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\title{Ambiguity and expectation-neglect in dilemmas of interpersonal trust}

\author{Anthony M. Evans\thanks{Department of Social Psychology,
Tilburg University,
P.O. Box 90153, 5000 LE Tilburg,
The Netherlands.
E-mail: A.M.Evans@uvt.nl.}
\and
Joachim I. Krueger\thanks{Brown University}
}

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\newcommand{\jhead}{Judgment and Decision Making, Vol.~12, No.~6}
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  \jdate \hfill Ambiguity and expectation-neglect in dilemmas of interpersonal trust \qquad}
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\begin{onecolabstract}
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Recent research suggests that people discount or neglect expectations of
reciprocity in trust dilemmas. We examine the underlying processes and
boundary conditions of this effect, finding that expectations have
stronger effects on trust when they are made accessible and when they
are provided as objective probabilities (Study 1). Objective
expectations have stronger effects when they are based on precise,
rather than ambiguous, probabilities (Study 2). We also find that trust
decisions differ from individual risk-taking decisions: people are more
willing to trust, and expectations have stronger effects on trusting
behavior (Study 2). These results show that the availability and
ambiguity of expectations shape trust decisions, and that people
differentially weight expectations in dilemmas of trust and individual
risk-taking.

\smallskip
\noindent
Keywords: trust, risk, expectations, bounded rationality
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{\renewcommand{\thefootnote}{}

\footnotetext{

Copyright: \copyright\ 2017.
The authors license this article under the terms of the
\href{http://creativecommons.org/licenses/by/3.0/}{Creative Commons
  Attribution 3.0 License.}
}}

\saythanks

\section{Introduction}

To what extent does trust among strangers depend on expectations of
reciprocity? This question is important to understand trust in
zero-acquaintance interactions, such as online exchanges, when future
interactions are unlikely and antisocial behavior is difficult to
sanction (Aggarwal, Goodell \& Selleck, 2015; Ert, Fleischer \&
Magen, 2016). Some theories assume that expectations are central to
trust, and that people trust others only insofar as they expect
positive reciprocity (Camerer, 2003; Rotter, 1967; Thielmann \& Hilbig,
2015). If so, then trust behavior can be encouraged by providing
information to bolster positive expectations. Yet, recent research
finds that expectations only weakly predict trust behavior (Dunning,
Anderson, Schlösser, Ehlebracht \& Fetchenhauer, 2014; Evans \&
Krueger, 2014), suggesting that merely strengthening expectations may
not substantially increase trust behavior. However, little is known
about why trustors neglect expectations or the boundary conditions of
this effect. Our working hypothesis is that people discount
expectations when they do not come to mind easily (Evans \& Krueger,
2011) and when they are based on ambiguous information (Einhorn \&
Hogarth, 1985).

If people neglect their own expectations in trust dilemmas, it is
important to ask whether similar processes occur in the domain of
individual risk-taking, where uncertain outcomes are determined by
chance. Even when trust and risky choice dilemmas are economically
equivalent (e.g., the probabilities and payoffs are identical), the
two situations have important psychological differences. Previous
studies focused on mean-level differences – asking if people are more
(or less) willing to trust than take personal risks (e.g., Bohnet \&
Zeckhauser, 2004; Fetchenhauer \& Dunning, 2009). In addition to these
mean-level differences, people may weight expectations differently in
the two domains. Indeed, it has been hypothesized that expectations
have weaker effects on trust decisions (Evans \& Krueger, 2016),
though previous work has not tested this claim directly. The present
work examines how expectations shape trust, and reveals the distinct
processes that influence behavior in dilemmas of individual and social
uncertainty.

\subsection{Trust dilemmas and expectations of reciprocity}
To investigate trust behavior, researchers use variants of the
sequential trust game (Camerer, 2003; Evans \& Krueger, 2009). Figure
1 shows the basic structure of the game as used here. By design, both
players have full knowledge of the game’s structure and potential
outcomes. In the first stage, Player 1 (the trustor) chooses between
the status quo and trust. Selecting the status quo terminates the
interaction with modest outcomes for both parties. If Player 1 chooses
to trust, thereby increasing the total available wealth, Player 2 (the
trustee) chooses between reciprocity and betrayal. Reciprocity leaves
both players with outcomes better than the status quo. Betrayal leaves
Player 1 with an outcome worse than the status quo, while giving
Player 2 the best possible outcome. The trustor’s dilemma is to choose
between the security of an inefficient status quo and the uncertainty
of trust. In turn, the trustee faces a moral dilemma: to honor trust
with reciprocity or to profit at the trustor’s expense.

\begin{figure}[t]
\includegraphics[clip=true,width=\columnwidth]{fig1.eps}
\caption{An example of the sequential trust game.}
\end{figure}

Formal models posit that expectations of reciprocity are essential to
trusting behavior (Thielmann \& Hilbig, 2015). Dispositional models
explore individual and societal differences as differences in
generalized expectations about the trustworthiness of other people
(Balliet \& Van Lange, 2013; Rotter, 1967; Yamagishi et al., 2015). In
other words, dispositional trust and positive expectations are
interchangeable. Likewise, game-theoretic models stipulate a direct
correspondence between expectations of reciprocity and trusting
behavior (Camerer, 2003; Krueger, Evans \& Heck, 2017). In short,
there is interdisciplinary consensus that trusting behavior should
depend on the belief that reciprocity will follow (Evans \& Krueger,
2016).

