NOTE: This is a post-print of an article accepted for publication in American Psychologist.
Words or Numbers?
Communicating Probability in Intelligence Analysis
Mandeep K. Dhami1 and David R. Mandel2
1Department of Psychology, Middlesex University
2Intelligence, Influence and Collaboration Section, Defence Research Development Canada
Funding for this work was provided to the first author by HM Government and to the second
author by Canadian Department of National Defence projects 05da and o5fa and
Canadian Safety and Security Program project CSSP-2018-TI-2394. This work
contributed to NATO System Analysis and Studies Panel Research Technical Group 114
on Assessment and Communication of Uncertainty in Intelligence to Support Decision
Making. We thank Daniel Irwin and Serena Tran for their research assistance.
We have no conflict of interest to disclose.
Correspondence concerning this article should be addressed to Mandeep K. Dhami, Department
of Psychology, School of Science and Technology, Middlesex University, The
Burroughs, Hendon, London, NW4 4BT.
Intelligence analysis is fundamentally an exercise in expert judgment made under
conditions of uncertainty. These judgments are used to inform consequential decisions.
Following the major intelligence failure that led to the 2003 war in Iraq, intelligence
organizations implemented policies for communicating probability in their assessments.
Virtually all chose to convey probability using standardized linguistic lexicons in which an
ordered set of select probability terms (e.g., highly likely) is associated with numeric ranges
(e.g., 80-90%). We review the benefits and drawbacks of this approach, drawing on
psychological research on probability communication and studies that have examined the
effectiveness of standardized lexicons. We further discuss how numeric probabilities can
overcome many of the shortcomings of linguistic probabilities. Numeric probabilities are
not without drawbacks (e.g., they are more difficult to elicit and may be misunderstood by
receivers with poor numeracy). However, these drawbacks can be ameliorated with
training and practice, whereas the pitfalls of linguistic probabilities are endemic to the
approach. We propose that, on balance, the benefits of using numeric probabilities
outweigh their drawbacks. Given the enormous costs associated with intelligence failure,
the intelligence community should reconsider its reliance on using linguistic probabilities
to convey probability in intelligence assessments. Our discussion also has implications for
probability communication in other domains such as climate science.
Keywords: Subjective Probability, Uncertainty, Verbal Probabilities, Policy-Making,
Psychological research on probability communication suggests that using numbers such as 70%
(or 65%-75%) rather than words such as likely provides a more clear and unambiguous way of
communicating uncertainty in judgments. Therefore, we recommend that the intelligence
community changes its current policy for probability communication in its assessments from the
verbal to numeric mode, in order to mitigate intelligence failures such as that which led to the
2003 war in Iraq.
Intelligence assessments are vital to decision-making in several consequential domains
including law enforcement, defense and national security. Analysts must answer questions of
strategic, tactical and operational importance for a variety of consumers including commanders,
government officials and other analysts. For example, “How will North Korea’s ballistic missile
capability develop over the next three years?” And, “Where are Islamic State’s financiers
located?” Such assessments are typically made under conditions of uncertainty (Fingar, 2011).1
This is because relevant information may be missing or even unknowable (such as a foreign
leaders’ intentions), information collection may be biased, and information may be unreliable as
well as purposefully misleading. Consequently, most assessments are subjective probability
judgments (Kent, 1964). Not only are analysts expected to judge probabilities accurately, they
are also expected to communicate them clearly to consumers. Even the best judgments, if poorly
communicated, can fail in their primary objective of supporting sound decision-making.
The deleterious consequences of poor probability communication were acutely evident in
the 2003 invasion of Iraq that expected to find weapons of mass destruction (WMD), which in
fact did not exist. Post-mortem analyses of this major intelligence failure criticized intelligence
organizations for understating the probability in their assessments and suggesting greater
certainty than was warranted by the available information (see UK House of Commons Foreign
Affairs Committee, 2003; UK Intelligence and Security Committee, 2003; US Congressional
Select Committee on Intelligence, 2005). The 2004 Butler review further questioned whether
intelligence products were “drafted and presented in a way which best helps readers to pick up
1" In intelligence analysis, uncertainty addresses both the probability of events and the confidence an analyst has in
his/her assessment. Probability refers to the degree of certainty assigned to the belief that an event will or will not
occur, and this is bounded from 0 (impossibility) to 1 (certainty), whereas confidence is treated as a multi-
dimensional construct referring to variables such as source reliability and information credibility (Friedman &
Zeckhauser, 2018). In this article, we examine how the intelligence community assesses and communicates
probability. The topic of confidence is beyond the scope of this article.
the range of uncertainty attaching to intelligence assessments” (p. 144). The issue of knock-on
errors in reporting was highlighted in the 2005 US Congressional report, which concluded that
building on prior intelligence “without carrying forward the uncertainty from the first layer, …
gave the impression of greater certainty about its judgments than was warranted” (p. 173). The
damaging effects on decision-making of this intelligence and the misinterpretation of the
probability attached to it, was emphasized in the Chilcot (2016) inquiry which noted that former
UK Prime Minister Tony Blair mistakenly believed that intelligence organizations were “sure”
about Iraq possessing WMD.
