This is related to the expected value, isn’t it? The expected value of something is its value if true times the probability of it being true. Where probability stands for degree of belief of it happening. I.e. EV(X)=P(X)V(X). Then presumably what you are proposing is the following formula:
Motivation(X)=ExpectedReward(X)−ExpectedCost(X).
Right? This would mean
Motivation(X)=P(X)Reward(X)−P(X)Cost(X).
However, the above assumes that the thing that gives reward is the same thing that has consequences (X in this case). Which can’t be the case as the probability of incurring the cost need not be the same as the probability of getting reward, contrary to the previous formula.
An arguably better formula comes from Richard Jeffrey’s theory. He models the value V of some possible fact (proposition) as the degree of desire for it to be true. The probability P is again the degree of belief that the proposition is true. Now both outcomes we care about and actions which could make those outcomes happen can equally be described by a proposition. And the degree of desire V toward an action can be interpreted as the motivation to do that action. In particular, for some action A and some outcome O he has the following theorem in his theory:
V(A)=V(O∧A)P(O∣A)+V(¬O∧A)P(¬O∣A).
Here there is no explicit distinction between cost of an action and the reward of the outcome. Those values are already combined in the terms V(O∧A) (both the action and the outcome happen) and V(¬O∧A) (the action happens but the outcome doesn’t happen). The two probabilities weigh those terms depending on the outcome happening/not happening conditional on the action. So the resulting value (degree of desire / motivation?) for the action A is a weighted average.
I’m afraid I can’t read probabilistic notation, but on first blush what you’ve described does sound like I’m simply reinventing the wheel—and poorly compared to Jeffrey’s Theory there. So yes, it is related to the expected value. And I like how Jeffrey’s theory breaks the degree of belief and the desire into two separate values.
This is related to the expected value, isn’t it? The expected value of something is its value if true times the probability of it being true. Where probability stands for degree of belief of it happening. I.e. EV(X)=P(X)V(X). Then presumably what you are proposing is the following formula:
Motivation(X)=ExpectedReward(X)−ExpectedCost(X).
Right? This would mean
Motivation(X)=P(X)Reward(X)−P(X)Cost(X).
However, the above assumes that the thing that gives reward is the same thing that has consequences (X in this case). Which can’t be the case as the probability of incurring the cost need not be the same as the probability of getting reward, contrary to the previous formula.
An arguably better formula comes from Richard Jeffrey’s theory. He models the value V of some possible fact (proposition) as the degree of desire for it to be true. The probability P is again the degree of belief that the proposition is true. Now both outcomes we care about and actions which could make those outcomes happen can equally be described by a proposition. And the degree of desire V toward an action can be interpreted as the motivation to do that action. In particular, for some action A and some outcome O he has the following theorem in his theory:
V(A)=V(O∧A)P(O∣A)+V(¬O∧A)P(¬O∣A).
Here there is no explicit distinction between cost of an action and the reward of the outcome. Those values are already combined in the terms V(O∧A) (both the action and the outcome happen) and V(¬O∧A) (the action happens but the outcome doesn’t happen). The two probabilities weigh those terms depending on the outcome happening/not happening conditional on the action. So the resulting value (degree of desire / motivation?) for the action A is a weighted average.
I’m afraid I can’t read probabilistic notation, but on first blush what you’ve described does sound like I’m simply reinventing the wheel—and poorly compared to Jeffrey’s Theory there. So yes, it is related to the expected value. And I like how Jeffrey’s theory breaks the degree of belief and the desire into two separate values.