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On Dual Nature of Uncertainty: Cues From Natural Language

Craig R. FoxUCLA Anderson School and Department of Psychology

Gülden ÜlkümenUSC Marshall School

Bertram F. MalleBrown University Department of Psychology

Address Correspondence to:Craig R. FoxUCLA Anderson School110 Westwood Plaza #D511Los Angeles, CA [email protected]/206-3403

mailto:[email protected]

Abstract

Probability theorizing since its inception has come in two forms: aleatory models that

deal with the relative frequency or propensity of events in the world, and epistemic

models that are concerned with subjective degree of belief. We argue that this stubborn

bifurcation reflects dual intuitions that people carry with them concerning the nature of

uncertainty. We review past behavioral research hinting at this distinction, and then

present a series of studies in which these variants of uncertainty are reflected in natural

language use. In particular, we show that speakers and listeners distinguish “internal

mode” statements (e.g., “I am 80% sure that…” or “I am reasonably confident that…”)

that express epistemic uncertainty (in the mind of the speaker) from external mode

statements (e.g., “I think there is an 80% chance that…” or “I believe there is a high

probability that…”) that express aleatory uncertainty (chance factors). Speakers place

more weight on singular information (e.g. feeling-of-knowing) when using internal

statements and more weight on distributional information (e.g. relative frequencies) when

using external statements. Meanwhile, listeners associate internal language with singular

reasoning and uncertainty attributed to the speaker’s mind whereas they associate

external language with distributional reasoning and uncertainty in the world. Moreover,

speakers using internal (versus external) mode statements are judged to be more

deserving of credit if they are right and blame if they are wrong. We close with a

discussion of the broader implications of this work for various domains of judgment and

decision making under uncertainty.

“Probability… is … a physical constant belonging to the experiment as a whole and comparable with all of its other physical properties. The theory of probability is only concerned with relations existing between physical quantities of this kind.” --von Mises (1957).

“All uncertainties are inherently the same kind … [and] probabilities are personal degrees of belief about uncertain outcomes.” --von Winterfeldt & Edwards (1986)

“Philosophers seem singularly unable to put asunder the aleatory and the epistimological side of probability. This suggests that we are in the grip of darker powers than are admitted into the positivist ontology. Something about the concept of probability precludes the separation…” --Hacking (1975)

Most judgments and decisions involve uncertainty. Whether we are choosing a

spouse, buying a car, assessing a budget, forecasting a job applicant’s performance, or

estimating the likelihood of rain, we cannot know in advance precisely how things will

turn out. In some situations uncertainty can be attributed entirely to gaps in our

knowledge (e.g., whether the Amazon is longer than the Nile); in other situations

uncertainty can be attributed to external causal factors that are for practical purposes

unpredictable beyond their propensities (e.g., whether a fair coin will land heads). A

voluminous behavioral literature in recent decades has explored judgment and decision

making under uncertainty (for collections of papers see, e.g., Kahneman, Slovic &

Tversky, 1982; Kahneman & Tversky, 2000; Gilovich, Griffin & Tversky 2002);

however, researchers rarely distinguish different varieties of uncertainty and generally

treat it as a unitary construct.

The history of probability theorizing, almost from its inception, is marked by a

bifurcation in the conception of uncertainty (Hacking, 1975). Probability theory is

traditionally traced to a correspondence between Blaise Pascal and Pierre de Fermat in

1654 concerning how one ought to divide the stakes of a game of chance that has been

prematurely interrupted (see e.g., Devlin, 2008). The early calculus of chance was based

on what some have termed an aleatory conception of uncertainty involving unknowns

that can differ each time we run an experiment under similar conditions. Shortly

thereafter Pascale framed the choice of whether or not to believe in the existence of God

as a wager with an “equal risk” of gain (infinite reward if God exists and one believes) or

loss (a finite mortal cost of believing). He thus advanced what some have termed an

epistemological or epistemic conception of uncertainty involving missing knowledge

concerning an event that is in principle knowable. Disagreement concerning the nature of

uncertainty has persisted to this day in the two dominant schools of probability

theorizing, with frequentists treating probability as long run stable frequencies of events,

and Bayesians treating probability as a measure of subjective degree of belief.

While probability theorists continue to debate philosophical questions concerning

the nature of uncertainty, our focus in this paper is to better understand how people

intuitively conceive of uncertainty and the behavioral implications of these conceptions.

We assert that the bifurcation of uncertainty in probability theory reflects an inherent

ambivalence concerning uncertainty that resides within most decision makers. On one

hand, people are often charged with assessing their epistemic uncertainty that a statement

is or will be true, or that a particular scenario will transpire. For instance, when a person

says she’s pretty sure that she left her cell phone on the nightstand, she is typically

assessing her knowledge concerning a fact that may or may not be true. On the other

hand, people are often charged with assessing the propensity that a particular event may

occur, selected from a class of possible events. For instance when a person observes that

if you send your child to daycare she’ll probably get sick in the first few months, he is

typically considering the relative frequency of a class of events (children in daycare

getting sick or not). Of course these forms of uncertainty are not mutually exclusive; in

fact, most judgments entail a mix of both forms of uncertainty. For instance, a statement

such as, “I think there is a good chance that this paper will be accepted if we submit to

the special issue, but I’m not sure” may reflect both a consideration of aleatory

uncertainty (the proportion of papers of similar quality that are accepted to this journal)

and epistemic uncertainty (degree of confidence in that assessment).

Evidence of an intuitive distinction between aleatory and epistemic uncertainty.

An intuitive distinction between aleatory and epistemic uncertainty appears to be

in evidence from an early age. In an ingenious study, Robinson et al (2006) presented

children 4-6 years old with one bag containing orange and green colored building blocks

in equal proportion and another bag containing black building blocks. On each trial the

experimenter pulled a block from one of the bags without the child seeing what was

drawn, then put the block drawn was placed on a shelf behind one of three doors (orange,

green, or black) that was cut into a cardboard screen. The child’s job on each trial was to

put trays underneath doors to make sure that the block would be caught. On

“unknowable” trials the experimenter told the children he would draw a block from the

orange-green bag and asked the participant to place trays before he did so. On the

“unknown” trials the experimenter drew a block from the orange-green bag, placed it

behind the screen (without the child seeing which color) and then asked the participant to

place trays. This minor procedural variation yielded a dramatic contrast in behavior. On

“unknowable” trials in which the experimenter was yet to engage in a chance selection

process and uncertainty might be deemed aleatory, most children correctly placed a tray

under the orange door and one under the green door. However, on “knowable” trials in

which the experimenter had already selected a block so that the uncertainty was purely

epistemic, most children a tray under a single door, apparently making their best guess

concerning of the color that had already been determined.