Yet, the empirical effect of expectations on trusting behavior is
relatively weak (Dunning et al., 2014; Schlösser, Mensching, Dunning
\& Fetchenhauer, 2015). When faced with trust dilemmas, people do not
fully engage in consequentialist thinking; in other words, they do not
focus on how trustees will respond in the event that they are trusted
(Kugler, Connolly \& Kausel, 2009). Instead, trust decisions are
influenced by other factors, such as the emotions felt at the moment
of decision-making (Martinez \& Zeelenberg, 2015; Schlösser,
Fetchenhauer \& Dunning, 2016) and the feeling that trust is the right
thing to do (Dunning et al., 2014). These findings led to the proposal
that trust decisions are blind and ``economically'' irrational, rather
than strategically self-interested (Dunning et al., 2014; Schlösser et
al., 2015).

The perspective of bounded rationality offers an alternative
explanation for why trustors neglect their own expectations of
reciprocity (Hertwig \& Herzog, 2009). People tend to focus on
salient, easy-to-process cues, thereby ignoring information that
requires effort to process (Gigerenzer, Todd \& ABC Research Group,
1999; Simon, 1955). In dilemmas of trust, people have ready access to
their own experiences and preferences (Krueger, 2003), and overriding
egocentrism requires time and cognitive effort (Lin, Keysar \& Epley,
2010; Tamir \& Mitchell, 2013). Consistent with this view, we found in
earlier work that changes in outcomes have stronger effects on
behavior than changes in expectations (probabilities of these
outcomes), even when outcomes and expectations have equivalent effects
on the expected value of trust (Evans \& Krueger, 2014).  Information
search and self-report data suggest that many trust decisions occur
without consideration of the trustee’s potential payoffs, information
that is critical for the formation of accurate expectations of
reciprocity (Evans, Athenstaedt \& Krueger, 2013; Evans \& Krueger,
2014). In other words, people focus on the potential payoffs
associated with trust, without fully considering the probabilities of
those payoffs occurring.

The reasons why people prioritize payoffs over expectations are not
fully understood, but one possible explanation is that expectations
are less salient and more ambiguous than outcomes. The present studies
are designed to test this account.

\subsection{Subjective and objective expectations}
We propose that the tendency to discount expectations (and
focus on outcomes instead) depends on the extent to which expectations
are based on subjective versus objective information: Fully subjective
expectations are generated by the decision-maker; they are based on
general beliefs about the trustworthiness of strangers (Evans \&
Revelle, 2008; Rotter, 1967) or on inferences from relevant cues
(Brunswick, 1955; Thielmann \& Hilbig, 2015). In contrast, fully
objective expectations are provided by a knowledgeable source and are
based on descriptive probability information (Hertwig \& Erev, 2009;
Van Dijk \& Zeelenberg, 2003). Expectations can also lie somewhere
between these two extremes; they may be based on a combination of
subjective and objective information. For example, even when trustors
have access to objective information about the probability of
reciprocity, they may also consider their subjective beliefs and
experiences.

Expectations based on subjective and objective information differ in two
important ways: First, subjective expectations are more ambiguous than
objective expectations (Einhorn \& Hogarth, 1985). Objective
expectations are described as exact numerical probabilities, but
subjective expectations may be vague or imprecise estimates (Olson \&
Budescu, 1997). The famous Ellsberg paradox illustrates that people are
more willing to accept gambles based on precise (vs.\ ambiguous)
probabilities (Einhorn \& Hogarth, 1995; Ellsberg, 1961; Van Dijk \&
Zeelenberg, 2003). Second, objective expectations based on descriptive
probabilities are more likely to be salient at the moment of
decision-making, especially if they are made available as descriptive
probabilities. Objective expectations are readily available to the
decision-maker, whereas subjective expectations must be derived from
cues, such as the trustee’s payoffs (Evans \& Krueger, 2011).
Decision-makers may be reluctant (or unable) to use cues to form and
update subjective expectations. One (or both) of these factors may
explain why subjective expectations have comparably weak effects on
trusting behavior.

\subsection{Trust and individual risk-taking}
The question of how expectations influence behavior has implications for
the comparison of trust and individual risk-taking decisions. Previous
studies focused on mean-level differences, asking if people are more
willing to accept uncertain outcomes in the domain of social trust
compared with non-social risk-taking. The results are mixed: Some
researchers found that people are more willing to take individual risks
than engage in trusting behavior (Aimone \& Houser, 2012; Hong \&
Bohnet, 2007; Bohnet, Greig, Herrmann \& Zeckhauser, 2008), whereas
others found the opposite (Dunning et al., 2014; Fetchenhauer \&
Dunning, 2012; Schlösser et al., 2015).

A problem pervading previous research is a confound between the
distinction between social trust and individual risk-taking and the
distinction between subjective and objective expectations. The typical
trust decision is based on subjective expectations (e.g., Berg,
Dickhaut \& McCabe, 1995), whereas the typical risk-taking decision is
based on objective expectations. This confound raises the possibility
that people weight information differently in the domains of trust and
risk-taking. For example, trust decisions may de-emphasize
expectations, whereas individual risk-taking decisions more closely
resemble expected utility calculation (Evans \& Krueger, 2016).

\subsection{Overview of studies}
We conducted two experiments to examine the effects of expectations in
dilemmas of trust and reciprocity. Study 1 compares decisions in the
typical trust game, where subjective expectations are elicited after
decisions are made, with decisions in a modified game where
expectations are measured at the moment of decision-making and a
condition where expectations are provided as objective probability
information. Study 2 considers how the ambiguity of objective
probability information affects trust and risk-taking decisions,
comparing the effects of ambiguous versus precise probabilities on
trust and individual risk-taking decisions.

