Minor comment/correction—VoI isn’t necessarily linked to a single decision, but the way it is typically defined in introductory works, it implicit that it is limited to one decision. This is mostly because (as I found out when trying to build more generalized VoI models for my dissertation,) it’s usually quickly intractable for multiple decisions.
Good to know. Can you link to another resource that states this? Wikipedia says “the amount a decision maker would be willing to pay for information prior to making a decision”, LessWrong has something similar “how much answering a question allows a decision-maker to improve its decision”.
The works on decision theory tend to be general, but I need my textbooks to find better resources—I’ll see if I have the right ones at home. Until then, Andrew Gelmans’ BDA3 explicitly formulates VoI as a multi-stage decision tree in section 9.3, thereby making it clear that the same procedure is generalizable. And Jaynes doesn’t call it VoI in PT:LoS, but his discussion in the chapter on simple applications of decision theory leaves the number of decision implicitly open.
Minor comment/correction—VoI isn’t necessarily linked to a single decision, but the way it is typically defined in introductory works, it implicit that it is limited to one decision. This is mostly because (as I found out when trying to build more generalized VoI models for my dissertation,) it’s usually quickly intractable for multiple decisions.
Good to know. Can you link to another resource that states this? Wikipedia says “the amount a decision maker would be willing to pay for information prior to making a decision”, LessWrong has something similar “how much answering a question allows a decision-maker to improve its decision”.
https://en.wikipedia.org/wiki/Value_of_information https://www.lesswrong.com/posts/vADtvr9iDeYsCDfxd/value-of-information-four-examples
The works on decision theory tend to be general, but I need my textbooks to find better resources—I’ll see if I have the right ones at home. Until then, Andrew Gelmans’ BDA3 explicitly formulates VoI as a multi-stage decision tree in section 9.3, thereby making it clear that the same procedure is generalizable. And Jaynes doesn’t call it VoI in PT:LoS, but his discussion in the chapter on simple applications of decision theory leaves the number of decision implicitly open.