The perception of epistemic uncertainty may have distinct neural correlates from

epistemic uncertainty. In a provocative set of studies Volz, Schubotz & von Cramon

(2004; 2005) presented participants with competitions between two cartoon UFOs that

varied color, shape, and pilot character, and asked them to predict which UFO would win

a virtual competition game. In one experiment participants learned that each pairing was

associated with a fixed proportion of victories for one figure over another (e.g., A beats B

70% of the time); this could be seen as a manipulation of aleatory uncertainty. In a

companion experiment participants learned a fixed set of rules that determined which

UFO would win each competition (e.g., yellow always beats blue), with participants

informed of some rules and practicing them to optimal performance, informed of other

rules but never practicing them, and never informed of or practicing other rules; this

study could be seen as manipulating the level epistemic uncertainty. Comparison of

BOLD signal using functional MRI suggests common neural correlates in a number of

areas including right posterior fronto-median cortex (Brodmann Area 8) and also

distinctive activation for the rule-based task in regions including middle frontal gyrus,

inferior frontal junction area, and inferior parietal sulcus, brain areas though to subserve

working memory functions.

Epistemic and aleatory uncertainty have distinct behavioral influences on decision

making. Holding information constant, people find betting on events less attractive when

their epistemic uncertainty is more salient. For instance, Rothbart and Snyder (1970)

found that undergraduates were willing to bet more on the roll of a die if they were asked

before the die was rolled (in which case, the outcome was presumably seen by most as

purely aleatory) than if they were asked after the die was rolled (in which case epistemic

uncertainty was more salient). Likewise, Heath and Tversky (1991) found that

participants preferred to bet on their guess of whether a randomly chosen stock would go

up or down the next day than bet on their guess of whether a randomly chosen stock went

up or down on the previous day, despite the fact they if anything they had more

information concerning the previous day’s stock movement. More generally they found

that people prefer to bet in situations where they feel more knowledgeable or competent,

holding judged probabilities constant. Fox and Tversky (1995) found that the aversion to

bet on less familiar events is triggered by a contrast with other events about which the

decision maker is more knowledgeable or other people who are more knowledgeable.

Building on this work, Fox and Weber (2002) report that people find gambles (e.g. bets

by Americans on the outcome of the upcoming Russian presidential election) more

attractive when they are reminded of less familiar events (e.g., the upcoming presidential

election in the Dominican Republic) than when they are reminded of more familiar

events (e.g. the upcoming presidential election in America). Likewise, naïve participants

(e.g., psychology students) were less willing to bet on an unfamiliar event (e.g., the

inflation rate in Holland) after they were provided relevant information that they did not

know how to use (GDP growth, interest rates, unemployment). Similarly, Chow and

Sarin (2002) found that people find bets less attractive when missing information (e.g.,

which of two apples has more seeds) is missing to all (they have not yet been cut) then

when they are available to someone else (an experimenter who has counted the seeds).

The increased salience of epistemic uncertainty after an outcome is realized may

also partially explain why events seem more predictable after they occurred than before

they occurred, a phenomenon known as “creeping determinism” or “hindsight bias”

(Fischhoff, 1975). Interestingly, this bias is pronounced when plausible deterministic

causes (human skill or lack of skill) are cited or when no causal attribution is provided,

but it is virtually eliminated when the outcome is attributed to aleatory factors such as an

unexpected act of nature (Wasserman, et al. 1991).

Studies of confidence in forecasts have found persistent differences in judged

probabilities of general knowledge items that entail purely epistemic uncertainty and

judged probabilities of future events that also presumably entail aleatory uncertainty. In

particular, Ronis and Yates (1987) found that participants were more confident,

overconfident, and had worse calibration scores when asked to judge probabilities

concerning general knowledge items compared with when these same participants were

asked to judge probabilities concerning which team would win each of several upcoming

professional basketball games. Interestingly, participants expressed complete certainty

for general knowledge items more than 15 times as they did for basketball games,

perhaps recognizing inherent limits to one’s ability to perfectly predict outcomes

entailing some aleatory uncertainty. Similar patterns of higher confidence and greater

willingness to express certainty for general knowledge questions than future events were

obtained by Fischhoff and MacGregor (1982), Wright (1982) and Wright & Wisudha

(1982).

Several studies have found that while participants tend to display overconfidence

on average when assessing probabilities that their answers to general knowledge

questions are correct item-by-item, they tended toward underconfidence when they asked

to estimate the proportion of items that they had answered correctly (Sniezek, Paese &

Switzer, 1990; Gigerenzer, et al., 1991; Griffin & Tversky, 1992). This is consistent with

the notion that evaluations of epistemic uncertainty (the likelihood that I answered this

item correctly) and aleatory uncertainty (the proportion of times I answered correctly)

entail reliance on distinct information and/or weight this information in distinct ways.

However, we assert that when a particular judgmental strategy or heuristic is especially

accessible, it will be employed regardless of elicitation mode (confidence versus

frequency). For example, Brenner et al. (1996) presented participants with responses

than another group had provided to various behavior question (e.g., “Are you often late

for class? Yes/No”) and their classification on a Myers-Briggs inventory; one group

predicted responses of a target subject with a particular score then assessed their the

probability that they were correct, while a second group assessed the percentage of target

subjects of a given profile who chose a particular answer. Interestingly, responses of

these two groups closely coincided with one another—and both responses correlated very

highly with a separate group’s assessment of the which of the two responses to the

behavior question was more representative of the personality profile in question (r

= .96, .86 with confidence and frequency assessments, respectively).

Similarly, one study showed that the planning fallacy—the tendency to

underestimate task completion times—is attenuated when participants judge the relative

frequency of tasks that will be completed on time than when participants judge the

probability of completing each task on time—but only when they judge relative

frequency after judging probability. However, the reasoning cited only showed a slight

tendency toward more of an “outside perspective” under frequency than probability

judgment (Griffin & Buehler, 1999).

There is a great deal of evidence that the conjunction fallacy—the tendency to

judge the conjunction of a plausible and implausible event as more likely than the

plausible event--is diminished when participants are asked to judge relative frequencies

rather than single event probabilities (e.g., Tversky & Kahneman, 1983; Fiedler, 1988;

Hertwig & Gigerenzer, 1994) or when they are presented frequentistic rather than case-

specific information (Reeves & Lockhart, 1993). This is consistent with the notion that

relative frequencies primes more extensional reasoning (Kahneman & Tversky, 1996).