\section{Study 1}

Study 1 had three conditions: In the subjective condition, players made
decisions in a trust game where they had to form subjective
expectations of trustees’ behavior, with expectations measured after
decisions were made. In the salient condition, players estimated, and
thereby expressly brought to mind, the likelihood of reciprocity
immediately before each decision. In the objective condition, players
received explicit information about the probability of reciprocity
before they made each decision.

We focus on two comparisons: First, we ask if the effects of
expectations on trust are comparable in the subjective and salient
conditions. If people neglect expectations because they do not easily
come to mind (Evans \& Krueger, 2014; Lin et al., 2010), then salient
expectations should predict trust more strongly than subjective
expectations. Reminding trustors to form an expectation at the moment
of decision-making may be enough to shift their process of
decision-making to favor expectations (Kugler et al., 2009). Second, we
ask if the effects of expectations are similar in the salient and
objective conditions. If trustors neglect expectations because
self-generated predictions are ambiguous and vague (Einhorn \& Hogarth,
1985; Van Dijk \& Zeelenberg, 2003), then objective expectations should
predict trust more strongly than salient expectations. If so, one may
infer that trustors discount self-generated expectations, even when
they are reminded of them before making a decision.

\subsection{Method}
\subsubsection{Participants}
A total of 244 (96 women) U.S. participants were recruited from
Mturk. The average age was 33.3 years, SD = 10.4. Each participant
received 60 cents for their time. The sample size was sufficient to
detect a medium sized effect (f = .20) with 80\% power.

\subsubsection{Materials and procedure}
Participants read detailed instructions explaining the rules of the
game, and learned that they had been assigned to the role of Player 1
(trustor). They also read that they would be randomly assigned to a
partner, and that those assigned to the role of Player 2 (trustee) had
already made their decisions. After reading the instructions,
participants completed 24 trials of the game, with the order randomized
for each participant (see Evans \& Krueger, 2014). For each trial, they
could choose “IN” (trust) or ”OUT” (the status quo).

Two factors were manipulated in the game’s payoff structure, the
cost-benefit ratio of choosing trust, $(p_1-S)/(R_1-S)$, and the
trustee’s financial temptation to choose betrayal, $(T-R_2)/T$ (see
Figure 2). When the cost-benefit ratio was high, the trustor had
little to gain (and much to lose) from choosing trust.\footnote{ Other
  studies refer to this cost-benefit ratio as the trustor’s “risk.”
  However, the present manuscript uses the term risk to refer to
  individual risk-taking behavior. We use the term cost-benefit ratio
  to reduce confusion.}  This ratio ranged from .20 to .79, M = .49,
SD =.26. We also manipulated the trustee’s temptation, her economic
incentive to choose betrayal instead of reciprocity. As this
temptation increased, Player 2 (trustee) earned more money from
choosing betrayal. The trustee’s temptation ranged from .13 to .71, M
= .45, SD = .20. The specific payoff values used in each round are
reported in the Appendix.

\begin{figure}[t]
\includegraphics[clip=true,width=\columnwidth]{fig2.eps}
\caption{The payoff structure of the trust game.}
\end{figure}

Participants were randomly assigned to the subjective, the salient, or
the objective condition:

\paragraph{Subjective expectations.} In this condition, participants
made all 24 trust decisions before they were asked to form explicit
expectations of reciprocity. After making all 24 decisions,
participants estimated the percentages of Player 2s (out of 100) who
would choose SHARE (reciprocity) in each trial of the game. Thus, each
participant provided 24 trust decisions and 24 expectations.

\paragraph{Salient expectations.} Participants in this condition were
instructed to estimate the percentages of Player 2s who would choose
“SHARE” (reciprocity) at the decision screen of the trust game. That
is, expectations were measured before participants made each trust
decision. Otherwise, they followed the same protocol as participants
in the subjective condition.

\paragraph{Objective expectations.} Participants in the objective
condition received explicit information about the probability of
reciprocity before each decision. They were informed that 100 workers
had previously made decisions as Player 2. At the decision screen,
participants were told how many trustees (out of 100) chose SHARE (and
the number who chose KEEP). The objective probabilities for each trial
were based on the average expectations of reciprocity stated by
participants from Study 2 of Evans \& Krueger (2014): \textit{M} =
45.9\%, \textit{Min} = 32\%, \textit{Max} = 64\%.  That is, at each
trial participants learned that the probability of reciprocity was the
average expectation stated by participants (for that trial) in the
previous study.

\subsection{Results and discussion}
\subsubsection{Analysis strategy}
To account for the clustered nature of the data, we used the lme4
package in R to estimate multilevel models (Bates, Maechler, Bolker \&
Walker, 2014) and the lmertest package to obtain p-values (Kuznetsova,
Brockhoff \& Christensen, 2015).

Expectations of reciprocity were scaled to range from 0 to 1. Note that
in the subjective and salient conditions, expectations at each trial
varied across participants (depending on participants’ differing
beliefs), whereas expectations in the objective condition were provided
by the experimenter and were therefore the same for all participants.
We used dummy variables to compare the three conditions, treating the
salient condition as a reference level.