Similar conclusions were reached decades earlier in a now declassified 1983 Central
Intelligence Agency (CIA) report into major intelligence failures. This concluded that analysts
“lacked a doctrine or a model for coping with improbable outcomes. Their difficulty was
compounded in each case by reluctance to quantify their theories of probability or their margins
of uncertainty. Findings such as “likely,” “probable,” “highly probable,” “almost certainly,” were
subjective, idiosyncratic, ambiguous between intelligence producer and consumer, uncertain in
interpretation from one reader to another, and unchallenged by a requirement to analyze or
clarify subordinate and lesser probabilities” (p. 5). The report went on to recommend the
quantification of probability in future intelligence assessments.
The intelligence community has long debated the pros and cons of using words (e.g.,
terms such as likely and unlikely) and numbers to communicate probability (see Marchio, 2014).
Rarely have these debates been informed by pertinent evidence. In the present article, we
examine current policies for communicating probability in intelligence assessments—policies
that continue to rely on linguistic rather than numeric probabilities. Probability communication
has received considerable attention in psychological research, and the extant evidence can be
used to inform policy-making. Our discussion also has implications for the assessment and
communication of threats and risk in the intelligence analysis domain (see Friedman, 2019), and
for probability communication in other domains such as medicine and climate science (e.g., see
Budescu, Por, & Broomell, 2012; Budescu, Por, Broomell, & Smithson, 2014; Mazur & Merz,
1994; Timmermans, 1994). The use of linguistic probabilities to communicate probability in
these domains is akin to the approach adopted by the intelligence community.
The paper is divided into three sections. We first discuss the intelligence community’s
reliance on a circumscribed set of probability terms, and we consider the benefits and drawbacks
of this approach to probability communication. In the second section, we highlight the
limitations of standardization—a common solution to the pitfalls of using words to communicate
probability. Finally, we propose numeric probabilities as an alternative to linguistic probabilities,
we consider the pros and cons of this approach, and we review research comparing the effects of
verbal and numeric modes of probability communication on decision-making.
Communicating Probability Using Words
Traditionally, the intelligence community has taken an unstructured approach to
probability communication. As a result, often probabilities were simply not communicated.
Friedman and Zeckhauser (2012) revealed that a notable proportion (i.e., 18%) of the 379
declassified National Intelligence Estimates (NIEs), which are the most authoritative intelligence
reports produced in the US, written between 1964 and 1994, did not provide any assessment of
the probability associated with the outcome being forecast. On the other hand, as we saw with
the earlier WMD example, suggesting greater certainty than warranted is also not uncommon.
Analyses of the contents of 120 NIEs written between the 1950s and 2000s (i.e., 20 per decade,
Kesselman, 2008) and of 2,013 Canadian intelligence assessments from 2006 to 2011 (Mandel &
Barnes, 2018) show that the term will, which represents certainty, was most commonly used by
analysts. However, probability statements should not be avoided. The 2005 US Congressional
report states, “As much as they hate to do it, analysts must be comfortable facing up to
uncertainty and being explicit about it in their assessments” (p. 408).
Intelligence Community Policies for Probability Communication
The US and the UK introduced formal policies for communicating probability in
intelligence assessments in the mid-2000s following recommendations made by inquiries into the
Iraq WMD intelligence failure. In the UK, the 2004 Butler review stated, “While not arguing for
a particular approach to [expressing]…uncertainty, …we recommend that the intelligence
community review their conventions again to see if there would be advantage in refreshing
them” (p. 146). In the US, the 2005 Congressional report stated, “Whatever device is used to
signal the degree of certainty—mathematical percentages, graphic representations, or key
phrases—all analysts in the Community should have a common understanding of what the
indicators mean and how to use them” (p. 419).
Policies for communicating probability in intelligence assessments have been developed
at both national and international levels. National policies include those developed in the US by
the Office of the Director of National Intelligence (ODNI), and in the UK by the Professional
Head of Intelligence Analysis (PHIA); both organizations responsible for overseeing the
intelligence community in their respective countries. Internationally, NATO has a policy for
probability communication to be used by member states. Despite the various options available,
policy-makers chose to convey probabilities in assessments using a standardized lexicon of
linguistic probabilities. These lexicons have undergone revisions over the years, and Figure 1
presents the most recent versions of the US, UK and NATO lexicons (NATO Standardization
Office, 2016; ODNI, 2015; PHIA, 2018 as published in College of Policing, n.d.).