Likewise, tendency to underweight base rates when updating based on case information

(Kahneman & Tversky, 1973) has been shown to diminish when aleatory factors are

made more salient. For instance, the use of base rate data increases when problems are

framed as repetitive rather than unique (Kahneman & Tversky, 1979 TIMS), when

presented after case information (Krosnick, Li & Lehman, 1990), varying base rates

across trials within participant (Bar-Hillel & Fischhoff, 1981), or when participants are

asked to think as “statisticians” (Schwarz, Strack, Hilton & Naderer, 1991). Likewise,

when participants were induced to make their judgments “as a scientist analyzing data”

they were more sensitive to base rates than when they are induced to “understand the

individual’s personality, professional inclinations and interests” (Zukier & Pepitone,

1984).

When one attributes uncertainty to human causes (e.g., deception by another) this

may facilitate a more clinical mindset and when attributes uncertainty to a stochastic

process this may lead to more rule-based behavior. Indeed, Schul, May, Burnstein,

Yahalom (2007) asked participants drew matchboxes that had either blue or yellow

stickers on them and either had blue or yellow tokens inside. All participants know that

the token color matched the sticker 2/3 of the time and were asked to predict the color

based on the token. Some participants were told that the allocation of tokens was

assigned at random whereas others were told that they were assigned by another

participant who had an incentive to deceive. Participants more frequently guessed the

color matching the sticker (i.e., using the optimal decision rule) when they thought the

tokens were assigned at random compared to when they thought that another person

made the assignments, in which case they more frequently searched for patterns in the

sequence. Likewise, several recent studies have suggested that the well-documented

tendency toward probability matching (i.e., choosing options in proportion to their

relative probability of success) reflects a search for patterns in random sequences

(consistent with a model of uncertainty that is largely epistemic) whereas optimizing

(choosing the option that offers the highest probability of success) reflects a more

sensible acknowledgment that no such patterns exist in random sequences (consistent

with a purely aleatory model of uncertainty (Wolford, Newman, Miller & Wig, 2004;

Unturbe & Corominas, 2007; Volkan, 2000). Inded, Gaissmaier and Schooler (2008)

find that probability matchers are more likely than maximizers to identify and take

advantage of predictable patterns when they encounter non-random outcome sequences.

Friedland (1997) categorized participants according to how much they attributed

outcomes in hypothetical scenarios to chance versus luck. Participants who attributed

more to luck tended to make betting decisions in a chance game that reflected a more

epistemic view of uncertainty in which “luck” was a scarce resource to be allocated: if

they had encountered a string of run of mostly unfavorable outcomes they subsequently

bet more money (i.e., expecting their luck to turn); if they had encountered a string of

mostly favorable outcomes then they subsequently bet less money (i.e., expecting their

luck to turn).

Intuitive Conceptions of Uncertainty

Several authors proposed frameworks for distinguishing between different

intuitive conceptions of uncertainty (Howell & Burnett, 1978; Kahneman & Tversky,

1982; Keren, 1991; Smith, Benson & Curley, 1991; Tiegen, 1994; Rowe, 1994;

Dequesch, 2004). Most of these were theoretical accounts with little data confirming that

participants intuitive drew similar distinctions. The central thesis of this paper is that

people

The most influential framework in the psychology literature was advanced by

Kahneman and Tversky (1982), who distinguished between internal uncertainty which is

attributed to one’s state of knowledge and external uncertainty, which is attributed to the

external world. They further distinguish internal uncertainty into reasoned mode which

is based on explicit arguments (e.g., I believe that New York is further north than Rome

because it has a cooler climate) and introspective mode that reflects a feeling-of-known

(e.g., I believe that I have correctly spelled a word because it ‘looks right’). They further

distinguish external uncertainty into the singular mode that entails an assessment of the

case at hand (e.g., I believe that I will complete a project on time because I’ve considered

the steps of my plan and adjusted for unforeseen contingencies) and the distributional

mode in which the case at hand is seen as an instance of a class of similar events (e.g., I

believe that I will complete the project on time because most similar projects have been

completed on time). We propose that what we have called epistemic uncertainty

encompasses both internal uncertainty an external uncertainty that is evaluated using

singular representations; aleatory uncertainty maps best onto distributional

representations of external uncertainty.

Howell & Burnett (1978) develop a taxonomy of uncertain events that includes:

(1) whether the event is part of a class of repeated events (“frequentistic”) or is unique

(“nonfrequentistic”); (2) whether the decision maker feels he or she has some control

over the outcome (“internal”) or has no control (“external”). For frequentistic, external

events, they further distinguish (3) whether or not the process is attributed to a stable

process familiar to the decision maker (“known”) or not (“unknown”). These authors

argue that different tasks (frequency estimation, probability estimation, prediction and

choice) engage different “cognitive elements” (e.g., past frequencies, heuristics)

depending on the nature of the event. For our purposes we would consider

nonfrequentistic, and internal uncertainty as more epistemic; frequentistic and external as

more aleatory.

Natural Language as a tool for probing intuitions.

The central thesis of this paper is that people intuitively distinguish epistemic and

aleatory uncertainty. Our method for examining these intuitions is natural language that

participants choose to express their uncertainty. Some statements that we call internal

mode (e.g., “I am fairly confident,” “I am 90% sure,” “I strongly believe) qualify or

quantify one’s degree of epistemic uncertainty. Other statements that we call external

mode (e.g., “I think there is a high probability,” “I’d say there is a 90% chance,” “I

believe it is fairly likely”) qualify or quantify one’s assessment of aleatory uncertainty.

Note that in the latter examples we preface the stems with words indicating subjectivity

(“I think,” “I’d say,” “I believe”) so that we do not confound subjective]ity/objectivity

statements with linguistic stems.

Some events are purely epistemic or aleatory and most naturally map onto internal

and external mode statements. For instance, it is much more natural to say that “I’m 90%

sure the Amazon is longer than the Nile” than it is to say “I think there is a 90% chance

that the Amazon is longer than the Nile.” Likewise it is much more natural to say that “I

think there is 5/6 chance that this fair die will land on a number less than 6” than it is to

say “I am 5/6 sure” of it. More often, events reflect a mixture of epistemic and aleatory

cues. For instance, the outcome of a basketball game may reflect consideration both of

how often each team tends to win and how well the teams match up on this particular

occasion. We assert that linguistic choices can both provide insight into the speaker’s

conception of uncertainty when the statement is made and that it can prime one form of

reasoning over another.