% table 1
\begin{table*}[t]\centering
\caption{The effects of expectation and experimental condition on trust. We report unstandardized beta weights (b); the standard errors of beta weights (SE); and the standard deviations of the random intercepts and random slopes estimated for each participant (SD).}
\begin{tabular}{lccc@{}ccccc}\toprule
 & \mc{2}{c}{Full model} & \mc{2}{c}{Subjective condition} &
 \mc{2}{c}{Salient condition} & \mc{2}{c}{Objective condition}\\\cmidrule(lr){2-3}\cmidrule(lr){4-5}\cmidrule(lr){6-7}\cmidrule(lr){8-9}
Fixed effects & b (SE) & p & b (SE) & p & b (SE) & p & b (SE) & p\\\midrule
Intercept & $-$1.98 (.38) & < .001 & $-$.01 (.17) & .92 & $-$2.14 (.49) & < .001 & $-$5.58 (.70)
& < .001\\
Expectation & {\ } 5.69 (.74) & < .001 & {\ } .82 (.25) & < .001 & {\ } 6.13 (.94) & < .001 & {\ } 12.73 (1.43)
& < .001\\
Subjective condition & {\ } 1.77 (.52) & .13 &  &  & &  &  & \\
Objective condition & $-$2.78 (.57) & .56 &  &  &  &  &  & \\
Subjective*Expectation & $-$4.37 (.98) & < .001 &  &  &  &  &  & \\
Objective*Expectation & {\ \ } 5.27 (1.10) & < .001 &  &  &  &  &  & \\\midrule
Random effects & SD &  & SD &  & SD &  & SD & \\\midrule
Intercept & 2.82 &  & 1.15 &  & 3.61 &  & {\ } 5.50 & \\
Expectation & 5.09 &  & {\ } .26 &  & 6.29 &  & 11.01 & \\\bottomrule
\end{tabular}
\end{table*}

\subsubsection{Mean-level differences in behavior}
To begin, we tested for mean-level differences in trusting behavior
across the three conditions. Here, we had no a priori predictions. We
submitted a logistic model with trust decisions (1 = trust; 0 = status
quo) as the dependent variable. The two condition dummy variables were
entered as predictors, and the model also included random intercepts
for each participant. The rates of trust were comparable in the
subjective (.55), salient (.55), and objective (.54) conditions,
b\textsubscript{subjective} = .0059, SE = .25, p = .98;
b\textsubscript{objective} = $-$.010, SE = .25, p = .67.

\begin{figure*}[t]\centering
\includegraphics[clip=true,width=5in]{figure3.eps}
\caption{The individual-level effects of expectations on trusting
  behavior. For each participant, we estimated a simple logistic model
  using expectation to predict trust. Top: Individual-level intercepts
  and slopes were then used to generate predicted probabilities of
  trust at different levels of expectation.  Bottom: The distribution
  of individual-level regression slopes (i.e., the effect of
  expectations on trust for each participant) is displayed for each
  condition.}
\end{figure*}

\subsubsection{Trust and expectations of reciprocity}
Our primary analyses compared the effects of expectations on trust
across conditions. To allow the effects of expectations to vary across
participants, we estimated a model that included both
random intercepts for participants and within-participant
random slopes for expectations (Table 1). Overall, expectations were
positively associated with trusting behavior, but the effects of
expectations differed significantly across conditions.

First, we compared the effects of expectations on behavior in the
subjective and salient conditions. Our hypothesis was that increasing
the salience of expectations would strengthen the positive relationship
between expectations and trusting behavior. Indeed, there was a
significant interaction, indicating that the effects of expectations
differed in the subjective and salient conditions:
b\textsubscript{subjective*expectation} = $-$4.37, p {\textless} .001. To
understand this interaction, we estimated the simple effects of
expectations within the subjective and salient conditions: Though the
effects of expectations were significant in both conditions, the simple
effect of expectations on trust was significantly stronger in the
salient condition (b = 6.13) compared to the subjective condition (b =
.82).\footnote{ Our simple effects models, which tested the effects of
expectations on trust within each experimental condition, included
random intercepts for each participant and random slopes for
expectations.} In other words, increasing the expectation of
reciprocity by +.01 was associated with a 6.3\% increase in the odds of
trust in the salient condition and a .82\% increase in the subjective
condition.

We also tested whether salient and objective expectations had different
effects on trust. Here, we predicted that expectations would have a
stronger influence on behavior when they were explicitly provided as
objective probabilities. Consistent with our prediction, we observed a
significant condition by expectations interaction:
b\textsubscript{objective*expectation} = 5.26, p {\textless} .001. We
then compared the simple effects of expectations in the objective and
salient conditions: the effect of expectations was stronger when they
were objective (b = 12.73) than when they were salient. Increasing the
expectation of reciprocity by +.01 was associated with a 13.5\%
increase in the odds of trust in the objective condition.

Figure 3 displays the effects of expectations on trust at the level of
individual participants. Trustors in the objective condition were the
most sensitive to expectations, and those in the subjective condition
were the least sensitive.

\renewcommand{\baselinestretch}{1.02} \large\normalsize

\subsubsection{Subjective and salient expectations of reciprocity.}
Finally, we asked whether participants generated equivalent expectations
in the subjective and salient conditions. We estimated a linear model
with expectations as the dependent variable. Condition (subjective vs
salient), temptation, and the cost-benefit ratio were entered as
predictors. Overall, expectations of reciprocity were similar in the
salient (.44) and subjective (.40) conditions,
b\textsubscript{subjective} = $-$.040, SE = .027, p = .13. Expectations
were, however, significantly affected by changes in payoffs:
participants expected less reciprocity when the trustee’s temptation
was large (b\textsubscript{temptation} = $-$.51, SE = .037, p {\textless}
.001) and when the trustor’s cost-benefit ratio was large
(b\textsubscript{cost-benefit} = $-$.028, SE = .012, p = .013).