Figure 1. Lexicons for communicating probability in intelligence assessments
As Figure 1 shows, analysts are required to use a list of select words or probability terms
that are ordered from the lowest to the highest degree of probability. These are combined with
numeric ranges. Sherman Kent (1964), who played a key role in founding the CIA’s Office of
National Estimates (the predecessor of today’s US National Intelligence Council), was the first to
advocate this type of standardization, although it was not implemented at the time. He was
prompted by the observation that both analysts and consumers varied considerably in their
understanding of the term serious possibility which was used to communicate the probability of a
Soviet invasion of Yugoslavia in 1951. Over a half-century later, current solutions to the problem
of probability communication in intelligence analysis are largely the same.
Benefits of Linguistic Probabilities
It appears that intelligence organizations strongly prefer to communicate probability
linguistically rather than numerically. In their analysis of NIEs, Friedman and Zeckhauser (2012)
revealed that only four percent contained numeric expressions of probability (e.g., percentages,
odds). Intelligence organizations are not alone in their inclination for using linguistic
probabilities. Several studies show that people may prefer to communicate probability
linguistically rather than numerically (e.g., Erev & Cohen, 1990; Wallsten, Budescu, Zwick, &
Kemp, 1993; but see Brun & Teigen, 1988 and Vahabi, 2010).
Some scholars have pointed to the potential benefits of using linguistic probabilities.
Zimmer (1983) proposed that people know the rules of language better than the rules of
probability, and they find it easier and more natural to use words when dealing with probability.
Wallsten and Budescu (1995) suggest that linguistic probabilities should be preferred when the
underlying uncertainty in a task is epistemic or internal (i.e., based on one’s knowledge). There
is some evidence to support these viewpoints. In one study, Wallsten et al. (1993) observed that
some people said it was easier and more natural to use language rather than numbers, and for
some, this preference was strongest when the issue was deemed to be unimportant and/or the
information was unreliable (see also Olson & Budescu, 1997).
The evidence for other claims, however, is either lacking or conflicting. For instance,
Zimmer (1984) suggests that people process information verbally through argumentation and so
asking them to respond in the verbal mode (as opposed to the numeric mode) requires less
cognitive effort and makes them less susceptible to bias and unreliability. Budescu, Weinberg,
and Wallsten (1988) did not find evidence to support this claim. Wallsten (1990) notes that
linguistic probabilities allow the decision-maker to retain control of the decision by choosing
how much risk to take. To our knowledge, this assertion has not been directly examined.
Drawbacks of Linguistic Probabilities
Notwithstanding the potential benefits that linguistic probabilities may offer, a substantial
body of evidence points to the drawbacks of using this approach to probability communication.
Research has repeatedly demonstrated considerable variability in how people understand
linguistic probabilities (e.g., Beyth-Marom, 1982; Brun & Teigen, 1988; Clarke, Ruffin, Hill, &
Beaman, 1992; Dhami & Wallsten, 2005; Lichtenstein & Newman, 1967). This variability is
evident both across- and within-individuals. Individuals have broad or fuzzy interpretations of
particular probability terms. In addition, different people may use different terms to refer to the
same probability value(s) and/or may use the same term to refer to different values.
Variability has also been demonstrated in the intelligence analysis context (Dhami, 2018;
Ho, Budescu, Dhami, & Mandel, 2015; Johnson, 1975; Wallsten, Shlomi, & Ting, 2008; Wark,
1964). For instance, Dhami (2018) reported that 145 unique terms were used to represent the 0 to
1 probability interval by a sample of 26 UK analysts. Eighteen terms were used to represent
10%. Unlikely was one of the most common terms used (i.e., by 58% of the sample), but it was
used to represent a wide interval (i.e., 10%-40%). Thus, the communication of probability using
words can mislead because they can be interpreted in different ways. This imprecision can also
mask disagreement in judgments and create the illusion of consensus.
Research also shows that the interpretation of linguistic probabilities may be affected by
the context in which they are used. Contexts can be externally provided such as the topic being
considered (Brun & Teigen, 1988: Mellers, Baker, Chen, Mandel, & Tetlock, 2017), the order in
which terms are presented (Bergenstrom & Sherr, 2003; Hamm, 1991), the base-rate of the event
being judged (Wallsten, Fillenbaum, & Cox, 1986; Weber & Hilton, 1990), the severity of an
outcome (Harris & Corner, 2011; Mazur & Merz, 1994; Merz, Druzdzel, & Mazur, 1991) and
the outcome’s valence (Cohen & Wallsten, 1992). Contexts may also be internal to the person
such as one’s attitude to the subject matter (Budescu et al., 2012; see also Piercey, 2009) and
even one’s locus of control (Hartsough, 1977).