We now turn to the presentation of data in support of our hypotheses. We first

present a number of studies in which we examine ways in which speakers systematically

differentiate between epistemic and aleatory uncertainty using internal versus external

modes. In these studies we also show that forcing people to quantify their beliefs in the

internal mode can make epistemic cues more salient whereas forcing them to quantify

their beliefs in the external mode can make aleatory cues more salient. Next, we turn to

the listener’s perspective and show that listeners draw a number of inferences about

information and cognitive process on which the speaker relies from the mode in which

the speaker chooses to express him or herself. Finally we examine the social

consequences (in particular the assignment of credit and blame) for speakers who choose

to express themselves in these modes following the resolution of uncertainty.

SPEAKER’S PERSPECTIVE

STUDY 1a: NYT STUDY

Procedure

Using the Proquest database, we screened articles that appeared in New York

Times during calendar years 2008 and 2009. We searched for terms that qualified or

quantified the uncertainty of the speaker. We included stems that communicate epistemic

uncertainty (sure, confident, certain), and aleatory uncertainty (chance, likely/likelihood,

probability). These statements were coded on speaker traits (perspective, expertise,

gender, control), characteristics of the prediction (source, backing), and characteristics of

the event (subject, negation, tense, desirability, temporality, locus). We considered five

sentences that come before and five sentences that come after the target statement to

facilitate coding of variables that required an understanding of the context (e.g., speaker’s

expertise).

Results

General. The search described above returned 967 statements. 754 of these

statements had external stems, and 372 had internal stems. Although speakers had an

overall tendency to qualify, rather than quantify their uncertainty, internal stems (11%)

were much less likely to be quantified than external stems (24%), Pearson Chi-Square (1)

= 23.52, p = .000.

Speaker traits. Statements were much more likely to use internal stems when

communicated from the 1st person’s perspective (41%) than the 2nd or the 3rd person’s

perspective (27%; p = .000) (see table 1). Mixed speakers were more likely to use

external statements (81%) than male speakers (58%) and female speakers (56%; p

= .000). When speakers are communicating the uncertainty experienced by others, they

are more likely to use internal stems when the other person is a friend, romantic partner

or close relative (67%), but more likely to use external stems when the other person is a

stranger or an acquaintance (77%, p = .002). The amount of control speakers had over the

event had a strong influence over the choice of language, such that the speakers were

more likely to use external stems when they had no control over the event (68%), but

they were more likely to use internal stems when they had influence over the event (79%)

or when they could bring about the event (73%; p = .000).

Characteristics of the prediction. Source of the prediction also had a strong effect

on language choice. Speakers were more likely to use an external stem when the

prediction was based on calculation or logic (94%), than when it was based on trends or

facts (79%), or intuition or no specific source (51%; p = .000). Speakers were more likely

to use external stems when the prediction involved backing (e.g., “because”) (72%) than

when it did not (60%, p = .000). Speakers were more likely to use external stems when

the prediction did not involve a negation (66%), but they were more likely to use an

internal stem when the prediction involved a negation (71%, p = .000).

Characteristics of the event. Speakers were more likely to use external stems

when prediction was about non-sentient targets (e.g., trends, facts, processes or events),

(71%) than about sentient targets (58%; p = .000). Events about sentient targets were

further categorized as behavioral (e.g., uncertainty about whether a person will speak) or

mental (e.g., uncertainty about what a person is thinking). Speakers were more likely to

use external stems when predicting behavioral events regarding a sentient target (62%),

but they were more likely to use internal stems when predicting mental events regarding a

sentient target (69%; p = .000). Speakers were more likely to use external stems when the

prediction involved hypothetical events or events that will take place in the future (71%),

but they were more likely to use internal stems for events that are currently happening

(53%) or events that happened in the past (55%; p = .000). We coded for the desirability

of the event separately from an objective perspective (a swimmer winning a medal) and

from a subjective perspective (a thief stealing a painting). External stems were much

more likely to be used for both objectively (83%) and subjectively (82%) undesirable

events than events that were desirable, or neutral (both p’s = .000). There was a very

strong effect of the locus of the event’s uncertainty. When the uncertainty about the event

lay outside the predictor (i.e., inherently random or probabilistic events), speakers were

more likely to use external stems (74%), but when the uncertainty lay fully within the

predictor (i.e., due to lack of knowledge or evidence), speakers were more likely to use

internal stems (61%, p = .000).

STUDY 1b: SENTENCE COMPLETION STUDY

Method

One hundred forty seven participants were given roots of sentences (stems), and

were asked to complete each stem with an event such that the complete sentence sounded

natural to them. Every participant completed four such stems: two internal and two

external. For half of the participants, the internal stem was “sure” and the external stem

was “chance,” and for the other half the internal stem was “confident” and the external

stem was “probability.” For every participant, one external and one internal stem were

quantified by 60%, and the remaining stems were quantified by 80%. The order of

presentation of the internal and external stems, as well as the order of presentation of the

percentages was counterbalanced. None of these between subjects variables had an effect,

and therefore we collapsed the data across them and compared internal and external

stems. Two independent coders, blind to the condition coded the stems on speaker traits

(control over the event), and characteristics of the event (subject, timing, and locus of

uncertainty). The two coders had a 97% initial agreement, and the disagreements were

resolved by discussion.

Results

Participants were more likely to complete internal stems with events that were

mostly controllable (74%) than events that were mixed, uncertain or those that they had

little or no control over (26%, p = .000). When completing internal stems, participants

were more likely to use a subject referring to themselves (i.e., I, me, my, we), (73%) than

to others or objects (27%, p = .000). Participants were more likely to complete external

stems with future events (90%), than present or past events (10%, p = .000). External

stems were completed such that the locus of uncertainty was more likely to be outside the

speaker (65%) than inside the speaker (35%, p = .012).

We also conducted a series of mixed binomial logit regression models with stem

type, and the two order variables as between subjects variables, and internal/external as

the within subject variable. We did not expect stem type or order variables to have a

significant effect on any of the dependent variables. As we expected, internal/external

independently and significantly predicted all of the dependent variables. Internal, as

opposed to external stems significantly and positively predicted the controllability of the

event (B = .793, p = .000), significantly and positively predicted use of first person

subject (B = .696, p = .000), negatively predicted use of future events (B = -.953, p

= .000), significantly and positively predicted the locus of uncertainty stemming from

inside the speaker’s mind (B = .399, p = .027). As expected, stem type did not have an

effect in any model, suggesting that there was no difference between sure and confident

stems in representing internal mode, and between chance and probability stems in

representing external mode. The only unexpected finding was that when predicting locus

of uncertainty, order of presentation of the percentages had a positive and significant

effect (B = 418, p = .020).

