Teruji Thomas
@terujithomas.bsky.social
Philosopher at Oxford. Ethics, epistemology, decision theory, usually stuff like that. Not a big fan of potatoes (or muzak) but don't these ones look cool?
https://users.ox.ac.uk/~mert2060/
https://users.ox.ac.uk/~mert2060/
Hmm I'm stuck on 2 and 6 but I like 3
August 12, 2025 at 10:52 AM
Hmm I'm stuck on 2 and 6 but I like 3
With this in mind, P2 really can be interpreted as eventwise dominance, even though on the surface it is eventwise separability. And P3 can indeed be interpreted as part of STP, but it can alternatively be interpreted as the principle that one's outcome preferences are state-independent.
July 22, 2025 at 12:46 PM
With this in mind, P2 really can be interpreted as eventwise dominance, even though on the surface it is eventwise separability. And P3 can indeed be interpreted as part of STP, but it can alternatively be interpreted as the principle that one's outcome preferences are state-independent.
To sum up: in Savage's framework, there are just unconditional preferences over acts, but to fully grasp his axioms we may want to interpret them in terms of (a) conditional preferences and (b) outcome preferences. There are potentially different ways to do this.
July 22, 2025 at 12:46 PM
To sum up: in Savage's framework, there are just unconditional preferences over acts, but to fully grasp his axioms we may want to interpret them in terms of (a) conditional preferences and (b) outcome preferences. There are potentially different ways to do this.
On this interpretation, P3 isn't really related to the sure-thing principle or eventwise dominance at all! If we want state-dependent preferences, then we'll keep P2 (and eventwise dominance) but reject P3.
July 22, 2025 at 12:46 PM
On this interpretation, P3 isn't really related to the sure-thing principle or eventwise dominance at all! If we want state-dependent preferences, then we'll keep P2 (and eventwise dominance) but reject P3.
If we do that, then what I said above doesn't apply: there's no further need to align one's conditional preferences with one's preferences over outcomes. Indeed, from this point of view P3 is better interpreted, not as a dominance principle, but as _ruling out state-dependent outcome preferences_.
July 22, 2025 at 12:46 PM
If we do that, then what I said above doesn't apply: there's no further need to align one's conditional preferences with one's preferences over outcomes. Indeed, from this point of view P3 is better interpreted, not as a dominance principle, but as _ruling out state-dependent outcome preferences_.
If we want to allow state-dependence, then we could (instead) define "preferring outcome x to outcome y in state s" as "preferring constant act with value x to constant act with value y, conditional on {s}".
July 22, 2025 at 12:46 PM
If we want to allow state-dependence, then we could (instead) define "preferring outcome x to outcome y in state s" as "preferring constant act with value x to constant act with value y, conditional on {s}".
To take a philosophy example, in Stefan Riedener's work on moral uncertainty, he takes states to specify moral (or axiological) theories; the value of an outcome depends on the moral theory.
July 22, 2025 at 12:46 PM
To take a philosophy example, in Stefan Riedener's work on moral uncertainty, he takes states to specify moral (or axiological) theories; the value of an outcome depends on the moral theory.
This assumption might not always be appropriate. Some people are interested in cases where one's preferences over outcomes are _state-dependent_.
July 22, 2025 at 12:46 PM
This assumption might not always be appropriate. Some people are interested in cases where one's preferences over outcomes are _state-dependent_.
A constant act is an act that has the same outcome in every state. The way I've glossed P3 assumes that "preferring outcome x to outcome y" is defined as "preferring constant act with value x to constant act with value y".
July 22, 2025 at 12:46 PM
A constant act is an act that has the same outcome in every state. The way I've glossed P3 assumes that "preferring outcome x to outcome y" is defined as "preferring constant act with value x to constant act with value y".
However, there's a different way of thinking about it! I've glossed P3 as being about one's preferences over outcomes, but this is a non-trivial interpretative step. It's actually about one's preferences over "constant acts".
July 22, 2025 at 12:46 PM
However, there's a different way of thinking about it! I've glossed P3 as being about one's preferences over outcomes, but this is a non-trivial interpretative step. It's actually about one's preferences over "constant acts".
Yep! The issue is that (as far as P2 goes) your conditional preferences might have nothing to do with your preferences over outcomes. P3 ensures that your conditional preferences relate to your outcome preferences in a sensible way. So indeed it's natural to think of P3 as rounding out STP.
July 22, 2025 at 12:46 PM
Yep! The issue is that (as far as P2 goes) your conditional preferences might have nothing to do with your preferences over outcomes. P3 ensures that your conditional preferences relate to your outcome preferences in a sensible way. So indeed it's natural to think of P3 as rounding out STP.
