Do Experts Use Vague Words Instead of Numbers When They Want to Persuade?
When experts want to persuade, do they trade precise numbers for vague words? In two experiments, de Chaisemartin, Thaler, and Toma (2026) test this. In one, 500 online participants described the odds of drawing a red ball; in the other, 145 academic researchers reported real study results to 66 government policymakers. When rewarded for persuading rather than informing, experts became 25 to 29 percentage points more likely to use words such as "substantial" instead of a number. Most still reported numbers honestly, but their words leaned toward the answer they wanted. It worked: policymakers guessed effects about 22 percent larger when researchers were trying to persuade them.
Why This Article Was Selected for The Policy Scientist
Nearly every public decision now passes through a summary of research: a briefing memo, a clearinghouse rating, a press release, a news story, and increasingly an automated digest. Each step lets a communicator choose between a number and an adjective, and that choice carries more weight as trust in scientific expertise becomes politically contested. This concern is central to The Policy Scientist, which reports effect sizes in numbers. The article extends a long literature on strategic communication (Crawford and Sobel 1982) and on aversion to lying (Abeler et al. 2019) by showing that the format of a message, not only its content, responds to incentives. Thaler has published on truthfulness and motivated reasoning, and Toma on how policymakers use research evidence. The design is strong: pre-registered randomized experiments with incentivized choices, plus a second study using real researchers, real policymakers, and real published effect sizes. Generalizability is the main limit, since the settings are stylized and the second study is small. The article is forthcoming in the American Economic Review, among the most selective journals in economics.
Full Citation and Link to Article
de Chaisemartin, V., Thaler, M., & Toma, M. (2026). Numbers tell, words sell. American Economic Review. Forthcoming.
Central Research Question
The study asks whether people who know a numerical fact choose imprecise language over a number when they have an incentive to persuade rather than inform. It also asks whether such language is slanted more than numbers, whether audiences are misled by it, and whether the pattern found in an abstract setting holds when academic researchers describe real policy evaluations to government officials.
Previous Literature
Theoretical work on "cheap talk" shows that a sender whose interests differ from the receiver's will transmit only coarse information (Crawford and Sobel 1982). Experimental research, summarized by Abeler et al. (2019), finds that many people pay a psychological cost for lying and therefore report more truthfully than strict self-interest predicts. Kartik (2009) models communication with such lying costs, and Serra-Garcia et al. (2011) find that people are more willing to mislead through vague statements than through direct lies. Observational evidence points the same way: Gentzkow and Shapiro (2006) document slanted wording in news coverage, and Edlin and Love (2022) find that only 37% of empirical economics abstracts include numbers. Cain et al. (2005) show that disclosing a conflict of interest does little to protect audiences. Policy fields such as intelligence analysis and climate science have adopted explicit mappings from words to probabilities in response (Dhami and Mandel 2021; Mastrandrea et al. 2011). What has been missing is causal evidence that incentives themselves push communicators from numbers toward words.
Data
Study 1 ran in April 2024 on Prolific with 1,000 U.S. adults (86 others who failed an attention check were excluded, as pre-registered): 500 "senders" and 500 "receivers." Each sender made eight decisions, yielding 4,000 choices. Senders learned the chance of drawing a red ball and wrote both a numeric message and a language message chosen from 13 phrases ranging from "practically impossible" to "practically guaranteed." Half of senders instead chose between a number and a 10-point interval. Study 2 ran from July to September 2024. Of 241 social science researchers invited, 145 participated (75% in tenure-track positions). They communicated real treatment effects, from 1.2 to 13.8 percentage points, drawn from six published policy evaluations in areas such as health insurance, criminal justice, and college access. Receivers were 66 civil servants from five countries, recruited through the University of Warwick's Policymakers Lab, who provided 129 predictions.
Methods
Both studies are randomized experiments. Senders were assigned either "aligned" incentives, paid when the receiver guessed accurately, or "directional" incentives, paid when the receiver guessed high (or, in Study 1, low). In Study 1 incentives varied across each person's eight decisions; in Study 2 each researcher was assigned to a single condition. Senders wrote both message types and then stated which they preferred. The preferred format was sent half the time and a random format the other half, so both messages had real consequences. The main outcome, preferring language, is estimated with linear regressions that include person and true-value fixed effects, with standard errors clustered by person. To measure how slanted a word is, a separate incentivized exercise asked participants which number each phrase represents (for example, "probable" maps to a median of 70%). Random assignment cleanly identifies the effect of incentives. The weaknesses lie in the stylized setting: one-shot anonymous exchanges with no reputation at stake, a fixed menu of phrases, senders who know the truth exactly, small bonuses, and a small, self-selected, evidence-friendly sample of policymakers.
Findings/Size Effects
Incentives to persuade sharply increased the use of language. In Study 1, senders with aligned incentives chose words 14% of the time, compared with 35% under incentives to push guesses high and 40% under incentives to push them low. The regression estimate is a 25.0 percentage-point increase, significant at the 1% level, roughly 2.8 times the aligned rate. Senders choosing between numbers and 10-point intervals shifted similarly (29.7 percentage points). In Study 2, researchers chose language 13% of the time when informing and 41% when persuading, a 29.1 percentage-point increase (p < 0.001). Researchers with persuasion incentives were especially likely to use words when the true effect was small: each additional percentage point of true effect reduced their use of language by 2.3 percentage points (p = 0.021).
Most people did not lie with numbers. In Study 1, 94% of aligned senders reported a number within 3 points of the truth, and under directional incentives the median numeric slant was zero. A minority slanted heavily, so numeric messages averaged about 10 to 12 percentage points in the favored direction, relative to aligned senders. Language was slanted more broadly: 49% of senders with high-direction incentives slanted words by more than 3 points, compared with 26% for numbers. Senders who preferred words slanted them 10.5 percentage points more than their own numbers (p < 0.001), comparing high- and low-direction incentives. Only 2% of responses slanted numbers but not words, while 28% slanted words but not numbers. In Study 2, persuading researchers reported numbers 13% larger than informing researchers (p = 0.006) but chose words implying effects 49% larger (p < 0.001). The share using "small" words such as "modest" or "tiny" fell from 44% to 17%, and the use of words like "considerable" and "substantial" rose from 31% to 54%.
Audiences were persuaded. In Study 1, receivers' guesses were 22.8 percentage points higher when paired with a sender pushing high rather than low, and that gap widened by a further 15.8 points when the message arrived in words. When informing, numbers produced an average guessing error of 2.5 points and words 8.7 points; when persuading, errors rose to 12.6 and 26.4 points. Telling receivers the sender's incentive barely helped; 85% of their written explanations took the message at face value. In Study 2, policymakers predicted effects 2.2 percentage points, or about 22%, larger when researchers were persuading (significant at the 5% level). Evidence that words persuaded policymakers more than numbers is only suggestive (3.3 points, p = 0.095).
Conclusion
The study shows, with randomized evidence, that incentives to persuade lead communicators to replace numbers with words, that those words are slanted more than the numbers the same people would report, and that audiences, including government officials, move toward the communicator's preferred answer. The pattern is consistent with "plausible deniability": a word such as "probable" can be defended across a range of values, while a wrong number cannot. The authors caution that the results do not show how often researchers face such incentives in practice, and most researchers in the study did not misreport numbers. The settings are short, anonymous, and stylized, so effects could be larger or smaller where reputations, repeated interactions, or genuine uncertainty matter. Future research could measure the strategic use of words in real reports and news coverage and test remedies such as requiring numbers alongside verbal descriptions, standard word-to-probability scales, or disclosure of conflicts of interest.
Comments