# Alternative “Facts” vs. Alternative “Inferences”

Suppose you have seen the following sequence in three coin tosses:

HHH

Which of the following statements is a “fact”?

1. The coin is fixed and will always land “head.”
2. The coin is fair.

The short answer is that neither of these statements constitutes a “fact.” They are both inferences, conditional on two things: the observer’s prior about the universe and the actual indisputable fact — that you have gotten three heads in a row. We may or may not believe that the coin is actually fair, more or less, and you just had a series of chance occurrence and that is not improbable (1/8). Since we don’t think, a priori, a coin that always lands “head” is very probable, if at all possible, we (rightly, I think) think that that is very likely. BUT there is nothing in the actual “fact” that is uncontested that makes the “fringe” belief that the coin is fixed improbable. If anything, it actually reinforces that beliefs.

We might believe that the coin is close to being fair, if not fair, for a variety of reasons. We might believe that the existence of a magic coin is not very likely, if at all actually possible. We might have seen many coin tosses before, even if not necessarily from this coin, and believe that (not improbably) that this is coin is just like any other (even if we have no explicit or informed reason to believe one way or another). Or, we might be lazy and think that 50–50 chance is reasonable. None of these actually says that the specific coin in question is not fixed. The “conspiratorialist” who believes that this particular coin is fixed has no reason to believe that his belief is wrong in terms of actual undisputed “facts.” The only “fact” that would convince him otherwise is the coin turning up “tail” in some toss. In other words, to prove the conspiratorialist otherwise, you need to invest in an actual experiment, where you are willing to pay a cost to show that, in some N tosses, where N>3, there is at least one “tail.” (or, if the conspiratorialist has a more nuanced belief, that true P(H) = .9 or something, enough of a result to tickle his p-value.)

The bottom line is that “alternative inferences” are easy, apparently quite common, rather natural, and in fact often undergirded by real facts that are beyond dispute. We often think others are wrong because they are drawing different inferences from ours from the same set of facts, but that only means that they are coming to the observations with different sets of priors through which the facts are evaluated.