The above quotation belongs to one of the lesser-known Shavian one-acts: The Jesus-Pilate Scene. This brief (3,116 words) conversation between the two eponymous characters, included in the preface to On the Rocks, takes place when Jesus was taken before Pilate for trial.
The whole rationale behind the scene lies on the great differences in perspective, which often remain unnoticed, that derive from whether one is a reader or an spectator. In Shaw's words,
"It may be asked why the incident of the trial and execution must fail on the stage, seeing that the gospel narrative is so pathetic, and so many of us have read it without disappointment. The answer is very simple: we have read it in childhood; and children go on from horror to horror breathlessly, knowing nothing of the constitutional questions at issue. Some of them remain in this condition of intellectual innocence to the end of their lives, whilst the cleverer ones seldom reconsider the impressions they have received as little children."
In order to justify Pilate's decision, and make it dramatically plausible, Shaw puts in his mouth the above words, explicitly indicating that Pilate was not a man of faith or a philosopher, but simply an administrator of justice. Hence his retort to Jesus's idea that "the peace of God is beyond our understanding."
Pilate: [...] "If you were a responsible governor instead of a poetic vagrant, you would soon discover that my choice must lie, not between truth and falsehood, neither of which I can ever ascertain, but between reasonable and well informed opinion and sentimental and ill informed impulse."
Apart from the illuminating content of this speech, it is interesting to note how the word "truth" vertebrates the whole narrative of the scene, given that "truth" and "true" occur 39 times in this brief text; that is, more than in any other play of the Shavian canon. Statistically, this figure is even more salient, given that the average occurrence-to-1,000 words ratio in all of Shaw's plays is roughly 0,9 - compare that to more than 12 in the Jesus-Pilate Scene.
When it came to separating the wheat from the chaff in Scripture, Shaw was sure to claim that "the truth shall make you free."