I see where you're coming from, but what if there is someone else who also needs emergency medical care and has a higher chance of survival? End-of-life care is among the most expensive kinds of medical treatment because often doctors are staving off the inevitable, and that sucks up resources that could be used to treat other people.
This seems like a very grim economic calculus, but following a disaster or disease epidemic doctors must make such decisions many times a day, sometimes with only minutes to evaluate patients. Likewise, those who run hospitals (especially public hospitals) have to balance the probability of a successful outcome against the cost of leaving other patients untreated.
It's not something that can be quantified, though. The problem is that meaning is an entirely subjective phenomenon, so when we talk about trying to save people who are more likely to live, we make the assumption that long life is the correct metric to use. More than that, we assume that there is a correct metric to use in the first place. As a concrete counter-point, what if the person saved will have a terrible life to look forward to? What if it's an abused wife or a (unknown to the doctors) drug addict? What if the person with the lower chance of survival is a parent or Mother Therasa? What if the person with the better survival rate doesn't want to live and will commit suicide shortly?
The problem with applying linear mathematics to human issues is that it's a gross oversimplification of a complex problem. Couple that with the relative weight of values (i.e. every person placing a different value on life) and it's clear that rather than being a more objective measure, it is in fact firmly grounded in subjectivity. I think that the objective illusion only serves to calm the conscience. A more objective and fair way of doing this, which also calms the conscience, would be to flip a coin.
The other issue is that the line of thinking you have described is the same one used to justify horrendous actions. Sacrificing someone who is seemingly less deserving of effort (again, by our completely subjective criteria) for someone more deserving is the logic used to justify locking people up in prisons, burning witches, gassing Jews, it's all the same - those "less deserving" are sacrificed for those who are "more deserving". And all that with a subjective metric.
I think that the root cause of this irrationality is that even the most rational people tend to miss the fact that perfecting one's logic is not enough. After that point, assumptions are everything. Logic is merely a tool for transforming one set of assumptions into another. If you use shit as the input, you'll get an equivalent output.
That's all true, but scarcity is a fact of life. Often, the scarce commodity is time for evaluating a complex decision. Part of responsibility is accepting the fact that your foresight and insight are limited and that you may have to face the results of a bad decision; most ethical codes require that you submit to the judgment of your professional peers in that event, but also direct the person to just dealing with the problem at hand, eg a patient's immediate medical condition rather than an overall life situation.
You're entitled to your preferences, but a community filled with people who always reject cost-benefit analysis will have more premature, preventable deaths than another community that does the macabre math.
I'd rather live longer, with more friends and family who live longer, in the cost-benefit community.
You don't want to do business with someone who points out that we value life so much that the costs expended to save those lives are independent of any consideration of benefits?
