# Do Losses Matter? The Effect of Information-Search Technologies on Risky
Choices111This version: September 2023. We would like to thank Marco Tecilla
for superb computer programming. We are grateful to Miguel A. Meléndez-Jiménez
for helpful suggestions. We also thank the seminar audience at the University
of Stirling for their comments. Any error is our own responsibility. Conflicts
of interest: none.

Luigi Mittone222University of Trento (Italy). E-mail<EMAIL_ADDRESS>
Mauro Papi333University of Aberdeen (UK). E-mail<EMAIL_ADDRESS>(corresponding author)

###### Abstract

Despite its importance, relatively little attention has been devoted to
studying the effects of exposing individuals to digital choice interfaces. In
two pre-registered lottery-choice experiments, we administer three
information-search technologies that are based on well-known heuristics: in
the ABS (alternative-based search) treatment, subjects explore outcomes and
corresponding probabilities within lotteries; in the CBS (characteristic-based
search) treatment, subjects explore outcomes and corresponding probabilities
across lotteries; in the Baseline treatment, subjects view outcomes and
corresponding probabilities all at once. We find that (i) when lottery
outcomes comprise gains and losses (experiment 1), exposing subjects to the
CBS technology systematically makes them choose safer lotteries, compared to
the subjects that are exposed to the other technologies, and (ii) when lottery
outcomes comprise gains only (experiment 2), the above results are reversed:
exposing subjects to the CBS technology systematically makes them choose
riskier lotteries. By combining the information-search and choice analysis, we
offer an interpretation of our results that is based on prospect theory,
whereby the information-search technology subjects are exposed to contributes
to determine the level of attention that the lottery attributes receive, which
in turn has an effect on the reference point.

JEL codes: C81, C91, D81.

Keywords: Alternative-Based Search, Characteristic-Based Search, Information
Search, Nudging, Risky Choice.

##  1 Introduction

Choice architecture and nudging have successfully been utilised to improve
people’s decisions in various domains, such as health (Johnson and Goldstein,
2003) and finance (Thaler and Benartzi, 2004).444See Thaler and Sunstein
(2008) for a review. At the same time, growing evidence has documented a
widespread use of ‘sludges’ or ‘dark patterns’, especially in the online
choice environment (Mathur, Acar, Friedman, Lucherini, Mayer, Chetty, and
Narayanan, 2019; Kozyreva, Lewandowsky, and Hertwig, 2020).555Mathur, Acar,
Friedman, Lucherini, Mayer, Chetty, and Narayanan (2019) define dark patterns
as ‘user interface design choices that benefit an online service by coercing,
steering, or deceiving users into making unintended and potentially harmful
decisions’. These refer to the phenomena whereby a choice architect, such as
an online firm, designs the choice environment with the objective of
exploiting the consumers’ cognitive biases at its advantage, by manipulating
the way information is presented, steering, using decoys, suitably selecting
the default option, etc.666We here use the term ‘choice architect’ in broader
sense than Thaler and Sunstein (2008), by considering a choice architect as an
agent who designs a choice environment to generate an economic advantage
(e.g., profit) for themselves, independently of the effects (positive or
negative) that this can have on the decision maker. Policy-makers, such as the
UK Competition and Markets Authority (CMA), have acknowledged the benefits of
online choice architecture, such as that of simplifying the overwhelming
amount of information available, but - at the same time - expressed concerns
about its potentially harmful effects and, in multiple occasions, taken
actions (Competition and Markets Authority, 2020).777For example, see
Competition and Markets Authority (2017).