STUDY 2a: PICK AND FILL

Method

Fifty six undergraduate students participated in the study in exchange for partial

course credit. Three participants provided incomplete responses, and were dropped. All

analyses are based on the remaining 53 participants. The participants were presented with

20 events. Half of these were about self (e.g., I will earn at least a 3.0 GPA this semester),

and half were about the world (e.g., Intelligent life exists in other planets). For each

event, participants’ task involved two parts. They were presented with a choice between

two different root phrases (e.g., “There is a ___ % chance that USC will play in the

Rose Bowl next January 1" and "I am ___ % sure that USC will play in the Rose Bowl

next January 1”). The first part of the task was to select the root phrase that sounded

most natural to them. On the next screen, they were presented with only the phrase they

selected. The second part of the task involved completing the phrase by entering a

number between 0 and 100 that best reflected their belief about the given event. The

order of presentation of these 20 events was randomized for each participant. In the

choice part of the task, for half of the participants sure phrase appeared above the chance

phrase. This order was reversed for the remaining participants.

Next, participants were asked to rate each event on five 7-point likert scales,

anchored by strongly disagree, and strongly agree. They indicated their perceived control

(I have control over the outcome), their knowledge about the topic (I know a lot about

this event), the likelihood that the event will happen (this event will definitely occur),

singular reasoning (Earlier, when I quantified my belief about this event, I had a specific

story in mind for how or why the event will happen), and distributional reasoning

(Earlier, when I quantified my belief about this event, I was thinking about how often this

kind of event tends to happen). The order of presentation of these items was

counterbalanced. Due to a programming error, we had incomplete responses for control

and distributional reasoning. We are focusing on knowledge and likelihood judgments for

the purposes of the analysis below.

Results

Overall, participants were equally likely to choose the sure mode (51%), and the

chance mode (49%).

Events that were assigned a probability of less than or equal to 50% were more

likely to be described by the chance mode (68%), than the sure mode (32%). In contrast,

events that were assigned a probability of more than 50% were more likely to be

described by the sure mode (63%), than the chance mode (37%). For those events that the

participants picked the sure mode, the mean probability was 73%. For those events that

the participants picked the chance mode, the mean probability was 53%.

64% chose the sure mode for events about self, and 63% chose the chance mode

for world events, as a natural way of communicating their uncertainty about these events

(Pearson Chi-Square = 75.04, p < .001).

Predicting choice of sure vs. chance mode. To see which factors influence

whether participants choose the sure mode or the chance mode, we used a repeated logit

model? (GENLIN), where the 20 events were included as the repeated factor and

knowledge and likelihood judgments were included as covariates. Therefore, this

analysis was conducted over a total of 1060 responses elicited from 53 participants. The

coefficient for knowledge (B = .036, p < .001) and likelihood (B = .059, p < .001) were

positive and significant, indicating that increases in these factors were associated with a

higher likelihood to choose the sure mode. The results were similar when a similar

analysis was conducted only for those participants who indicated probability estimates

higher 50% (637 responses elicited from 53 respondents). The coefficient for knowledge

(B = .048, p < .001) and likelihood (B = .071, p < .001) were positive and significant.

Next, we added into the model an indicator of whether the events were self-

related or not (I-statements). We used a repeated logit model? (GENLIN), where the 20

events were included as the repeated factor and knowledge and likelihood judgments

were included as covariates, and self-relevance was included as a factor. The coefficient

for likelihood (B = .060, p < .001), and self-relevance (B = .174, p < .001) were positive

and significant. However, the coefficient for knowledge was not significant anymore (B =

.012, p >.05). The results were similar when a similar analysis was conducted only for

those participants who indicated probability estimates higher 50% (637 responses elicited

from 53 respondents). The coefficient for likelihood (B = .064, p < .01), and self-

relevance (B = .169, p < .005) were positive and significant, and the coefficient for

knowledge was only marginally significant (B = .025, p =.062).

We also ran a repeated logit model? (GENLIN), where the 20 events were

included as the repeated factor and knowledge and likelihood judgments, and the

probability estimates were included as covariates. The coefficient for knowledge (B

= .038, p < .001), and probability (B = .003, p < .001) were positive and significant.

However, the coefficient for likelihood was not significant anymore (B = .020, p >.05).

The results were similar when a similar analysis was conducted only for those

participants who indicated probability estimates higher 50% (637 responses elicited from

53 respondents). The coefficient for knowledge (B = .038, p < .005), and probability (B

= .010, p < .001) were positive and significant, but the coefficient for likelihood was not

significant (B = .025, p > .05). When we conduct this analysis for only those who

indicated probability estimates less than or equal to 50% (420 responses, 53 respondents),

the only significant factor was probability (B = -.004, p < .05), indicating that for low

probability events, as the probability decreased, participants were more likely to choose

the sure mode.

STUDY 2b: PICK AND FILL STUDY WITH LOC

Method

Forty one undergraduate students participated in the study in exchange for partial

course credit. Participants were presented with 20 events. Half of these were about self

(e.g., I will earn at least a 3.0 GPA this semester), and half were about the world (e.g.,

Intelligent life exists in other planets). For each event, participants’ task involved two

parts. They were presented with a choice between two different root phrases (e.g.,

“There is a ___ % chance that USC will play in the Rose Bowl next January 1" and

"I am ___ % sure that USC will play in the Rose Bowl next January 1”). The first part of

the task was to select the root phrase that sounded most natural to them. On the next

screen, they were presented with only the phrase they selected. The second part of the

task involved completing the phrase by entering a number between 0 and 100 that best

reflected their belief about the given event. The order of presentation of these 20 events

was randomized for each participant. In the choice part of the task, for half of the

participants sure phrase appeared above the chance phrase. This order was reversed for

the remaining participants. Finally, participants completed the Locus of Control Scale

(Rotter 1966).

Results

For the ten "I" statements in which there could plausible be varying levels of

control (e.g. I will get at least a 3.0 GPA this term), LOC significantly correlates with the

tendency to use "sure" over chance (especially when controlling for the fill #).

There is no such correlation (nonsignificant in the opposite direction) for the ten "world"

statements for which there is little or no plausible control (e.g., there will be an

earthquake of at least 6.0 in LA in the next 5 years) (see table 2).

STUDY 3a: MANIPULATING EXTERNAL CERTAINTY

One hundred and thirty six participants took part in this study. Participants were

presented with scenarios about three different events. All scenarios comprised of one

sentence reflecting an internal cue, and one sentence reflecting an external cue about the

probability of the event. We manipulated the external certainty to be high (Suppose that

you are married and that you and your spouse are leaning toward the decision to have a

baby but have not yet made up your minds. A fertility expert tells you that you will have

a very easy time conceiving), or low (Suppose that you are married and that you and your

spouse have nearly decided to have a baby. A fertility expert tells you that it may be a

little difficult for you to conceive).

