Could you use Bayes Theorem to figure out whether or not a given war is just? If so, I was wondering how one would go about estimating the prior probability that a war is just.
I think it is a fascinating question. After all, if we claim to be Bayesians, we ought to be interested in applying our art to useful public issues. But coming up with a prior: P(H), is only part of the problem. We also need to specify our evidence: E, the probability of encountering that evidence in any old war: P(E), the probability of encountering that evidence if the hypothesis is true that the war is just: P(E|H), and most importantly, the specification of the hypothesis: H.
In this regard Just War doctrine gives certain conditions for the legitimate exercise of force, all of which must be met:
H1. the damage inflicted by the aggressor on the nation or community of nations must be lasting, grave, and certain;
H2. all other means of putting an end to it must have been shown to be impractical or ineffective;
H3. there must be serious prospects of success;
H4. the use of arms must not produce evils and disorders graver than the evil to be eliminated. The power of modern means of destruction weighs very heavily in evaluating this condition.
Well, as compared to a typical law passed by the US Congress, that seems pretty clearcut. So I guess we can just define H ::= H1 & H2 & H3 & H4. Note that it is assumed that for a war to be just from the standpoint of one side, the other side must be the aggressor. It is not easy to be just—you need to clear some legal hurdles to even defend yourself from aggression justly.
So, to see whether Bayesianism can help us here, let us try to estimate P(H3|E) where E is taken to be “We lost the first three battles in this war”. Well, that certainly seems to be evidence that our prospects of success are not good, and hence that our war is not just. But just how strong is this evidence, and how severely does it depress our estimate of P(H3)?
Well, I suppose we could look at statistics from past wars—how often did a side that lost the first three battles eventually “succeed”? Of course H3 doesn’t require that we actually succeed, only that we have “serious prospects of success”. If we arbitrarily define “serious prospects” as a probability > 20%, and our historical statistics tell us that the defender succeeds against the aggressor 40% of the time, but only 25% after losing the first three battles, do we have the information we need to compute P(H3|E)?
To be honest, I don’t know. Perhaps better Bayesians than me can help us out. But I’m certainly beginning to see that applying Bayes to real-world questions can get difficult very quickly.
I think it is a fascinating question. After all, if we claim to be Bayesians, we ought to be interested in applying our art to useful public issues. But coming up with a prior: P(H), is only part of the problem. We also need to specify our evidence: E, the probability of encountering that evidence in any old war: P(E), the probability of encountering that evidence if the hypothesis is true that the war is just: P(E|H), and most importantly, the specification of the hypothesis: H.
Specifying the hypothesis is the easy part, if you are Roman Catholic. Here is what the Catholic catechism says about just war:
Well, as compared to a typical law passed by the US Congress, that seems pretty clearcut. So I guess we can just define H ::= H1 & H2 & H3 & H4. Note that it is assumed that for a war to be just from the standpoint of one side, the other side must be the aggressor. It is not easy to be just—you need to clear some legal hurdles to even defend yourself from aggression justly.
So, to see whether Bayesianism can help us here, let us try to estimate P(H3|E) where E is taken to be “We lost the first three battles in this war”. Well, that certainly seems to be evidence that our prospects of success are not good, and hence that our war is not just. But just how strong is this evidence, and how severely does it depress our estimate of P(H3)?
Well, I suppose we could look at statistics from past wars—how often did a side that lost the first three battles eventually “succeed”? Of course H3 doesn’t require that we actually succeed, only that we have “serious prospects of success”. If we arbitrarily define “serious prospects” as a probability > 20%, and our historical statistics tell us that the defender succeeds against the aggressor 40% of the time, but only 25% after losing the first three battles, do we have the information we need to compute P(H3|E)?
To be honest, I don’t know. Perhaps better Bayesians than me can help us out. But I’m certainly beginning to see that applying Bayes to real-world questions can get difficult very quickly.