The phrase "any possible consequences" is correct and usable in written English.
You use it to indicate that there may be potential outcomes or results of an action. For example, "I knew that if I took the risk, there could be any possible consequences".
It's of course true that any real game would impose some upper limit N, producing a finite number of possible consequences of the game; but this does not solve the St . Petersburgpuzzle because these finite games are not St.
Choices are presumably between actions, or between possible consequences of those actions.
Thus there would be only a finite number of possible consequences.
where the Sj are the possible consequences of the acts Ai, and U gives the utility of its argument.
In decision theory, the decision-making units are individuals with preferences over the possible consequences of their actions.
None of these methodological decisions could be made without consideration of the possible consequences that could occur.
Considering the possible consequences of one's actions is further complicated as computer technologies make it possible for humans to do things that they could not do before.
An agent is supposed to make decisions based on her belief-strengths about the state of the world, her belief strengths about possible consequences of actions, and her assessment of the desirability (or utility) of these consequences.
According to legend, Duell declared that everything that can be invented has already been invented; and even though this wonderful story is probably apocryphal, it nonetheless illustrates in a humorous way the possible consequences of an impoverished imagination.
Someone who didn't realize that his finite bank couldn't cover possible consequences might sincerely offer the game, as might someone who realized that, but took the risk of owing what he couldn't pay.
In response, Brandt argues for what he calls ideal rule utilitarianism, which makes the frame of reference for rule consideration not the actual rules available, but the ideal rule, i.e., the rule that would be optimific (productive of the best possible consequences), were it employed.