Although more research is needed, context effects have been documented in the
intelligence analysis domain. In one study, Mandel (2015a) reported that a sample of 17 analysts
(and a student sample of 40 who did not differ in responses from the analyst sample) provided
significantly less discriminating numeric interpretations of probability terms in a Canadian
intelligence organization’s lexicon when the event in question was described as a failure than
when it was described as a success. For example, will not was interpreted as close to a 0%
chance when it referred to a success, but it was interpreted as roughly a 10% chance when it
referred to a failure. Conversely, will was interpreted as closer to a 100% chance in the success
than the failure condition. In another study, using a mixed sample of 596 “superforecasters” (i.e.,
forecasters at or above the 98th percentile in accuracy in a geopolitical forecasting tournament),
regular forecasters and undergraduates, Mellers et al. (2017) found that numeric interpretations
of probability terms were affected by the geopolitical context in which they appeared. For
instance, across five topics, the average interpretation of almost certain ranged from a 20% point
spread (for superforecasters in Study 1) to a 39% point spread (for undergraduates in Study 2).
Such contextual effects suggest that the interpretation of probability terms cannot simply be
anchored through standards that stipulate a fixed (context independent) meaning for each term.
Not only do linguistic probabilities vary in their interpretation, as we noted earlier, they
are also imprecise, and this coarsens the probability scale, creating fewer distinguishable levels
of probability that may be communicated to receivers. Such coarsening can artificially inflate (or
decrease) the expressed likelihood of low (or high) probability events occurring. A particular
concern is with rare events, tail risk, or so-called “black swans”—namely, events that have
extremely low probabilities but extremely severe consequences (Makridakis & Taleb, 2009).
While terms such as remote chance represent the lowest probability categories in the lexicons,
these do not convey the exceedingly small chances required to accurately characterize tail risks,
and they may be orders of magnitude off. Indeed, a study of 34 Canadian and 27 UK analysts
found that the average best interpretation of remote chance in the UK was about 23% and it was
about 17% in Canada (Ho et al., 2015). Clearly, an analyst could not use this term to effectively
communicate a 1% chance, let alone a one in a million chance.
Beyond making it difficult to communicate tail risks, coarsening the probability scale has
also been shown to adversely affect forecasting accuracy, especially amongst the most competent
forecasters (Friedman, Baker, Mellers, Tetlock, & Zeckhauser, 2018). That is, when precise
forecasts were binned into varying numbers of categories, accuracy declined with decreasing bin
size. Efforts to constrain the meanings of terms by attaching numeric ranges as in the current
UK, US and NATO lexicons (see Figure 1) does not overcome the imprecision as it simply
divides the 0 to 1 probability interval into a small number of categories (usually less than ten).
It is also doubtful that linguistic probabilities can be effectively combined because words
do not easily lend themselves to arithmetic operations (see Budescu, Zwick, Wallsten, & Erev,
1990; Wallsten, Budescu, & Tsao, 1997; Zwick, Budescu, & Wallsten, 1988). This is of
particular concern in intelligence assessment where analysts are often required to express how
the probability of a number of (independent as well as interacting) events may combine to lead to
an outcome or set of outcomes or where a decision-maker receives multiple assessments and
wants to know their average value. Imagine a chain of four independent events that must occur in
order for a particular threat scenario to manifest. In one case, the probabilities of the events are
communicated numerically as being .75, .10, .70, and .01. In another case, these probabilities are
given using the US standard equivalents, likely, very unlikely, probable, and almost no chance.
In two recent experiments comparing these two modes of communication, participants were
significantly more accurate in computing averages and products from values provided in numeric
rather than comparable verbal form (Mandel, Dhami, Tran, & Irwin, 2020).
Finally, linguistic probabilities convey more than probability. In particular, probability
terms convey “directionality” to recipients (Teigen & Brun, 1995, 1999, 2003; see also Budescu,
Karelitz, & Wallsten, 2003; Honda & Yamagishi, 2006). Directionality is a pragmatic feature of
probability statements that subtly conveys the speakers’ attitude towards the focal event. For
instance, two speakers who agree that the probability of a given event is low may nevertheless
differ by communicating an optimistic attitude using a directionally positive term such as some
chance or by communicating a pessimistic attitude using a directionally negative term such as
doubtful. Directionality can, in turn, shape receivers’ beliefs about the sender’s implicit
recommendations (Teigen & Brun, 1999, 2003). For example, Collins and Mandel (2019) found
that whereas probability information was rated as significantly clearer when it was conveyed
numerically rather than verbally, the clarity of implicit recommendations (which were not
explicitly communicated) was significantly greater when it was conveyed verbally rather than
numerically. These findings suggest that it will not only be harder to infer probability levels from
linguistic probabilities, but also that assessments communicated using probability terms are more
likely to suggest recommendations to decision-makers. This runs contrary to, and threatens, the
intelligence community’s longstanding mandate to remain policy neutral.
