Chapter Questions
Imagine that Newcomb's problem is reformulated such that box $B_1$ contains $$\$ 0$$ instead of $$\$ 1,000$$. Then this would no longer be a decision problem in which two major decision principles seem to come into conflict. Explain!
Newcomb's problem has little to do with the principle of maximising expected utility. Propose an alternative rule for decision making under risk, and show that it comes into conflict with the dominance principle in Newcomb-style cases.(a) Suppose that $p(X \square \longmapsto Y)=p(\neg X \square \longmapsto Y)=0$. What can you then conclude about $Y$ ?(b) Suppose that $p(X \square \longmapsto Y)=p(\neg X \square \longmapsto Y)=1$. What can you conclude about $Y$ ?
In the Paul-and-the-psychopath case we stipulated that the number of psychopaths in the world was known to be small. Why?(a) Suppose that $p((X \square \longmapsto Y) \mid X)=p((\neg X \square \longmapsto Y) \mid \neg X)=0$. What can you then conclude about $Y$ ?(b) Suppose that $p((X \square \longmapsto Y) \mid X)=p((\neg X \square \longmapsto Y) \mid X)=1$. What can you conclude about $Y$ ?
Death offers you a choice between $$\$ 50$$ and $$\$ 100$$. He adds that if you make a rational choice, he will kill you. What should you do? (You think $$\$ 100$$ is better than $$\$ 50$$, and you have no desire to die.)