Molinism and correlations

Assume Molinism.

Suppose T is a set of character traits that makes one be equipoised between freely taking and refusing a $5000 bribe for a city contract. Let C₁, C₂, ... be distinct and highly specific possible circumstances of Curley being offered such a bribe, differing in morally unimportant ways that are not very relevant to Curley’s character. Perhaps he is offered the bribe in an Italian restaurant, or in a Thai restaurant, or while walking in the park. Perhaps the bribe is being offered by a man or by a woman. Maybe it’s in the morning or the evening. Etc.

Consider the counterfactual of free will:

• Q_i: Were Curley to have T and be offered a $5000 bribe for a city contract in C_i, he would accept the bribe.

Intuitively, P(Q_i) ≈ 1/2 for any i. Let’s accept that intuition. But now here is an interesting question: What kinds of statistical correlation is there between Q₁, Q₂, ...?

The intuition behind van Inwagen’s re-run thought experiment says that if Curley were offered a sequence of exactly similar bribes, with memory erased in between, then Curley’s acceptance/rejection decisions would behave like an independent sequence of random variables. That intuition suggests that Q₁, Q₂, ... are also statistically independent.

On the other hand, one might have the conflicting intuition that Q_i and Q_j are more correlated when the circumstances C_i and C_j are more similar.

On the third hand, one might think that although each of Q_i has probability around 1/2, the probabilities of conjunctions of the Q_i are undefined, and hence it makes no sense to talk about their correlations.

These seem to me to be the three most plausible views on the correlation question. Call these the Independence, Similarity, and Undefined views.

On Molinism plus Independence, God has a vast amount of providential power. He is nearly certain to be able to get Curley (or any other free agent) to freely do anything he wants, simply by choosing minor and unimportant features of circumstances. Given independence, it is extremely unlikely that all the Q_i have the same truth value. Thus, God can just choose the circumstances to get the truth value he wants—to get Curley to accept or to get Curley to reject the bribe. In particular, on Independence, free will does not do much to help the theist.

On the Similarity view, there are some more serious constraints of God’s providential power. However, I think there is another problem with the Similarity view. On Similarity, there is presumably some complicated function from the degree of similarity between circumstances to the degree of correlation (say, measured by covariance) between the truth values of the corresponding counterfactuals. Where does this function come from? Normally correlations between events are explained by laws of nature. But counterfactuals of free will are prior to laws of nature. I suppose the correlation function would have to be something necessary. But it does seem mysterious.

I think that if I were a Molinist, I would find the Undefined view somewhat appealing. The version of it that seems most plausible would be that P(Q_iQ_j) is not defined as a number, but can be represented as the interval [max(0,P(Q_i)+P(Q_j)−1),min(P(Q_i),P(Q_j))]. But I still find it a bit odd that P(Q_i) and P(Q_j) are defined but P(Q_iQ_j) is not. Nonetheless, this seems possible.