12  Conclusion

TK

% Given all that, here is the positive theory, what I’m calling Gamified Decision Theory (GDT). The core is that rational choices are ratifiable. That is, they maximise expected utility from the perspective of someone who chooses them. Formally, that means that in a particular problem, with choices o₁, \(\dots\), o_m, and causally independent states s₁, \(\dots\) s_n, a choice o is rational iff there is some probability function Pr that is a rational credal distribution over the s after choosing o, and such that for all o_j, \(\Sigma\)Pr(s_i)V(os_i) ≥ \(\Sigma\)Pr(s_i)V(o_js_i). % % There are two extra clauses. First, o is choiceworthy only if it is not be weakly dominated by any other option. Second, if one is making a series of decisions in a tree, and one knows that one will be rational and not change one’s preferences throughout, then both the decisions one makes at any given time, and the set of decisions one collectively makes, must satisfy all the other conditions of rational choice. That is, they must be ratifiable and not weakly dominated. % % The big advantage of this theory is that it satisfies the nine conditions I mentioned at the start, and that it is consistent with Exit Principle. These turn out to be very sharp constraints on a theory. For example, any theory that associates some number with each choice, and says to maximise the number, will violate the Indecisiveness constraint. Any theory that simply the chooser’s credences as given will violate the Substantiveness constraint. The vast bulk of decision theories on the market in philosophy do at least one of these two things, and typically both. So we have strong reason to prefer GDT to them. % % GDT does require that mixed strategies are available to choosers, on pain of saying that a lot of decision problems are dilemmas. That is not a problem for GDT, since ideal agents can perform mixed strategies. It is a shortcoming to not be able to perform them, and ideal agents don’t have these kinds of shortcomings. But it does suggest an important research program in working out how GDT should be altered for agents who lack one or other idealisation. In fact it suggests two research programs: a descriptive one, setting out what choosers who don’t satisfy one or other idealisation in fact do; and a normative one, setting out what these choosers should do. But those projects are for a very different paper.[^33] % % [^33]: Thanks to many people for conversations on these topics, especially Dmitri Gallow and Ishani Maitra, and audiences and ACU and UBC, and students in my group choices classes at University of Michigan.