most economically valuable person to spend all our extra money on?

Since the research efficacy of our health care dollars rises exponentially with the amount of extra years we add to one person’s life, the most effective way of lowering the cost of N for the unborn would be to spend all our health care dollars on one person. Now, we have to get the money to spend it, so we would try to extend the lives of those people who live in the present as long as it was profitable to do so. But once we could no longer spend the money profitably, we would want to spend the extra money on the life of the person that we had already extended by most years. That is because spending more on that person would be the most efficient way of reducing N which is the best way of helping the most possible people.

Further thoughts…..

Working on this thought experiment caused me to think that anyone who believed that the greatest good for the greatest numbers is the proper decider of right and wrong could argue that United States has the most moral health care system around. Now I know that the real economics of health care are nothing like that in my experiment. But….

If people can argue that we should go to tremendous expense to avoid Global Warming for the sake of the unborn, they should also put a higher value on health care advances than on lives saved in the present for reasons similar to my thought experiment.

Also, this thought experiment has further confirmed me in my belief that a moral system based on the greater good is just as abhorrent as a moral system based on the selfishness of one individual.

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