  Consider a predictor who ranks eventualities on the basis of past cases: for
instance a search engine ranking webpages given past searches. Resampling past
cases leads to different rankings and the extraction of deeper information. Yet
a rich database, with sufficiently diverse rankings, is often beyond reach.
Inexperience demands either "on the fly" learning-by-doing or prudence: the
arrival of a novel case does not force (i) a revision of current rankings, (ii)
dogmatism towards new rankings, or (iii) intransitivity. For this higher-order
framework of inductive inference, we derive a suitably unique numerical
representation of these rankings via a matrix on eventualities x cases and
describe a robust test of prudence. Applications include: the success/failure
of startups; the veracity of fake news; and novel conditions for the existence
of a yield curve that is robustly arbitrage-free.