After reading each scenario, participants indicated their belief about the event by

entering a number between 0 and 100. They did this either in a sure mode (e.g., I’m

______% sure that we will have a baby in the next year or two), or the chance mode (I’d

say there is a ______% chance that we will have a baby in the next year or two).

We counterbalanced the order of presentation of the three scenarios. I am just presenting

the results for one of the scenarios where results were strongest and significant, for the

order in which this scenario came first.

The results of a 2 (External Probability Cue: High, Low) x 2 (Communication

Mode: Sure, Chance) between subjects ANOVA revealed a main effect of external cues

(F (1, 62) = 4.07, p < .05), such that participants’ probability estimates were higher when

the external cue was high (M = 71.74%), than when it was low (M = 54.64%). The two-

way interaction was also significant (F (1, 62) = 4.07, p < .05). Planned contrasts

revealed that in the sure mode, high and low external cues did not lead to a difference in

probability estimates (Mhigh = 67.88%, Mlow = 63.88%; F (1, 66)< 1), whereas in the

chance mode, high external cues resulted in higher probability estimates than lower

external cues (Mhigh = 75.59%, Mlow = 45.39%; F (1, 66) = 10.80, p < .005). These results

show that the external cues influenced participants’ probability estimates in the chance

mode, but not in the sure mode.

STUDY 3b: FORCED MODE STUDY FULLY CROSSED

Method

Two hundred ninety nine participants participated in the study. Participants were

presented with two sentences, one related to external sources of certainty and the other

related to internal sources of certainty. External certainty was manipulated to be either

low (Your friend Tom wears a cap a few times a week), or high (Your friend Tom wears

a cap almost every day). Similarly, internal certainty was manipulated to be either low

(You were in the same large lecture class with him yesterday and you have the vague

sense that he might have been wearing a cap), or high (You were in the same large lecture

class with him yesterday and you have the impression that he was wearing a cap). After

reading these two sentences, participants were asked to indicate the probability that Tom

was wearing a cap by completing a sentence with either a chance stem (I’d say there is a

_____% chance ), or a sure stem (I’m _____% sure).

Results

A 2 (Mode of Communication: Sure, Chance) x 2 (External Certainty: High, Low)

x 2 (Internal Certainty: High, Low) ANOVA revealed a main effect of external certainty

information (F(1,291) = 76.11, p < .001), and a main effect of internal certainty

information (F(1,291) = 17.02, p < .001), where higher levels of both types of

information lead to higher probability estimates. The mode of communication did not

have a significant main effect (F(1,291) = 2.161, p > .1). There was a significant

interaction between external certainty information and the mode of communication

(F(1,291) = 12.97, p < .001), as well as between internal certainty information and the

mode of communication (F(1,291) = 8.81, p < .005). When completing sure sentences,

probability estimates were affected by both external and internal certainty information.

However, when completing chance sentences, probability estimates were influenced only

by external, but not by internal certainty information.

We also conducted a regression analysis predicting probability estimates from

external and internal certainty, communication mode, and the two-way interactions

between communication mode and information type. The results reveal a significant

effect of external certainty information (B = 8.71, p < .001). Although the effect of

internal certainty information is significant in a model with only main effects, it is no

longer significant in this model with the interaction terms. More importantly, there is a

significant interaction between communication mode and external information (B = -

14.82, p < .001), suggesting that the effect of external certainty information is stronger in

the chance mode than in the sure mode. Moreover, there is a significant interaction

between communication mode and internal information (B = 12.22, p < .005), suggesting

that the effect of internal certainty information is stronger in the sure mode than in the

chance mode.

STUDY 4: PICK AND FILL – NUMBERS PART

To see which factors influence probability estimates for different events, we used

a repeated logit model? (GENLIN), where the 20 events were included as the repeated

factor and knowledge and likelihood judgments were included as covariates. This

analysis was conducted over a total of 1057 responses elicited from 53 participants. The

coefficient for likelihood (B = .11.897, p < .001) was positive and significant, but the

coefficient for knowledge was not significant (B = -.287 p > .05).

We run another analysis with the 20 events was the repeated factor, knowledge

and likelihood judgments were covariates, and the choice of communication mode (sure

vs. chance) was included as a factor. This analysis was conducted over a total of 1057

responses elicited from 53 participants. The coefficient for likelihood (B = 11.455, p

< .001), and coefficient for communication mode (B = 7.275, p < .001) were positive and

significant. However, the coefficient for knowledge was not significant (B = -.560 p > .1).

These results indicate that the probability estimates are positively associated with

likelihood judgments, and the choice of sure mode.

We added self relevance (I-statements) to the above analysis. For this analysis, the

20 events was the repeated factor, knowledge and likelihood judgments were covariates,

and the choice of communication mode (sure vs. chance), and self-relevance (I-

statements) were included as factors. This analysis was conducted over a total of 1057

responses elicited from 53 participants. The coefficient for likelihood (B = 11.389, p

< .001), and the coefficient for communication mode (B = 7.823, p < .001) were positive

and significant. The coefficient for self-relevance (B = 4.267, p < .05) was negative and

significant. The coefficient for knowledge was not significant (B = .029, p > .1). These

results indicate that the probability estimates are positively associated with likelihood

judgments, and the choice of sure mode, and negatively associated with the self-relevance

of the event.

Next, to more clearly understand the effects of knowledge and likelihood on

probability estimates, we examined the effects of these factors separately among events

with high and low probability estimates, and the choice of sure vs. chance modes.

In summary, this analysis revealed several interesting findings about the factors

that affect probability estimates (the details can be found in the following paragraphs).

First, knowledge has a positive and significant effect only for high probabilities, whereas

likelihood judgments always have a positive and significant effect for all modes and

probability levels. Second, likelihood moderates the relationship between knowledge and

probability judgment in the high probability, sure cell. Third, in the chance mode, for

high probabilities (e.g., p >50%), participants provide more extreme probabilities, the

more knowledgeable they are. In contrast, in the chance mode, for low probabilities (e.g.,

p <=50%), participants provide more extreme probabilities, the less knowledgeable they

are. These results are consistent with an ignorance prior account in which less knowledge

leads to probabilities closer to 50%.

For events that were assigned probability estimates of 50% or less. We ran a

repeated logit model? (GENLIN), with the 20 events as the repeated factor and likelihood

judgments as covariates, only using the events that were assigned probability estimates of

50% or less. Among events that chance was chosen as the preferred mode of

communication, this analysis revealed that the coefficient of likelihood was positive and

significant (B = 3.899, p < .001). Among events that sure was chosen as the preferred

mode of communication, this analysis revealed that the coefficient of likelihood was

positive and significant (B = 5.191, p < .001).