Similar to previous studies, trustors believed that the trustee’s
financial incentives (i.e., temptation) could be used to form an
educated expectation of the other player’s behavior (Evans \& Krueger,
2014; Snijders \& Keren, 1999). Importantly, the time at which
expectations were measured (pre vs.\ post decision) did not significantly
influence average expectations or the specific information trustors
used to form expectations. The time of measurement only influenced the
effect of those expectations on trustors’ final decisions.

\subsection{Summary}
Study 1 showed how that the salience and the objectivity of social
expectations can strengthen their effects on trust. When participants
first formed expectations, thereby making them salient, they relied on
them more in their final decisions. Expectations had the strongest
effect on trust decisions when they were externally and objectively
provided. In short, decisions in the salient condition fell somewhere
in between the two patterns of behavior observed in the subjective and
objective expectations conditions. A limitation of comparing the
effects of expectations in the salient and objective conditions is that
expectations varied between participants in the salient condition,
whereas those in the objective condition received identical expectation
information. Hence, variance in expectations (rather than ambiguity)
may have attenuated the effects of expectations in the salient
condition. Study 2 was designed to address this concern.

\section{Study 2}

The first study showed that even when subjective expectations are
salient, they have weaker effects on behavior than objective
expectations. Study 2 was designed test the hypothesis that trustors
discount expectations – even ones based on explicit information – when
they are ambiguous, rather than precise, probabilities (Einhorn \&
Hogarth, 1985; Van Dijk \& Zeelenberg, 2003). We therefore manipulated
the ambiguity of objective expectations: In the low-ambiguity
conditions, participants learned about the precise probability of
reciprocity (e.g., 20\%). In the high-ambiguity conditions,
participants received the same probability described as the midpoint
of a range. For instance, participants were told that the probability
of reciprocity was between 10 and 30\%. Consistent with previous
studies (Van Dijk \& Zeelenberg, 2003), we predicted that ambiguous
expectations would have a weaker effect on trusting than precise
expectations.

We also introduced an individual risk-taking condition, where
participants made decisions that were equivalent – in terms of
probabilities and personal outcomes – to trust decisions. Outcomes in
the individual risk-taking condition were determined by chance, rather
than by another person. This condition allowed us to test for
mean-level differences in the rates of trust and risk-taking, and
allowed us to ask if expectations differently influenced trust and
risk-taking decisions. Previous studies speculated that expectations
have stronger effects on risk-taking decisions (Dunning et al., 2014;
Evans \& Krueger, 2014), but did not directly test this claim.

\subsection{Method}
\subsubsection{Participants}
A total of 200 U. S. American participants (74 women) were recruited
from Mturk. The average age was 33.6, \textit{SD} = 9.8. Participants
received 50 cents for their time and a bonus based on one randomly
selected choice. Given the 2 x 2 design, the sample size was sufficient
to detect medium sized effects (\textit{f} = .20) with 80\% power.
Decisions were incentivized and no deception was employed.

\subsubsection{Materials}
The study had a 2 (ambiguity: low vs.\ high) X 2 (decision type: trust vs
risk-taking) design. Participants made a series of 24 trust or
risk-taking decisions. The instructions and trust game parameters were
based on the materials used in Study 1.

\paragraph{Pre-test}
We conducted a pre-test where we collected responses for Player 2 in the
trust game, so that participants in the role of Player 1 could interact
with actual partners. This “past partners” design allowed us to fully
incentivize participants’ decisions (Camerer \& Mobbs, 2017). We
recruited an initial group of 100 American participants on Mturk to
make a series of 24 decisions as Player 2 in the trust game. These
participants were informed that they would be randomly partnered with
trustors who would make decisions at a later time. Trustees always made
decisions about whether to reciprocate, but they understood that their
decisions would matter only if their partner chose to trust them in the
first stage of the game. This means that each Player 2 made 24 separate
reciprocity decisions.

Rates of reciprocity ranged from 31 to 72\%, with an overall average of
48.0\%. Across trials, the rate of reciprocity was strongly correlated
with the trustee’s temptation, r(22) = $-$.92, p {\textless} .001, and
uncorrelated with the trustor’s cost-benefit ratio, r(22) = .051, p =
.81. Participants in the trust game conditions were randomly partnered
with these initial 100 participants.

\paragraph{Ambiguity manipulation}
Before making a decision, participants received information about the
probability of reciprocity. In each trial of the game, the probability
of reciprocity was based on the actual reciprocity decisions of workers
from our pre-test. In the low-ambiguity conditions, the probabilities
given to participants were precise values (e.g., 60\%). In the
high-ambiguity conditions, these probabilities were presented as
estimates with a 20\% range of possibility. For example, if the
probability of reciprocity was 60\%, participants were informed that
the probability of reciprocity was between 50 and 70\%. Participants
did not receive any further information about the distribution of
probabilities within the given interval.

\paragraph{Trust and risk-taking conditions}
Participants in the trust conditions followed the procedure outlined in
the objective condition from Study 1.

Participants in the risk-taking conditions read about individual
gambles that were equivalent to the trust game in terms of personal
outcomes, probabilities, and the presence (vs.\ absence) of ambiguity. They made a
series of 24 decisions, choosing between “IN” (the risky option) and
“OUT” (the safe option). They were informed that the consequences of
their choices would be determined by a random number generator, and
they would learn the chances of receiving “LEFT” (winning the gamble)
and “RIGHT” (losing the gamble).  At the decision screen for each
trial, they were informed about the “chance of receiving LEFT” and the
“chance of receiving RIGHT.” These probabilities were reported as
percentages.

