*Should decision theory guide the formulation of the principal principle?*

Jenann Ismael, philosophy, Columbia

Itzhak Gilboa, economics, Tel Aviv & HEC Paris

Stephen Senn, statistics, consultant

Sherrilyn Roush, philosophy, UCLA

If you know objective probabilities, you should adopt them as your subjective probabilities. The typical 21^{st}-century mathematical statistician (call this mythical creature “Typ”) takes this for granted. If challenged to explain, Typ might point out that the only use for subjective probabilities is to combine them with utilities to make decisions. Over the course of many such decisions, your average achieved utility will be maximized by using objective probabilities. If you and your brother both know the objective probabilities, and you offer to bet with him at rates that differ from these objective probabilities, he can make money from you almost surely in the long run.

In 1980, the philosopher David Lewis gave a name to the principle that you should adopt known objective probabilities as subjective probabilities. He called it the *principal principle*. Lewis’s principle is mentioned in 16 different articles in the Stanford Encyclopedia of Philosophy, and it has been cited 287 times in philosophy journals indexed by *JSTOR*. But it has never been cited in statistics journals indexed by *JSTOR*.

The exact formulation of Lewis’s principal principle is a topic of continuing discussion. Lewis revised his initial formulation in his 1980 paper and later replaced it with a *new principle*. Other philosophers, including several who have spoken in our seminar, have proposed variations or qualifications. At first glance, Typ’s reasoning seems relevant to the discussion. Is it?

*Questions for the panel:*

- Is Typ’s reasoning sound?
- If so, and Lewis’s principle derives from principles of decision making, is it fundamental enough to be labelled “principal”?
- If not, how should we understand the relationship between the principal principle and decision theory?

- Can Typ’s reasoning help us choose among formulations of the principal principle?
- Can Typ’s reasoning be found in the philosophy literature? Did Lewis discuss it?
- Why don’t statisticians discuss Lewis’s principal principle?

*References*

- David Lewis (1980), A subjectivist’s guide to objective chance, in his
*Philosophical Papers*2:83-132 - Barry Loewer (2004), David Lewis’s Humean theory of objective chance,
*Philosophy of Science*71:1115-1125