This paper describes a novel framework for the Open World face recognition problem, where one has to provide for the Reject option. Based upon algorithmic randomness and transduction, a particular form of induction, we describe the TCM-kNN (Transduction Confidence Machine – kNearest Neighbor) algorithm for Open World face recognition. The algorithm proposed performs much better than PCA and is comparable with Fisherfaces. In addition to recognition and rejection, the algorithm can assign credibility (“likelihood”) and confidence (“lack of ambiguity”) measures with the identification decisions taken.