% is this correct?

% table 2
\begin{table*}[t]\centering
  \caption{The effects of ambiguity, decision
    type, and expectations on behavior (Study 2).}
\begin{tabular}{lrr@{\quad}rr}\toprule
Fixed effects &b {\ } &95\% CI {\ } &SE {\ } &p {\ } \\\midrule
Intercept &.027 &$-$.18, .22 &.10 &.79 \\
Decision type (risk vs.\ trust) &.47 &.094, .80 &.20 &.020 \\
Ambiguity &.23 &$-$.18, .63 &.20 &.25 \\
Expectation &5.42 &4.39, 6.48&.55 &< .001 \\
Ambiguity*Decision type &$-$.13 &$-$.89, .63 &.28 &.64 \\
Expectation*Ambiguity &$-$2.80 &$-$4.66, $-$.99  &1.09 &.010 \\
Expectation*Decision type &2.60 &.46, 4.52 &1.09 &.017 \\
Expectation*Decision*Ambiguity&$-$2.94 &$-$5.70, .11&2.17 &.17 \\\midrule
Random effects &SD &95\% CI {\ } &\mc{2}{l}{Correlation} \\\midrule
Intercept &1.32 &1.13, 1.47& & \\
Expectation &6.10 &4.87, 6.92&\mc{2}{c}{$-$.03} {\ } \\\bottomrule
\end{tabular}
\end{table*}

\renewcommand{\baselinestretch}{1.00} \large\normalsize

\subsection{Results and Discussion }
\subsubsection{Mean-level differences in behavior}
To begin, we tested the effects of ambiguity and decision type on
mean-level differences in behavior. We estimated a logistic model of
trust with ambiguity (low = $-$.5; high = +.5), decision type
(risk-taking = $-$.5; trust = +.5), and the ambiguity by decision type
interaction entered as predictors; random intercepts were also included
for each participant. The rate of trust was significantly higher (.52)
than the rate of individual risk-taking (.44), b = .37, SE = .18, p =
.036. Ambiguity had no significant effects on the overall rates of
trust or risk-taking behavior, b = .25, SE = .18, p = .16, and there
was no significant ambiguity by decision-type interaction, b = $-$.10, SE
= .35, p = .77.

\begin{figure*}[t]\centering
\includegraphics[clip=true,width=6in]{figure4.eps}
\caption{The effects of expectation, decision
type (risk-taking vs.\ trust), and ambiguity (low vs.\ high) on behavior.
Left: For each participant, we estimated a simple logistic model using
expectation to predict behavior, and intercepts and slopes were then
used to the generated predicted probabilities. Right: The distribution
of individual-level regression slopes (i.e., the effect of expectations
on trust and risk-taking for each participant) is displayed across
conditions.}
\end{figure*}

\subsubsection{Ambiguity and expectations of reciprocity. }
Our primary analyses focused on whether ambiguity influenced the
relationship between expectations and behavior, with the hypothesis
that precise expectations would have a stronger effect on decisions
than ambiguous expectations. We estimated a logistic model with trust
and risk-taking behavior as the dependent variable. This model included
terms to test the potential interactions of decision type, ambiguity
and expectations, as well as random intercepts for participants and
random slopes for expectations. The results reported in Table 2.

Expectations were positively associated with both trust and risk-taking
behavior. There were, however, two important qualifications: First,
ambiguity moderated the relationship between expectations and behavior,
p = .010. To understand this interaction, we estimated the simple
effects of expectations in the low- and high-ambiguity conditions: As
predicted, expectations in the low-ambiguity conditions had stronger
effects on behavior (b = 6.93, SE = .90, p {\textless} .001)
than expectations in the high-ambiguity conditions (b = 3.80, SE = .69,
p {\textless} .001). Increasing the expectation of a positive outcome
by +.01 was associated with a 7.17\% increase in trusting/risk-taking
behavior in the low-ambiguity conditions and a 3.87\% increase in the
high-ambiguity conditions.

Second, the effects of expectations were different for decisions
involving trust versus individual risk, p = .017. We compared the
simple effects of expectations on trust and risk-taking decisions:
Expectations had a stronger positive effect in the trust conditions (b
= 7.78, SE = 1.12, p {\textless} .001) than in the risk-taking
conditions (b = 3.73, SE = .58, p {\textless} .001). Increasing the
expectation of a positive outcome by +.01 was associated with a 8.11\%
increase in the odds of trusting behavior and a 3.80\% increase in the
odds of individual risk-taking.

There was no significant three-way interaction between ambiguity,
decision type, and expectations (b = $-$2.94, SE = 2.17, p = .17),
indicating that the tendency to discount ambiguous expectations was
similar for trust and risk-taking decisions. Figure 4 displays the
effects of expectations on behavior at the level of individual
participants. Expectations had stronger effects for trust (vs
risk-taking) decisions and when probabilities were precise (vs
ambiguous).