Is Standardization the Solution?
The approach (i.e., standardized lexicons) adopted by intelligence organizations to
communicating probability in intelligence assessments cannot mitigate the pitfalls of using
linguistic probabilities. In addition to the concerns raised above, research shows that people
cannot easily suppress their normal, context-dependent meanings of probability terms and adopt
new (mandated) meanings that deny context dependence (e.g., Wallsten et al. 1986; see also
Budescu & Wallsten, 1990). For instance, studies on the lexicons used by the Inter-
Governmental Panel on Climate Change (IPCC) have demonstrated that recipients of terms in
lexicons often do not interpret the words as intended when reading statements that contain them,
and default to their personal interpretation of the terms, thus defeating the purpose of the lexicon
(e.g., Budescu et al., 2012, 2014; Wintle, Fraser, Wills, Nicholson, & Fidler, 2019). Budescu et
al. (2014) found that the proportion of respondents whose numeric interpretations of IPCC terms
that fell in the stipulated ranges varied from 21%-35% across 25 countries, with roughly 200
respondents per country. In addition, in an attempt to increase compliance rates, researchers have
examined the effect of presenting the stipulated numeric ranges alongside the probability terms
used in the statements (e.g., "likely [55%-80%]"; Budescu et al., 2012, 2014; Wintle et al.,
2019). Although this hybrid approach yields higher compliance rates, they still fall short of
acceptable levels. For example, Budescu et al. (2014) found that with the hybrid approach, the
proportion of compliant respondents ranged from 28%-54% in the same set of 25 countries.
However, even if compliance rates were much higher, using numeric ranges alongside
probability terms in assessments can be confusing to receivers who may interpret them as
credible intervals that pertain directly to the assessment. Imagine applying this approach to the
US lexicon, a decision-maker who reads that “The Xs are very likely [80%-95%] to attack
country Y in the next month” might think that the analyst believes there is an 80%-95% chance
that the attack will occur. Yet, the analyst may, if pressed, give lower and upper bounds that cut
across stipulated ranges, such as 70%-85%. Another analyst, who agrees perfectly with this latter
range, may nevertheless assign the term likely, in which case the decision-maker would instead
receive the estimate, “The Xs are likely [55%-80%] to attack country Y in the next month.”
In the intelligence community, the problem with standardization is no doubt further
compounded by having multiple lexicons in operation at one time. Figure 1 illustrates the lexical
differences across nations that share intelligence. In addition, national lexicons may be
implemented with slight variations across organizations within a country. For instance, the
National Crime Agency in the UK uses a visual representation of PHIA’s lexicon (National
Crime Agency, 2018). Probabilities below 50% are depicted in shades of blue, whereas
probabilities above 50% are depicted in shades of purple. Due to organizational differences in
lexicons, analysts (and other intelligence consumers) must rapidly shift their use and
understanding of probability terms and mentally juggle different lexicons. Furthermore, revisions
of lexicons impose additional mental juggling due to intra-organizational changes over time. All
of these undermine interoperability and can exacerbate communication errors.
Problems with the intelligence community’s use of standardized lexicons have also been
highlighted in recent years by researchers who have examined the effectiveness of these lexicons.
Studies have employed quantitative methods inspired by Zadeh’s (1965) fuzzy sets theory in
mathematics, to elicit analysts’ lexicons for probability communication and to measure how people
numerically interpret linguistic probabilities. The emerging evidence points to discrepancies
between policy (what lexicons stipulate) and practice (what analysts do). Specifically,
interpretations of terms in the current US and UK lexicons do not map directly onto the prescribed
numeric ranges (Dhami, 2018; Ho et al., 2015, Study 2; Mandel, 2015a; Wallsten et al., 2008). In
some cases, interpretations were either below or above the category ranges. For instance, in the UK
lexicon, whereas highly unlikely represents 10%-20%, the corresponding 95% confidence interval
on the median best estimate in Mandel’s (2015a) study of a combined sample of Canadian analysts
and students, was 8%-10%. Similarly, whereas likely is intended to represent 55%-75% in the US
lexicon, the 95% confidence interval on the median estimate of this term was 75%-80%.
Furthermore, terms that the lexicons intend to be substitutable such as likely and probably/probable
were not so in participants’ minds (see also Dhami, 2018). Finally, although the rank order of
terms in analysts’ lexicons may generally correspond to that in the US and UK lexicons, analysts
whose lexicons contained terms that appeared in these lexicons did not use them as mandated. For
example, Dhami (2018) found that while likely was ranked before highly unlikely in UK analysts’
lexicons, they used the terms to represent ranges with higher maximum probabilities than that
mandated (see also Wallsten et al., 2008).
