Thanks to some very good points made by wakaba I’ve decided to write a followup post.
More cash is always worth more than less cash. Rationally trading two differing amounts of the same currency is thus impossible. A stock has risk; its future dividend is not guaranteed. Estimating the value of a stock involves constructing a probability distribution for the future stock dividends.
Different people have different information, and may thus infer different distributions. However, even when they have the same beliefs and infer the same distribution, they will still price the stock differently depending on their differing appetites for risk. For example, a grad student would be willing to pay less than a millionaire for the same 50% chance at winning $10,000. See also the St Petersburg Paradox.
A corollary of this line of logic: given that two people infer the same probability distribution A, they will arrive at the same price for the stock as the uncertainty of A becomes smaller and the appetite for risk becomes irrelevant.