Probability from a Perspective

Note

Ozzie Gooen · December 2025 · Completeness: ★★★ (near-publishable)

Unpublished QURI draft, posted as-is — rough and unfinished; collaborator comments have been removed.

Opus 4.8’s take

Argues that probability is best understood as the posterior from a defined perspective with defined information, rather than universal or a private feeling. Brief and informal, with placeholder values and acknowledged open philosophical questions. Explicitly motivated by AI systems estimating odds for a specific person.

Opus 4.8’s summary

A short draft (December 2025) arguing for interpreting probability as the posterior of a defined “perspective” with defined information, positioned between frequentist (one universal probability) and standard Bayesian views. It uses a Texas Hold-em example to show how the same question has different answers from the universe’s perspective versus each player’s, and extends this to hypothetical all-knowing perspectives and to shared “group perspectives” constructed from commonly held information. It motivates the framing with the case of an AI estimating odds tailored to a specific person or presented under a defined public perspective. The piece is brief and largely informal; it leaves placeholder variables (“roughly X,” “roughly Y”), acknowledges open philosophical questions about objective probability, and ends by noting the author’s surprise at not finding similar prior work.

Probability from a Perspective

The two most common understandings of probability are the Frequentist interpretation and the Bayesian one.

The frequentist one can be summarized as:“For any uncertainty, there is one true universal probability for it.”

While the Bayesian one says something more like:“For any uncertainty, you have to begin with the prior of a certain person.” And yet, a lot of Bayesian analyses won’t make the results customizable for specific individual. Often the answer is to use an “uninformative prior” or to provide the prior of a certain party of experts. This can be a decent approach when the tooling is basic (doesn’t allow great infrastructure), but is clearly lacking. I’m in the Bayesian camp, and would like to take things a bit further. I think that a useful framing is to contextualize probability coming from a certain perspective.Two players are playing Texas Hold-em. One has two aces, one two 5s. A 5, 8, and 10 are put on the table. What are the chances that the next two cards will include another 5?

From the perspective of the universe, either 0 or 1. The cards are ordered, it’s a matter of physics. This is not a particularly interesting answer.

From the perspective of the first person, roughly X. From the second, roughly Y. You can further customize a function to say, “For any Perspective X, where said perspective knows the down cards plus one or two cards A and B, what would they consider the chances of another 5 being?”

Here the “bayesian prior” isn’t some fuzzy feeling. It’s a straightforward outcome of the fact that different people, at different times, have different information.

I have a lot of uncertainties about greater philosophical questions regarding objective probabilities. But in real use cases, most probabilities I come across make most sense to me when discussed as coming from a certain perspective. What are the perspectives? Well, each person clearly has some perspective of their own. One might define some perspectives like, “The perspective from the view of a hypothetical being with all knowledge of the universe in its current state”. This perspective would be uncertain about future quantum events, but would have certainty about the card example.

Often, it’s useful for a group of people to settle on some group perspective. White it would be great to have a custom calculator that each person could individualize, it’s sometimes easier to have one “good enough” number. But how should this work, given that each member is different?

For this, tips such as use an “uninformative prior” or an “expert panel” make more sense. But hopefully it’s more clear what’s going on. We’re not trying to estimate some “universal probability”. Instead, we want to estimate something like a “certain perspective that represents our group”.

There are rigorous examples. A simple way to do this would be to imagine the Perspective of the Group being the probability one would give, using information that everyone in said group shares. For example, if two people are playing cards, one has a 5 and a 9, the other a 5 and a 10, then you’d take the probability using just the 5. (This assumes they can’t share/trust information, which is often reasonable!)

What is this useful? It’s a formalization of what probability means and how to use it at scale. Say we have an AI estimating odds for people. What does that mean? One thing we could do is that when we show one person the answer, we customize the odds to represent the estimated enlightened beliefs of that person. And if we show the results publicly, we might then provide them in the context of a certain defined Perspective.This all seems very straightforward and obvious to me. I’m frustrated that I haven’t seen much other work that gets at this concept.