\subsection{Summary}
The central finding of Study 2 was that precise expectations had a
stronger effect on behavior than ambiguous expectations, consistent
with the idea that people discount ambiguous information. Moreover, we
observed two findings related to the difference between trust and
risk-taking decisions: people were more willing to trust, and trust
decisions were more sensitive to changes in expectations. The finding
that expectations had stronger effects on trust decisions is
particularly striking, given that previous accounts have argued that
expectations matter more in non-social risk-taking dilemmas (Dunning et
al., 2014; Evans \& Krueger, 2014). Previous work, however, confounded
decision domain (trust vs.\ risk-taking) with type of expectations
(subjective vs.\ objective). The present results suggest that when type
of expectations is held constant across domains, expectations more
strongly influence trust than risk-taking decisions.

\section{General discussion}

To what extent are trust decisions based on expectations of reciprocity?
Previous studies suggested that trustors neglect expectations (Dunning
et al., 2014) and rely too heavily on their own anticipated outcomes
(Evans \& Krueger, 2014). However, these earlier studies were focused
on participants’ subjective expectations of reciprocity. Here, we find
that making expectations salient and giving people access to objective
probability information dramatically changes how they make decisions.
When trustors have access to objective probabilities, they strongly
rely on the expectations suggested by these probabilities. In contrast,
subjective expectations play a muted role in decision-making because
they are not immediately accessible (Study 1) and because they are
discounted due to their ambiguity (Study 2).

\subsection{Trust and individual risk-taking reconsidered}
Models of betrayal aversion (Bohnet \& Zeckhauser, 2004) and principled
trustfulness (Dunning \& Fetchenhauer, 2013) have been proposed to
explain how interpersonal trust decisions differ from individual
risk-taking decisions. Consistent with principled trustfulness,
participants in Study 2 were more likely to trust than engage in
individual risk-taking behavior. Yet, closer inspection of the evidence
also shows that people favor different types of information when making
trust decision and when making nonsocial decisions under risk. Holding
outcomes and probabilities constant, trust decisions were more
influenced by expectations than individual risk-taking decisions. This
finding contradicts the idea that expectations matter less for dilemmas
of trust (Evans \& Krueger, 2014).

The present results highlight that the extent to which trust is based on
instrumental concerns versus other considerations, such as respect for
norms, depends on the situation. We found that the effect of
expectations is stronger when trustors have access to objective
probability information. However, other variables can suppress the
influence of expectations. For example, Evans and Van Beest (2017)
found that trust decisions were less sensitive to changes in
expectations when potential outcomes were described as losses (versus
gains). Arguably, trust decisions involving losses are less calculative
because self-regarding decisions involving losses are perceived as more
overtly harmful to others than equivalent decisions involving gains
(Baron, 1995; Leliveld, van Dijk \& van Beest, 2008; Van Beest et al.,
2005). When considering how a variable, such as gain-loss framing,
influences trust, it is important to consider its effects on mean-level
behavior and the underlying process of decision-making (e.g., the
extent to which decisions are based on expectations).

\subsection{Expectations and cue processing}
The present research showed that subjective expectations have a
comparatively weak effect on trust. Yet, this effect becomes stronger
when trustors are prompted to generate expectations (Study 1),
suggesting that trustors may rely on expectations insofar as they
readily come to mind (Hertwig, Herzog, Schooler \& Reimer, 2008).
Consider how this process may influence trust when people have access
to different trustworthiness cues: The ease (or difficulty) of forming
subjective expectations may depend on the type of information at hand.
In our studies, when trustors formed expectations they had to rely on
the trustee’s temptation to betray trust (i.e., the trustee’s economic
payoffs). Trustors may be more inclined to rely on subjective
expectations when these are based on more easily processed cues, such as
those observed in the trustee’s appearance (Todorov, Pakrashi \&
Oosterhof, 2009) and nonverbal behavior (DeSteno et al., 2012).
Researchers have identified a comprehensive list of situational and
personal cues that trustors use to form subjective expectations of
reciprocity (Evans \& Krueger, 2016; Thielmann \& Hilbig, 2015), yet
little is known about how different types of cues alter the
relationship between expectations and behavior, or how trustors
integrate or prioritize competing trustworthiness cues. Previous
taxonomies have differentiated between personal and situational cues
(Thielmann \& Hilbig, 2015), but it may also be informative to define
cues based on how much effort they require to process (Bonnefon,
Hopfensitz \& De Neys, 2013).

\subsection{Expectations and beliefs in social decision-making}
The present studies contribute to a broader literature examining how
expectations and subjective beliefs influence behavior in different
strategic contexts. Several studies have argued that (subjective)
expectations are underemphasized in trust decisions (Dunning et al.,
2014; Evans \& Krueger, 2014), but other work has found that beliefs
play an important role in reciprocity decisions. The theory of trust
responsiveness suggests that trustees reciprocate when they believe
they have been trusted, and the trustee’s second-order beliefs (i.e.,
what the trustee believes the trustor expects her to do) are more
important than the trustee’s general preferences for fairness or
equality (Bacharach, Guerra \& Zizzo, 2007; Guerra \& Zizzo, 2004).
Reciprocity is less likely to occur when the trustee believes that the
other party doubts that reciprocity will occur, as when the trustor
takes a long time to reach a decision (Van de Calseyde, Keren \&
Zeelenberg, 2014) or when the trustor purchases insurance against the
possibility of betrayal (Van de Calseyde, Keren \& Zeelenberg, 2017).
Trust, in other words, can act as a self-fulfilling prophecy. As this
comparison between trust and reciprocity illustrates, the extent to
which social decisions are based on expectations depends on the
specific role of the decision-maker.