We ran a repeated logit model? (GENLIN), with the 20 events as the repeated

factor and knowledge judgments as a covariate, only using the events that were assigned

probability estimates of 50% or less. Among both chance and sure events, coefficient of

knowledge was not significant.

When both likelihood and knowledge were included in the model, for chance

events, coefficient of likelihood was positive and significant (B = 4.345, p < .001), and

the coefficient of knowledge was negative and significant (B = -1.179, p < .05). For sure

events, coefficient of likelihood was positive and significant (B = 5.294, p < .001), but

the coefficient of knowledge was not significant (B = -.715, p > .05).

For events that were assigned probability estimates of more than 50%. We ran a

repeated logit model? (GENLIN), with the 20 events as the repeated factor and likelihood

judgments as covariates, only using the events that were assigned probability estimates of

more than 50%. Among events that chance was chosen as the preferred mode of

communication, this analysis revealed that the coefficient of likelihood was positive and

significant (B = 3.630, p < .001). Among events that sure was chosen as the preferred

mode of communication, coefficient of likelihood was positive and significant (B =

5.746, p < .001).

We ran a repeated logit model? (GENLIN), with the 20 events as the repeated

factor and knowledge as a covariate, only using the events that were assigned probability

estimates of more than 50%. The coefficient of knowledge was significant for both

chance events (B = 2.184, p < .001), and sure events (B = 2.767, p < .001).

When both likelihood and knowledge were included in the model, for chance

events, both the coefficient of likelihood (B = 2.958, p < .001), and the coefficient of

knowledge (B = 1.063, p < .05) were positive and significant. For sure events, coefficient

of likelihood was positive and significant (B = 5.502, p < .001), but the coefficient of

knowledge was not significant (B = .302, p > .05). These results are summarized in Table

3.

LISTENER’S PERSPECTIVE

STUDY 5: WHAT WERE THEY THINKING?

Method

One hundred and twenty eight undergraduate students participated in the study in

exchange for partial course credit. Participants were presented with 10 pairs of

statements. For each statement pair, one speaker communicated their probability

judgment about an event in the sure mode (e.g., Colin says: “I am 70% sure I’ll win the

poker tournament”), and the other speaker communicated their probability judgment

about the same event in the chance mode (e.g., Shane says: “I think there is a 70% chance

I’ll win the poker tournament”). Below these statements, participants were presented

with one or two thoughts that might have been going through the minds of these speakers

when they made their statements (e.g., ____ is thinking about his own poker skill, ____ is

thinking about the poker skill of all players in the tournament). Participants’ task was to

indicate which speaker was more likely to have relied on which thought in forming their

statement. If there were two thoughts listed, their task was to choose one thought for each

speaker.

The order of questions was randomized for each participant. Half of the

participants saw the sure mode statement at the top of the page, followed by the chance

mode statement. For the remaining participants, this order was reversed. The order in

which the thoughts appeared on the screen was also counterbalanced.

Results

Below, we report the results for all participants (n = 128), and also for the subset

of participants (n = 105, in parentheses) who matched one speaker with one thought, and

the remaining speaker with the remaining thought. The pattern of results remains the

same.

For the first question, 62% (62%) of the participants paired the speaker who

communicated their statement in the sure mode (Doctor Ames says: “I am 80% sure that

you have Crohn’s disease”), with the diagnosticity-related thought (is thinking “This

patient has most of the signs and symptoms of Crohn’s disease”), and 61% (62%) of the

participants paired the speaker who communicated their statement in the chance mode

(Doctor Baker says: “There is an 80% chance that you have the Crohn’s disease”) , with

the thought related to the posterior probability (is thinking “Most of the patients I have

seen with these signs and symptoms have Crohn’s disease”). Table 4 summarizes the

results for all 10 questions.

Discussion

The results of this study suggest that when a speaker communicates a statement in

the sure mode, participants infer that the speaker is thinking about singular information

(questions 1-4), their direct experience with the subject (questions 5-6), self- related

thoughts (questions 7-8), and internal locus of control (questions 9-10). In contrast,

when a speaker communicates a statement in the chance mode, participants infer that the

speaker is thinking about distributional information (questions 1-4), distributional

knowledge (questions 5-6), competition- related thoughts (questions 7-8), and external

locus of control (questions 9-10).

STUDY 6a: POETRY JOURNAL

We asked 185 participants to imagine that they would like to publish an essay in a

poetry journal. Each participant was then presented with two beliefs, expressed by two

poetry journal editors. Editor of Journal A expressed her belief in the sure mode (If you

submit to Journal A, I’m 80% sure that we’ll publish the essay), and the editor of Journal

B expressed her belief in the chance mode (If you submit to Journal B, I think there is an

80% chance we’ll publish your essay). Participants were asked to select which journal to

send their work on the basis of these statements. Half of the participants saw statements

made by journal editors, and the remaining participants saw statements made by the mail

clerks at these journals. We counterbalanced whether the sure statement or the chance

statement appeared at the top of the page.

Results

When statements were made by editors, 76% of the participants (n = 93) chose

journal of the editor who communicated her belief in the sure mode. When the

statements were made by mail clerks, 65% of the participants (n = 92) chose the journal

of the clerk who expressed her belief in the sure mode (Fischer exact, p < .05, one-sided).

These results indicate that overall, listeners infer greater belief strength when the same

belief is expressed in the sure mode than in the chance mode. This effect is moderated by

the expertise of the speaker such that for people who are not considered to be experts, the

belief-strengthening effect of the sure-mode seems to diminish, perhaps due to lack of

credibility of the novices. Unfortunately, we do not get a reversal here.

General Discussion

In this paper we have shown that speakers and listeners distinguish “internal

mode” statements (e.g., “I am 80% sure that…” or “I am reasonably confident that…”)

that express epistemic uncertainty (in the mind of the speaker) from external mode

statements (e.g., “I think there is an 80% chance that…” or “I believe there is a high

probability that…”) that express aleatory uncertainty (chance factors). Speakers place

more weight on singular information (e.g. feeling-of-knowing) when using internal

statements and more weight on distributional information (e.g. relative frequencies) when

using external statements. Meanwhile, listeners associate internal language with singular

reasoning and uncertainty attributed to the speaker’s mind whereas they associate

external language with distributional reasoning and uncertainty in the world. Moreover,

speakers using internal (versus external) mode statements are judged to be more

deserving of credit if they are right and blame if they are wrong.

