Causal decision theory

Causal decision theory is a mathematical theory intended to determine the set of rational choices in a given situation. In informal terms, it maintains that the rational choice is that with the best expected causal consequences. This theory is often contrasted with evidential decision theory, which recommends those actions that provide the best expected outcome conditional on one’s best evidence about the world.Further, David has studied works on psychology and political science which teach him the following: Kings have two personality types, charismatic and uncharismatic. A king's degree of charisma depends on his genetic make-up and early childhood experiences, and cannot be changed in adulthood. Now, charismatic kings tend to act justly and uncharismatic kings unjustly. Successful revolts against charismatic kings are rare, whereas successful revolts against uncharismatic kings are frequent. Unjust acts themselves, though, do not cause successful revolts; the reason uncharismatic kings are prone to successful revolts is that they have a sneaky, ignoble bearing. David does not know whether or not he is charismatic; he does know that it is unjust to send for another man's wife. (p. 164)Paul is debating whether to press the ‘kill all psychopaths’ button. It would, he thinks, be much better to live in a world with no psychopaths. Unfortunately, Paul is quite confident that only a psychopath would press such a button. Paul very strongly prefers living in a world with psychopaths to dying. Should Paul press the button?Consider an agent that would pay up in response to a counterfactual blackmail. The blackmailer would predict this and blackmail the agent. Now, instead, consider an agent that would refuse to pay up in response to a counterfactual blackmail... The blackmailer would predict this too, and so would not blackmail the agent. Therefore, if we are constructing an agent that might encounter counterfactual blackmail, then it is a better overall policy to construct an agent that would refuse to pay up when blackmailed in this way. Causal decision theory is a mathematical theory intended to determine the set of rational choices in a given situation. In informal terms, it maintains that the rational choice is that with the best expected causal consequences. This theory is often contrasted with evidential decision theory, which recommends those actions that provide the best expected outcome conditional on one’s best evidence about the world. Informally, causal decision theory recommends the agent to make the decision with the best expected causal consequences. For example: if eating an apple will cause you to be happy and eating an orange will cause you to be sad then you would be rational to eat the apple. One complication is the notion of expected causal consequences. Imagine that eating a good apple will cause you to be happy and eating a bad apple will cause you to be sad but you aren't sure if the apple is good or bad. In this case you don't know the causal effects of eating the apple. Instead, then, you work from the expected causal effects, where these will depend on three things: (1) how likely you think the apple is to be good and how likely you think it is to be bad; (2) how happy eating a good apple makes you; and (3) how sad eating a bad apple makes you. In informal terms, causal decision theory advises the agent to make the decision with the best expected causal effects. In a 1981 article, Allan Gibbard and William Harper explained causal decision theory as maximization of the expected utility U {displaystyle U} of an action A {displaystyle A} 'calculated from probabilities of counterfactuals': where D ( O j ) {displaystyle D(O_{j})} is the desirability of outcome O j {displaystyle O_{j}} and P ( A > O j ) {displaystyle P(A>O_{j})} is the counterfactual probability that, if A {displaystyle A} were done, then O j {displaystyle O_{j}} would hold. David Lewis proved that the probability of a conditional P ( A > O j ) {displaystyle P(A>O_{j})} does not always equal the conditional probability P ( O j | A ) {displaystyle P(O_{j}|A)} . If that were the case, causal decision theory would be equivalent to evidential decision theory, which uses conditional probabilities. Gibbard and Harper showed that if we accept two axioms (one related to the controversial principle of the conditional excluded middle), then the statistical independence of A {displaystyle A} and A > O j {displaystyle A>O_{j}} suffices to guarantee that P ( A > O j ) = P ( O j | A ) {displaystyle P(A>O_{j})=P(O_{j}|A)} . However, there are cases in which actions and conditionals are not independent. Gibbard and Harper give an example in which King David wants Bathsheba but fears that summoning her would provoke a revolt.