In an early survey examining the effect of the verbal mode of probability communication
on recipients, Wark (1964) compared 240 US analysts’ and 63 consumers’ interpretations of
specific probability terms. He reported that consumers had lower numeric interpretations of
terms than did analysts. In other contexts, studies also show differences in communicators’ and
receivers’ interpretations of probability terms. For instance, in the climate change context,
Budescu et al. (2012) revealed that the public consistently misinterprets the probabilistic
statements in IPCC reports in a regressive fashion (i.e., they underestimate high probabilities and
overestimate low probabilities; see also Budescu et al., 2014). The public thus does not interpret
the reports’ conclusions as intended by the authors of the reports.
Some have suggested that standardization could be effective if the lexicons were
empirically derived. Ho et al. (2015, Study 2) used data from 34 Canadian analysts to derive
evidence-based lexicons that utilized the terms common to the US and UK lexicons. The lexicons
were developed using statistical methods that optimized the fit between the stipulated numeric
ranges and analysts’ numeric interpretations of the terms. The resulting lexicons were then
validated using data from a sample of 27 UK analysts by examining the proportion of their
numeric interpretations that fell in the ranges stipulated by the various lexicons. Ho et al. (2015)
found that they could improve agreement between analysts’ interpretations and the standards by
using an evidence-based lexicon. Specifically, they showed that both the UK lexicon and their best
performing evidence-based lexicon outperformed the US lexicon at the extremes (i.e., for the
lowest and highest probabilities), whereas the US and evidence-based lexicons outperformed the
UK lexicon for the less extreme probabilities. Wintle et al. (2019) replicated the advantage of using
an evidence-based lexicon over the existing US standard, using a larger, non-expert sample.
To the best of our knowledge (which draws, in part, from extensive consultation with
intelligence analysts and managers in several intelligence organizations), the current US, UK and
NATO lexicons are not empirically grounded and were not rigorously tested prior to adoption.
Policy development in the intelligence community has historically occurred without
consideration of relevant evidential bases beyond the anecdotal “lessons learned” following
intelligence failures (Chang, Berdini, Mandel, & Tetlock, 2018; Dhami, Mandel, Mellers, &
Tetlock, 2015; Mandel & Tetlock, 2018). Regardless, for the reasons mentioned, we do not view
evidence-based lexicons as an effective solution to the intelligence community’s requirement to
communicate probabilities clearly to consumers. While such lexicons can improve compliance
rates, they cannot circumvent the fact that linguistic probabilities are context dependent, coarse,
difficult to combine, and imply unstated policy recommendations.
Communicating Probability Using Numbers
An obvious alternative to the intelligence community’s current approach to probability
communication is to use numeric probabilities. This can be accomplished by using precise
numeric point values (e.g., “the probability is .75” or “there is a 75% chance”) or imprecise
values (e.g., 65% chance plus or minus 10% or 20%-40% chance). Given that probability terms
in the current US, UK and NATO lexicons have numeric ranges assigned to them suggests that
numbers are deemed necessary to help analysts convey probability in their assessments.
In fact, research shows that while most communicators prefer to send linguistic
probabilities, most recipients prefer to receive numeric probabilities (Brun & Teigen, 1988; Erev
& Cohen, 1990; Murphy, Lichtenstein, Fischhoff, & Winkler, 1980; Olson & Budescu, 1997;
Vahabi, 2010; Wallsten et al., 1993). The preference for receiving numeric probabilities appears
to be especially pronounced when those expecting to receive information (e.g., decision-makers)
consider the issue to be important and when precision was considered possible. Although more
research is required with intelligence consumers, this preference has been documented by early
studies in the intelligence community (see Marchio, 2014; see also Barnes, 2016).
Benefits of Numeric Probabilities
There are several benefits of using numeric probabilities beyond reducing the resource
burdens and logistical challenges associated with standardization efforts. Whereas linguistic
probabilities have unreliable ordinal scale properties, numeric probabilities have reliable ratio
scale properties. Consumers are less likely to misinterpret probabilities expressed numerically
because numbers are explicitly scaled. This reduces the intra- and inter-individual variability in
the values they represent. All agree that 25% is greater than 10%, and that the difference between
these two values is the same as that between 75% and 90%.