Despite its importance, relatively little attention has been devoted to the
study of the effects of exposing consumers to different online choice
interfaces. As pointed out by Weinmann, Schneider, and vom Brocke (2016),
research on ‘digital nudging’ is still in its infancy phase and ‘information
systems designers must understand the behavioral effects of interface design
elements so that digital nudging does not happen at random and unintended
effects do not occur’. A particularly important domain of applicability of
digital nudging is that of financial decisions (Benartzi, 2017). In fact, it
is well-known that (i) people typically struggle to understand probabilistic
objects (Benjamin, 2019), and (ii) certain financial decisions, such as those
pertaining to retirement savings and mortgages, are made infrequently, which
limits the possibility of learning from mistakes (Erta, Hunt, Iscenko, and
Brambley, 2013). Furthermore, the rapid expansion of digital technologies has
enhanced the possibilities of creating even more sophisticated online choice
interfaces (Cai, 2020) that - if suitably designed - can possibly further
exploit the behavioural biases observed in the offline environment. Thus, the
purpose of this work is to investigate, in a controlled laboratory setting,
whether administering different information-search technologies has an effect
on people’s decisions in a risky-choice setting.

In two pre-registered experiments, we administer three information-search
technologies that are based on well-known heuristics by suitably modifying the
Mouse-Tracing paradigm (Payne, Bettman, and Johnson, 1993): in the ABS
(alternative-based search) treatment, subjects explore the attributes within
alternatives; in the CBS (characteristic-based search) treatment, subjects
explore the attributes across alternatives; in the Baseline treatment,
subjects view the attributes all at once.888Theoretical examples of ABS and
CBS procedures are expected-utility maximisation and lexicographic procedures,
respectively (Payne, Bettman, and Johnson, 1993). Our design involves binary
lotteries, which - although considerably simpler - can be thought of as an
abstraction of financial products, such as loans, mortgages, and insurance
contracts.999Nieddu and Pandolfi (2020) experimentally investigate the impact
of financial literacy on people’s willingness to invest by modelling financial
assets as binary lotteries. They argue that the financial skills needed in
their setup are key to make knowledgeable decisions in the real world. In
particular, every choice problem in these experiments comprises one risky and
one safe lottery, with the property that every risky lottery is a mean-
preserving spread of every safe lottery (Rothschild and Stiglitz, 1970). The
experiments are between-subject and treatments are identical, except for the
technology subjects are administered to explore the lottery
attributes.101010In these experiments, the lottery attributes (or lottery
characteristics) are given by the ‘high prize’, the ‘probability that the high
prize occurs’, and the ‘low prize’.

Our contribution is three-fold. First, we identify an interplay between the
technology subjects are exposed to and the lottery-outcome domain. In
particular, we provide evidence that, when lottery outcomes comprise gains and
losses (experiment 1), the subjects that are administered the CBS technology
make relatively safer choices, compared to the subjects that are exposed to
the ABS or are not induced to use any particular procedure (Baseline
treatment). In contrast, when lottery outcomes comprise only gains (experiment
2), we obtain the opposite result: the subjects that are administered the CBS
technology make relatively riskier choices. The lotteries used in experiment 2
are identical to those used in experiment 1, up to a summation to all lottery
outcomes of the same positive constant. We also find that the ABS subjects and
the subjects that are not to induced to use any procedure do not exhibit a
different choice behaviour across lottery-outcome domains.

The key aspect of our results is that we obtain preference reversals by simply
exposing subjects to different information-search technologies, while holding
both the outcomes and the corresponding probabilities of the lotteries
available constant. Our second contribution is thus to propose an alternative
rationalisation of our results that is based on prospect theory (PT). At the
core of the matter is the combined effect on the formation of the reference
point of, not only the lottery-outcome domain, but also the procedure subjects
are induced to use. In particular, we argue that the information-search
technology subjects are exposed to contributes to determine the level of
attention that the lottery attributes receive, which in turn has an effect on
the PT preference parameters.111111Results were largely unexpected, and turned
out to be more interesting than initially conjectured. As such, the proposed
explanation has been derived ex post.

