More than 50% or Less than 70% Chance: Pragmatic Implications of Single‐Bound Probability Estimates

Abstract

Probability estimates can be given as ranges or uncertainty intervals, where often only one of the interval bounds (lower or upper) is specified. For instance, a climate forecast can describe La Niña as having "more than 70% chance" or "less than 90% chance" of occurring. In three experiments, we studied how research participants perceived climate-related forecasts expressed with lower-bound ("over X% chance") or upper-bound ("under Y% chance") probability statements. Results indicate that such single-bound statements give pragmatic information in addition to the numeric probabilities they convey. First, the studies show that these statements are directional, leading the listeners' attention in opposite directions. "Over" statements guide attention towards the possible occurrence of the event and are explained by reasons for why it might happen, while "under" statements direct attention to its possible non-occurrence and are more often explained by reasons for why the target event might not appear, corresponding to positive (it is possible) versus negative (it is uncertain) verbal probabilities. Second, boundaries were found to reveal the forecaster's beliefs and could be perceived as indicative of an increasing or a decreasing trend. Single-bound probability estimates are therefore not neutral communications of probability level but might "leak" information about the speaker's expectations and about past and future developments of the forecast.

Framing experts' (dis)agreements about uncertain environmental events

“…were more inclined to expect the event to occur (Hohle & Teigen, 2018a). The same study also showed that an expert stating that the probability is "over 30%" was thought to have made a lower estimate last year, whereas "under 50%" indicated a decreasing trend.…”

“…The magnitude of this difference is indeterminate, as “over 50%” and “under 50%” could, in principle, mean a whole range of probabilities. However, we know from previous research (Ferson et al, ; Hohle & Teigen, , see also Footnote 5; Teigen et al, ) that such expressions are usually taken to indicate amounts that are rather close to the reference value, so the difference between an “over” and “under” estimate is probably small rather than large. However, we do not know the exact magnitude of this difference, or how people will judge a comparison of different directional terms involving different probabilities that converge towards an intermediate number (e.g., over 50% vs. under 70%).…”

“…Imagine, for instance, two experts stating that the probability of a glacier shrinking to half its size is either “over 30%” or “under 50%”. Although participants in a recent study believed the implied point probability of the first expert was lower (36%) than that of the second expert (48%), they nevertheless reported that experts using “over” were more inclined to expect the event to occur (Hohle & Teigen, ). The same study also showed that an expert stating that the probability is “over 30%” was thought to have made a lower estimate last year, whereas “under 50%” indicated a decreasing trend.…”

Guidance on Communication of Uncertainty in Scientific Assessments

“…(), and other publications) show that people (including doctors and people with statistical training) perform very poorly at deducing probabilities of interest from conditional probability information and perform much better if provided with information in the form of frequencies. It is better to avoid the problem altogether by providing frequencies for the outcome of interest directly and not requiring readers to make deductions from conditional information5See Evidence and reasoning for 3.1.3 point 5 (above)6Evidence: when receiving a message such as ‘more than X’, people tend to infer extreme values (Teigen (), Hohle and Teigen (), Hoorens and Bruckmüller ())7Reasoning: This is desirable because it requires assessors to draft an expression of the uncertainty that is concise enough to serve as a starting point for crafting communications, without the communicators having to interpret it (and potentially misinterpret it) from more detailed technical material. It also makes the information more accessible to the communicators Box 1 Reasoning: Standardised procedures usually have standard language for expressing their conclusions (e.g.…”

“…Evidence: when receiving a message such as 'more than X', people tend to infer extreme values (Teigen (2008), Hohle and Teigen (2018), Hoorens and Bruckm € uller (2015)) 7 Reasoning: This is desirable because it requires assessors to draft an expression of the uncertainty that is concise enough to serve as a starting point for crafting communications, without the communicators having to interpret it (and potentially misinterpret it) from more detailed technical material. It also makes the information more accessible to the communicators Box 1…”