@Conifold Bayesianism doesn't try to tell you what probabilities it is rational to believe, only how it is rational to update them. In some cases you may also be able to form objective priors based on maximum entropy or some similar criterion. But rational or not, an agency announcing that the probability of a Trump victory is 0.5 just means that is the prediction yielded by their stochastic model. You are always at liberty to criticise the reliability of their model...

Constructing a reliable model is not that different from the familiar problem of attempting to construct general theories from a finite number of particular observations. Though of course stochastic theories are harder to falsify than deterministic ones.

If I go outside with an umbrella because I believe it will rain, where does credence play a role here? I don’t attach a number to this belief consciously, so what makes you think this is happening unconsciously? And if you think it’s not happening at all, what is the point of this concept? You haven’t answered this

@Bumble “Constructing a reliable model is not that different from the familiar problem of attempting to construct general theories from a finite number of particular observations.” It’s miles and leagues different. In a scientific theory, you have an explanation for why a certain thing happens. You have no such explanation for a “stochastic theory”. There is no explanation for why an atom decays at time t instead of t + 1. That’s not a theory

@JD I expect that means the same or similar, though the physical phenomenon itself does not have to be random. It could be chaotic. Or it could be just that we are modelling our best understanding of a complex system and we are using epistemic probabilities to allow for our lack of knowledge.

@Syed If you take an umbrella when you go out it is because you have some credence that it will rain. If you were certain that it will not rain you wouldn't bother with the umbrella. Whether the decision process is conscious or not and whether you put numbers to it or not is irrelevant. The whole point of decision theory is to put numbers to our degree of credence and our utility. We have to make decisions with uncertain and incomplete information and we make better decisions when we can quantify those things.

Also I strongly disagree that stochastic theories are fundamentally different. We can explain radioactive decay. It is an example of quantum tunnelling. But our best theories about it are stochastic and not deterministic. That does not mean they are not theories. All the non-trivial predictions of quantum mechanics are probabilistic and not deterministic. We would hardly say that quantum mechanics does not qualify to be called a theory because it does not make deterministic predictions.

@Conifold Defenders of objective Bayesianism usually speak of calibration and equivocation. Calibration means your credences must align with known frequencies. Equivocation means your priors should make the least possible assumptions about the information you possess. This is where maximum entropy and Kullback-Leibler divergence come in: they can be thought of as highly generalised forms of the principle of indifference.

As to how we construct stochastic models: in a similar way that we construct deterministic ones. By finding all the variables, identifying the fundamental elements, and doing our best to understand the dependencies and relationships between them. We can't perform controlled experiments on the weather and we can't repeat an election. But many sciences are observational, e.g. geology and astronomy. That doesn't stop us making theories. We have theories of stellar evolution, but they are probabilistic and the evolution of any given star is unrepeatable.

@Bumble You just asserted your conclusions again. Your argument is circular. I pointed out that when we make a decision to use an umbrella, there seems to be no conscious or unconscious process requiring credences or numbers. You then responded to this by saying “the whole point of decision theory is to put numbers to our degree of credence.” You have not provided any argument as to why we should use the concept of a degree of credence in the first place

secondly, the part of quantum mechanics that we can actually outline are the deterministic parts of it, such as Schrodinger’s equation. We have no explanation for why an atom decays a time t instead of t + 1. A stochastic prediction isn’t a prediction and is unfalsifiable. If you tell me that an atom has 90% chance of decaying in a certain period, it doesn’t tell you whether it will decay. If it decays, you can say “there was a 90% chance. Makes sense” If it doesn’t, you can say “see, there was a 10% chance.”

@Syed The point of decision theory is not to describe our mental processes but to provide a theory of what constitutes good decision making. All the standard forms of decision theory use probabilities and utilities. I do not need to argue why we should use degrees of credence, I am pointing out that decision theory does so and it is a well established field of study.

Quantum mechanics is a theory and it makes probabilistic predictions. It does not fail to be a theory for that reason. Its predictions are testable in the same way that those of any statistical theory are. What do you suppose statistical hypothesis testing is about? Lots of theories provide probabilistic predictions. Econometrics, epidemiology, weather forecasting, climate modelling, business analytics, reliability engineering, financial modelling, risk analysis, bioinformatics, the list is almost endless.

@Bumble The tests aren’t actually based on probability though. When we test things in QM, we are testing frequency related facts which have no notion of credence or probability. We are testing, for example, how many atoms decay in a certain period.

@Syed That rather depends on your preferred interpretation of quantum mechanics. Some people do interpret it as a Bayesian theory. Similarly with statistical mechanics and the information theoretic interpretation of entropy. In any event, what we are doing is testing a probabilistic prediction from a theory, e.g. half the atoms will decay in the next 10 minutes, using statistical methods.