In addition to reducing the misinterpretation of probability, numeric probabilities confer
other important advantages. In many cases, it may be difficult to provide a precise probability
estimate, but considerably easier to estimate a range. In effect, using linguistic probabilities
involves assigning fuzzy ranges, whereas estimating lower and upper numeric bounds involves
assigning crisp ranges. A crisp range can be easily converted to a point estimate with an
uncertainty interval using interval analysis (see Moore, Kearfott, & Cloud, 2009). For instance, a
55%-80% chance could easily be reframed as a 67.5% chance
12.5%. Using the same
approach, numeric probabilities can be easily combined (i.e., added, subtracted, multiplied and
divided) even if they are expressed as imprecise ranges. By contrast, this would be difficult if
estimates were given using the existing US, UK or NATO lexicons.
Unlike linguistic probabilities, as mentioned, numeric probabilities can be used to
describe rare events. An analyst could easily distinguish one in ten from one in a million—
something that is impossible to do with the current standards. Collapsing all orders of magnitude
less than 1 in 10 will not serve policy-makers tasked with planning for and responding to low-
probability, high-consequence-severity threats. A single black swan that could have been better
prepared for through more granular analyses is likely sufficient to merit adopting communication
methods that enable quantification and discrimination between orders of magnitude.
The numeric approach is also verifiable, allowing the intelligence community to track the
accuracy of intelligence assessments and measure components of analytic skill (Mandel, 2015a;
National Research Council, 2011). Studies on geopolitical forecasting using numeric
probabilities have illustrated the feasibility of measuring the accuracy of such forecasts using
Brier scores and other quantitative measures of forecasting skill such as calibration and
discrimination (e.g., Chang, Chen, Mellers, & Tetlock, 2016; Mandel & Barnes, 2014, 2018;
Mellers et al. 2015). Similarly, quantifying forecasts has enabled comparisons to be made
between the accuracy of traditional analytic methods and alternative methods, such as classified
prediction markets for analysts (Mandel, 2019; Stastny & Lehner, 2018). Thus, adopting a
numeric approach can make the intelligence community both more accountable and informed
(e.g., Dhami et al., 2015; Friedman et al., 2018), which may render it less susceptible to the
“blame game” that typically ensues after intelligence failures (Tetlock & Mellers, 2011).
Drawbacks of Numeric Probabilities
Although numeric probabilities confer many advantages over linguistic probabilities as a
basis for probability communication, they are not without drawbacks. Numbers or numeric
quantifiers are not immune from context effects (Bilgin & Brenner, 2013; Mandel, 2014;
Verplanken, 1997), although their resistance to them is greater than for linguistic probabilities,
which derive their meaning from the context in which they are used. Numeric probabilities can
also convey directionality (Teigen & Brun, 2000), although compared to linguistic probabilities
they are directionally more ambiguous and therefore less prone to conveying implicit
recommendations for action by decision-makers (Bilgin & Brenner, 2013; Collins & Mandel,
2019). Accordingly, while numeric probabilities are not immune from exploitation, they are less
susceptible than linguistic probabilities to being misused. For instance, in research directly
comparing numeric and linguistic probabilities, Piercey (2009) found that under conditions of
motivated reasoning, judgments made using numeric probabilities were less biased than those
made using linguistic probabilities. Budescu et al. (2012) similarly observed that motivated
reasoning had less impact on interpretations of statements about climate change containing
probability terms when these were presented along with numeric ranges than alone.
Another potential limitation of numeric probability use is that individuals may find it
difficult to quantify their uncertainty. For instance, Lanir and Kahneman (2006) described the
difficulties that 19 intelligence analysts, academic experts and foreign affairs personnel had in
judging conditional probabilities in a 1975 case study where Israeli experts numerically
forecasted the consequences of alternative outcomes of US brokered negotiations between Israel
and Egypt. These researchers also noted that one of the two consumers of the report
misunderstood the numeric estimate. However, over time, people may adapt to using numeric
probabilities. In recounting efforts to require Canadian analysts who were under his direction to
communicate probability numerically, Barnes (2016, p. 7) states that, “With experience, analysts
became more comfortable using numeric probabilities.” Nevertheless, the use of numbers will
likely require investment in upskilling analysts, their managers and consumers. Fortunately,
statistical and probabilistic reasoning skills can be improved through training (Chang et al.,
2016; Sedlemeier & Gigerenzer, 2001). In fact, in the late 1970s a course called “Statistical
Concepts for Analysts and Managers” was introduced in the US (Marchio, 2014), although this
was short-lived. More recently, Mandel (2015b) showed that even brief training in Bayesian
reasoning using natural-sampling trees can improve the coherence and accuracy of analysts’
probability judgments. However, such studies have yet to demonstrate how long these
improvements endure beyond the immediate post-training period.
