Measuring Non-Probabilistic Uncertainty: A cognitive, logical and computational assessment of known and unknown unknowns

Abstract: There are two reasons why uncertainty may not be adequately described by Probability Theory. The first one is due to unique or nearly-unique events, that either never realized or occurred too seldom for frequencies to be reliably measured. The second one arises when one fears that something may happen, that one is not even able to figure out, e.g., if one asks: "Climate change, financial crises, pandemic, war, what next?" In both cases, simple one-to-one cognitive maps between available alternatives and possible consequences eventually melt down. However, such destructions reflect into the changing narratives of business executives, employees and other stakeholders in specific, identifiable and differential ways. In particular, texts such as consultants' reports or letters to shareholders can be analysed in order to detect the impact of both sorts of uncertainty onto the causal relations that normally guide decision-making. We propose structural measures of cognitive maps as a means to measure non-probabilistic uncertainty, eventually suggesting that automated text analysis can greatly augment the possibilities offered by these techniques. Prospective applications may concern actors ranging from statistical institutes to businesses as well as the general public.