A firm is interested in marketing a new product to its customers. These are connected in a social network that is known to the firm: the network represents the trust relationships between customers. The firm has decided to adopt a marketing strategy that involves giving the product for free to a number of its customers, in the hope that these influence the other customers and entice them to buy the product. The firm wants to choose the customers to which marketing is applied so that its return is maximized. This involves computing the probability that the non-marketed customers will acquire the product given the action to the marketed customers.
This viral marketing scenario is inspired by [1].
We can model this domain with an LPAD where the predicate trust/2 encodes the links
between customers in the social network and predicate has/1 is true of customers that possess
the product, either received as a gift or bought. Predicate trust/2 is defined by a
number of certain facts, while predicate has/1 is defined by two rules, one expressing the
prior probability of a customer to buy the product and one expressing the fact that if a trusted customer has the product, then there is a certain probability that the trusting customer buys the
product.
In the example code below the social network is:
We want to compute the probability that customer 2 buys the product if
we perform the action of giving the product to customer 3. We need to
use causal reasoning so we use the action do(has(3)) as evidence:
If instead we compute the effect of the action using regular probabilistic inference, we get:
So not distinguishing seeing from doing leads to an overly optimistic estimate.