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Table 1. Use of External and Internal Language by Characteristics of the Speaker, Prediction

and Event

Internal External p value

Speaker Perspective 1st Person 290 410 p = .0002nd or 3rd Person 70 193

Expertise Expert 195 299 p = .09Non-expert 166 307

Gender Male 249 347 p = .000Female 71 90Mixed 40 167

Relation Stranger or acquaintance 49 166 p = .002Friend, romantic partner or close relative

8 4

Control No control 262 575 p = .000Influence 70 19Can bring about event 29 11

Prediction Source None/Intuition 282 289 p = .000Trends/Facts 77 286Calculation/Logic 2 31

Backing None 294 432 p = .000Backing/Justification 67 173

Negation Non-negation 306 583 p = .000Negation 55 22

Event Subject Sentient 266 372 p = .000Facts/Things/Processes/Events

95 234

Type (if sentient) Mental event 54 24 p = .000Behavioral event 212 348

Timing Past 71 58 p = .000Present 100 88Future 190 460

Objective desirability Undesirable 55 261 p = .000Neutral/Indeterminate 155 191Desirable 151 154

Subjective desirability Undesirable 56 263 p = .000Neutral/Indeterminate 117 181Desirable 183 162

Temporality One-time 194 319 p = .000Extended 74 189Timeless 93 98

Locus Epistemic uncertainty 182 115 p = .000Aleatory uncertainty 176 491

Table 2

Statement (I-statements) BLOC pLOC Bprobability pprobability

I will go to a party this weekend -.09 .316 .024 .009

I will earn at least a 3.0 GPA this semester -.27 .087 .113 .053

I will go to bed before 1AM tonight -.066 .518 .043 .005

I will speak to my parents at some point in the next week -.643 .021 .099 .023

I will attend my 10 year high school reunion -.217 .033 .039 .012

I will get married by the time I am 30 -.066 .55 .095 .001

I will travel out of state this summer -.096 .364 .05 .004

I will attend graduate school -.091 .36 .045 .004

I will get at least a B- in BUAD 307 this semester -.28 .074 .16 .012

I will go to the beach sometime in March -.113 .228 .029 .009

Statement (World-statements) BLOC pLOC Bprobability pprobability

President Obama will be reelected in 2012 -.132 .212 .053 .015

there will be a commercially available cure for AIDS by 2020 .088 .394 .004 .814

Intelligent life exists on other planets .242 .053 .026 .037

USC will play in the Rose Bowl next January 1 .163 .096 .054 .028

A major earthquake (at least 6.0) will hit Los Angeles in the next five years

.029 .759 .018 .327

The high temperature in Downtown LA will be at least 70 degrees next Tuesday

-.086 .395 -.005 .744

Slumdog Millionaire will win the Academy Award for Best Picture -.047 .69 .05 .04

The U.S. unemployment rate will go up in the next month .223 .058 -.002 .906

Britney Spears will go back into rehab sometime in the next five years

.064 .476 .009 .484

The Lakers will win most of their games in March .231 .019 .023 .199

Table 3

Probability <=50% Probability > 50%Chance Mode Model: likelihood (B = 3.899, p < .001)

Model: knowledge(ns)

Model: likelihood, (B = 4.345, p < .001) knowledge (B = -1.179, p < .05)

Model: likelihood (B = 3.630, p < .001)

Model: knowledge (B = 2.184, p < .001)

Model: likelihood (B = 2.958, p < .001) Knowledge (B = 1.063, p < .05)

Sure Mode Model: likelihood (B = 5.191, p < .001)

Model: knowledge (ns)

Model: likelihood (B = 5.294, p < .001) knowledge (ns)

Model: likelihood (B = 5.746, p < .001)

Model: knowledge (B = 2.767, p < .001)

Model: likelihood (B = 5.502, p < .001) knowledge (ns)

Table 4

Questions Statements and Inferred Thoughts Proportion of Respondents

Question 1 Doctor Ames says: “I am 80% sure that you have Crohn’s disease.”“This patient has most of the signs and symptoms of Crohn’s disease.”

62% (62%)

Doctor Baker says: “There is an 80% chance that you have the Crohn’s disease.”“Most of the patients I have seen with these signs and symptoms have Crohn’s disease.”

61% (62%)

Question 2 Dick says: “I am 70% sure that the Celtics will beat the Knicks tonight.”“The Celtics have a stronger lineup of players than the Knicks.”

72% (75%)

George says: “I think there is a 70% chance the Celtics will beat the Knicks tonight.”“The Celtics have a better win-loss record than the Knicks.”

73% (75%)

Question 3 Cade says: “I am 80% sure that I will be married within three years.”has a specific person in mind to marry.

86% (86%)

Peter says: “I think there is an 80% chance that I will be married within three years.”

Question 4 Ellen says: “I am 60% sure I will go to the beach this month.”

Sarah says: “I think there is a 60% chance I will go to the beach this month.”is thinking about how often she tends to go the beach in a typical month.

66% (66%)

Question 5 Derek says: “I am 90% sure that Chip wore a vest sometime last week.”saw Chip last week.

92% (92%)

Lyle says: “I think there is a 90% chance that Chip wore a vest sometime last week.”is thinking about how often Chip tends to wear vests.

91% (92%)

Question 6 Miguel says: “I am 80% sure the Warriors won last night.”is trying to recall the outcome of the game that he read in the newspaper.

81% (85%)

Noah says: “I think there is an 80% chance the Warriors won last night.”

Question 7 Emily says: “I’m 70% sure Brian parked his car in lot C today.”

Sabrina says: “I think there is a 70% chance Brian parked his car in lot C today.”is thinking “Brian parks in lot C on most days.”

75% (61%)

Question 8 Mr. and Mrs. Adams say: “We are 90% sure we are going to have a baby in the next few years”are uncertain about their decision to conceive.

71% (74%)

Mr. and Mrs. Bing say: “We think there is a 90% chance we will have a baby in the next few years”are uncertain about their ability to conceive.

72% (74%)

Question 9 Suzanne says: “I am 60% sure my new restaurant will be profitable.”thinks that success depends mostly on individual effort and ability.

91% (91%)

Wendy says: “I think there is a 60% chance my new restaurant will be profitable.”thinks that success depends mostly on factors outside of one’s control.

91% (91%)

Question 10

Colin says: “I am 70% sure I’ll win the poker tournament.”is thinking about his own poker skill.

80% (83%)

Shane says: “I think there is a 70% chance I’ll win the poker tournament.”is thinking about the poker skill of all players in the tournament.

81% (83%)

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