\renewcommand{\baselinestretch}{1.05} \large\normalsize

\subsection{Limitations}
In Study 2, we compared trust and individual risk decisions without
measuring behavior in risky dictator games, where players make
risk-taking choices with added interpersonal consequences. Risky
dictator games have been used as a control condition in studies
comparing trust and risk (e.g., Bohnet \& Zeckhauser, 2004) to account
for the possibility that the trustor may have interpersonal motives
related to equality or efficiency of outcomes (Fehr \& Schmidt, 1999;
Van Lange, 1999). However, previous studies have found that mean-levels
of behavior are similar in risky dictator games and individual
risk-taking decisions (Bohnet et al., 2008; Bohnet \& Zeckhauser, 2004;
Hong \& Bohnet, 2007; Schlösser et al., 2015). Furthermore, the
trustee’s temptation to be selfish has a relatively small effect on
trusting behavior (Evans \& Krueger, 2011; Snijders \& Keren, 1999) and
trustors often decide without searching for information related to the
trustee’s outcomes (Evans \& Krueger, 2014). Therefore, we think it
likely that the risky dictator game would produce results similar to
the individual risk-taking conditions used in Study 2.

The present studies also relied on participants recruited through
Mturk.  Recent work has noted that Mturk participants may have prior
experience with canonical judgment and decision-making tasks (Stewart
et al., 2015), and this experience may influence the strength of
different experimental manipulations (Chandler, Paolacci, Peer,
Mueller \& Ratliff, 2015; Rand et al., 2014). However, we believe
that task experience would --- if anything – reduce the differences we
observed in the present studies. For example, it seems likely that
experienced participants would be less likely to differentiate between
trust and individual risk-taking decisions because they recognize the
same underlying structure of these dilemmas. Still, studies of the
trust game conducted on Mturk may fail to capture some elements of
laboratory (and real-life) trust decisions: When strangers interact on
Mturk, they may not fully experience the social norm that they should
trust in others (Dunning et al., 2014) or suffer the fear of
anticipated betrayal (Koehler \& Gershoff, 2003). We believe it is
valuable for future studies to consider the potential differences
between online and laboratory studies of trust among strangers.

\renewcommand{\baselinestretch}{1.00} \large\normalsize

\subsection{Concluding remarks}
Recent work on the psychology of trust proposed that expectations of
reciprocity have little impact on the final decision (Dunning et al.,
2014; Evans \& Krueger, 2014). We find that this claim holds for trust
decisions based on subjective expectations. The pattern changes,
however, when trustors’ expectations are based on objective,
unambiguous information. The strategic processes underlying trust are
flexible and heterogeneous, and the way that people reason in dilemmas
of trust is shaped by the availability and ambiguity of information.
People focus on what comes to mind easily at the moment of
decision-making and neglect imprecise information. Understanding how
people reason in dilemmas of trust (and how trust differs from
individual risk-taking) requires a better understanding of how people
attend to information.

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%\vfill
%\break
\end{hangparas}

\bigskip\bigskip

%\renewcommand\arraystretch{1.0}

\section*{Appendix Table A1: Trust game values}

%\begin{table}[h!]\centering
%\caption*{Table A1. Trust game values.}
\begin{tabular}{lm{.5in}m{.5in}rrrrrr}\toprule
Trial & Cost-benefit ratio & Temp\-tation & P\textsubscript{1}
 & {\ } P\textsubscript{2} & R\textsubscript{1} & R\textsubscript{2} & S & T {\ } \\\midrule
1 &  Low & Low & 48 & 25 & 81 & 84 & {\ } 36 & 97 \\
2 &  &  & 59 & 29 & 107 & 100 & 46 & 125 \\
3 &  &  & 44 & 23 & 78 & 76 & 32 & 92 \\
4 &  &  & 36 & 18 & 63 & 61 & 28 & 71 \\\cmidrule{3-9}
5 &  & Med & 51 & 25 & 91 & 90 & 41 & 125 \\
6 &  &  & 55 & 27 & 90 & 94 & 41 & 131 \\
7 &  &  & 24 & 12 & 42 & 40 & 19 & 62 \\
8 &  &  & 41 & 21 & 67 & 68 & 31 & 98 \\\cmidrule{3-9}
9 &  & High & 36 & 17 & 64 & 63 & 28 & 147 \\
10 &  &  & 28 & 15 & 48 & 49 & 21 & 110 \\
11 &  &  & 23 & 12 & 43 & 41 & 18 & 94 \\
12 &  &  & 46 & 23 & 88 & 87 & 35 & 200 \\\cmidrule{2-9}
13 & High &  Low & 29 & 14 & 36 & 36 & 7 & 44 \\
14 &  &  & 44 & 22 & 54 & 53 & 10 & 65 \\
15 &  &  & 19 & 10 & 26 & 26 & 5 & 29 \\
16 &  &  & 52 & 25 & 63 & 64 & 13 & 75 \\\cmidrule{3-9}
17 &  & Med & 25 & 12 & 31 & 30 & 6 & 48 \\
18 &  &  & 28 & 13 & 36 & 36 & 7 & 57 \\
19 &  &  & 25 & 12 & 31 & 29 & 6 & 49 \\
20 &  &  & 28 & 15 & 37 & 36 & 7 & 59 \\\cmidrule{3-9}
21 &  & High & 23 & 12 & 29 & 30 & 6 & 87 \\
22 &  &  & 42 & 21 & 50 & 48 & 11 & 134 \\
23 &  &  & 28 & 14 & 34 & 35 & 7 & 99 \\
24 &  &  & 37 & 19 & 45 & 44 & 9 & 102 \\\bottomrule
\end{tabular}
%\end{table}
\end{document}