OK, so if P2 can be interpreted as eventwise dominance, then what is the other dominance principle, P3, about? P3 is a simple form of "statewise dominance": roughly, if you prefer the outcome of f to that of g in every state, then you prefer f to g. Isn't this also "the sure thing principle"?
July 22, 2025 at 12:46 PM
OK, so if P2 can be interpreted as eventwise dominance, then what is the other dominance principle, P3, about? P3 is a simple form of "statewise dominance": roughly, if you prefer the outcome of f to that of g in every state, then you prefer f to g. Isn't this also "the sure thing principle"?
Savage's P2 says that we *do* get the same answer for every h. As a result eventwise dominance holds with respect to the defined notion of conditional preference. It's in this way that P2 earns the name "STP".
July 22, 2025 at 12:46 PM
Savage's P2 says that we *do* get the same answer for every h. As a result eventwise dominance holds with respect to the defined notion of conditional preference. It's in this way that P2 earns the name "STP".
...Moreover, if we take this as the definition of conditional preference, then eventwise dominance holds automatically! (Assuming transitivity, anyway.) The catch is that this only works as a definition if we get the same preference for every h.
July 22, 2025 at 12:46 PM
...Moreover, if we take this as the definition of conditional preference, then eventwise dominance holds automatically! (Assuming transitivity, anyway.) The catch is that this only works as a definition if we get the same preference for every h.
How to do this? Well, *if* eventwise dominance holds, then, for any f,g,h, "preferring f to g conditional on E" is equivalent to "preferring (f if E, otherwise h) to (g if E, otherwise h)"...
July 22, 2025 at 12:46 PM
How to do this? Well, *if* eventwise dominance holds, then, for any f,g,h, "preferring f to g conditional on E" is equivalent to "preferring (f if E, otherwise h) to (g if E, otherwise h)"...
The issue is that Savage takes unconditional preference as basic. So even to formulate eventwise dominance, we would have to define conditional preference (preferring f to g conditional on E) in terms of unconditional preference (preferring f to g).
July 22, 2025 at 12:46 PM
The issue is that Savage takes unconditional preference as basic. So even to formulate eventwise dominance, we would have to define conditional preference (preferring f to g conditional on E) in terms of unconditional preference (preferring f to g).
So people sometimes use "STP" to refer to event-wise dominance, and sometimes use it to refer to event-wise separability, and sometimes P3 counts as STP, sometimes not. At the very least, I'm personally guilty of equivocation! It's a bit confusing. What's going on?
July 22, 2025 at 12:46 PM
So people sometimes use "STP" to refer to event-wise dominance, and sometimes use it to refer to event-wise separability, and sometimes P3 counts as STP, sometimes not. At the very least, I'm personally guilty of equivocation! It's a bit confusing. What's going on?
Moreover, Savage has a _different_ principle (P3) which superficially looks a lot like eventwise dominance!
July 22, 2025 at 12:46 PM
Moreover, Savage has a _different_ principle (P3) which superficially looks a lot like eventwise dominance!
This is basically how Savage motivates STP. However! The principle that he officially calls STP (his P2) looks quite different. Specifically, P2 would naturally be called "eventwise separability" rather than "eventwise dominance"...
July 22, 2025 at 12:46 PM
This is basically how Savage motivates STP. However! The principle that he officially calls STP (his P2) looks quite different. Specifically, P2 would naturally be called "eventwise separability" rather than "eventwise dominance"...
Calling eventwise dominance "STP" makes some sense: whether or not it rains, it's a sure thing that you'll prefer to bring your umbrella. (As many have pointed out, this gloss is a bit misleading, but it still explains the name.)
July 22, 2025 at 12:46 PM
Calling eventwise dominance "STP" makes some sense: whether or not it rains, it's a sure thing that you'll prefer to bring your umbrella. (As many have pointed out, this gloss is a bit misleading, but it still explains the name.)
E.g. if you prefer bringing your umbrella, supposing that it rains, and you prefer bringing your umbrella supposing that it doesn't rain, then, by gum, you prefer bringing your umbrella. ("Preferring f to g conditional on E" is meant to be something like preferring f to g on the supposition that E.)
July 22, 2025 at 12:46 PM
E.g. if you prefer bringing your umbrella, supposing that it rains, and you prefer bringing your umbrella supposing that it doesn't rain, then, by gum, you prefer bringing your umbrella. ("Preferring f to g conditional on E" is meant to be something like preferring f to g on the supposition that E.)