Decision-Making Using Numeric Versus Linguistic Probabilities
In further considering the pros and cons of numeric versus linguistic probabilities, the
intelligence community may be enlightened by research comparing the effects of these two
modes of probability communication on decision-making. Evidence suggests that moving from
probability words to numbers is unlikely to adversely affect decision-making, and it may have a
positive effect. Studies comparing the effects of the verbal and numeric modes find little
difference in outcomes between the two modes (Budescu & Wallsten, 1990; Erev & Cohen,
1990; Gonzalez-Vallejo & Wallsten, 1992; Wallsten, Budescu, & Zwick, 1993). In some cases,
researchers report that the best performing mode depends on the structure of the task (Gonzalez-
Vallejo, Erev, & Wallsten, 1994; Olson & Budescu, 1997), whereas in other cases the numeric
mode leads to better outcomes such as accuracy relative to a Bayesian calculation when judging
the likelihood of alternative hypotheses and expected monetary gain in a gambling task (Budescu
et al., 1988; Rapoport, Wallsten, Erev, & Cohen, 1990; see also Budescu & Wallsten, 1990).
This is partly because the numeric mode results in less variability than the verbal mode.
Although more research is needed on the effects of numeric and verbal modes of
probability communication, research applied to professional domains has also demonstrated the
potential positive effects of the numeric mode compared to the verbal mode. For instance,
Timmermans (1994) found that medical professionals were more likely to agree on treatment
decisions and were better at Bayesian reasoning when probabilistic information was presented
numerically rather than verbally. In a study comparing 407 US national security officials’
responses to verbal and numeric probability estimates, Friedman, Lerner, and Zeckhauser (2017)
found that quantifying probabilities did not prompt officials to take riskier actions, even for
optimistic scenarios. Nor did quantification result in overconfidence. Rather, quantification led to
greater willingness to gather additional information.
Barriers to Using Numeric Probabilities in Intelligence Assessments
Past calls for the use of numbers to communicate probability in intelligence assessments
(e.g., CIA, 1983; Johnson, 1973) have resulted in “false starts”. Barnes (2016) concluded that
“Overall, the division’s experience in using numeric probabilities was positive…. It enhanced the
discussion between director and analyst during the review process: both now had a common
understanding of the degree of certainty attached to a judgment, which allowed for a more
effective discussion of the key factors and chain of logic that underpinned the analyst’s
conclusion.” (p. 7). Despite this, the use of numeric probabilities only lasted from 2004 to 2011,
and ended when Barnes retired. Marchio (2014) describes a trial conducted within the US
Defence Intelligence Agency in the late 1970s where analysts, among other things, used precise
percentage values to represent the uncertainty in their conclusions. The majority of the 128
consumers who were later questioned about these assessments favored quantification of
probability. These helped to increase their confidence in the analytic conclusions and gave
greater credibility to briefings. Nevertheless, the brief foray to quantification lost momentum and
soon ended. Even the statistical training given to analysts and managers at that time was not
supported when graduates were back on the job (Marchio, 2014).
Much of the intelligence community’s reluctance to quantify probability reflects
widespread misconceptions about probability and its quantification. Common arguments include
that it would be wrong to use numeric probabilities because they convey a false sense of
precision and suggest a scientific basis to the estimate. Neither of these are reasonable
inferences. As already noted, numeric probabilities can be stated as precisely or imprecisely as a
sender intends them to be. Precision may actually be useful as it can reveal disagreement that can
be informative (e.g., it may suggest the need for more intelligence collection, or even the need
for lowering one’s confidence in an assessment). Barnes (2016) recalled that his analysts debated
the appropriateness of assigning specific values to an event in question and focused on the
judgment process. Regardless of the degree of precision, quantification does not imply anything
about the use of the scientific method. The belief that quantification necessitates science suggests
that many in the intelligence community do not understand the concept of subjective probability.
Barnes (2016) also noted that his analysts needed to gain a better understanding of subjective
probability before being comfortable with using numeric probabilities.
Part of the problem is that the intelligence community has traditionally considered
analysis as an “art” and analysts as “poets” rather than “mathematicians” (Kent, 1964).
Consequently, analysts and intelligence organizations may be resistant to quantifying probability.
However, these barriers are not insurmountable. Barnes (2016), for example, observed that the
initial apprehension his analysts had in using numeric probabilities soon dissipated. Analysts
outside his unit who criticized the use of numbers to communicate probability nevertheless used
them, and those consumers who were provided with numeric estimates also found them useful.
In fact, the barriers to communicating probability numerically may be lowering in the age of ‘big
data’ as intelligence organizations find themselves increasingly needing to recruit data scientists.
The mathematician-to-poet ratio may thus be increasing. Regardless, it is clear that moving from
probability words to numbers would constitute a major shift from the intelligence community’s
current policy and organizational culture. We believe that by exploiting the extant psychological
evidence on probability communication, the community can improve its current policies for
communicating probability in its assessments. This can better mitigate the risk of future
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