In PT the reference point is typically given by a function of the lottery
attributes (Baillon, Bleichrodt, and Spinu, 2020). Thus, by transitioning from
the gain-loss lottery-outcome domain (experiment 1) to the gain lottery-
outcome domain (experiment 2), the reference point is likely to increase.
Since the subjects who are induced to use a CBS procedure view one outcome at
a time, then the ‘high prize’ becomes relatively more salient and - as a
result - gains more weight in the formation of the reference point. This leads
to a further rightward shift of the reference point in the gain domain. As
such, the CBS subjects are more likely to perceive a given lottery outcome as
a loss compared to the subjects assigned to the other treatments. Given that
in the loss domain PT decision-makers are risk lovers (Kahneman and Tversky,
1979), CBS subjects tend to make riskier choices in the gain domain.

On the other hand, the ‘holistic view’ that is enforced in the ABS and
Baseline treatments - whereby subjects simultaneously view both outcomes and
corresponding probabilities of each lottery - acts as a moderator in the
formation of the reference point, which results in the other lottery
attributes (other than the ‘high prize’) gaining relatively more importance.
This implies that, when the lottery-outcome domain comprises gains and losses
(experiment 1), the reference point tends to be relatively higher, and when
the lottery-outcome domain comprises only gains (experiment 2), the reference
point tends to be relatively smaller, compared to that of the CBS treatment.
Thus, the subjects assigned to the ABS and Baseline treatments choose in a
relatively riskier (resp., safer) way in experiment 1 (resp., experiment 2).

In an earlier study (Mittone and Papi, 2020) we find that, when lottery
outcomes comprise only gains, inducing subjects to use a CBS heuristic makes
them choose riskier options. The results of experiment 2 have been obtained by
considering different lotteries than those used in Mittone and Papi (2020) and
recruiting from a different subject population. As such, our third
contribution is that experiment 2 constitutes a replication of our earlier
results by providing an additional robustness check of the identified
phenomenon.

We conclude this section by discussing two wider implications of our results.
First, in standard and behavioural models of risky choice, such as prospect
theory (Kahneman and Tversky, 1979) and salience theory (Bordalo, Gennaioli,
and Shleifer, 2012), the way the decision-maker allocates attention is
determined by the lottery attributes.121212For example, in prospect theory,
rare events are over-weighted (Kahneman and Tversky, 1979). On the other hand,
in salience theory, a state of the world $\tilde{s}$ is more salient than some
other state $s$ whenever $\tilde{s}$ stands out, i.e., the payoff range of
state $s$ is contained in the payoff range of state $\tilde{s}$ (Bordalo,
Gennaioli, and Shleifer, 2012). In contrast, our evidence is in line with the
principle whereby the attention that the decision-maker pays to the lottery
attributes - which in these experiments is induced by the exposure to a
certain procedure - is a primitive element of the decision process, and, as
such, is an input (and not an output) of the decision process (Orquin and
Mueller Loose, 2013). By letting the reference point depend on, not only the
lottery-outcome domain, but also the procedure subjects are induced to use,
the proposed explanation of the results is consistent with this idea (Pachur,
Schulte-Mecklenbeck, Murphy, and Hertwig, 2018; Hirmas and Engelmann, 2023).

Second, this paper demonstrates that, in a controlled laboratory setting, the
combined effect of the lottery-outcome domain and the administered
information-search technologies can affect people’s risky choices in specific
ways. Therefore, our results are of significant importance for the design and
the framing of real-world digital choice platforms (Erta, Hunt, Iscenko, and
Brambley, 2013; Cai, 2020; Competition and Markets Authority, 2020). For
example, suppose that an online financial firm prefers customers to purchase
‘risky mortgages’ because they are more profitable. According to our results,
one way of achieving the desired objective would be for the firm under
consideration to frame the mortgage characteristics in terms of gains and
implement a choice interface that mimics the CBS technology.131313One could
argue that in the real world no ‘lottery’ guarantees only gains. However, we
observe that presenting a financial product in a certain way can produce an
illusion whereby the decision-maker thinks that they are in the presence of
investment alternatives with ‘almost certain’ returns. On the other hand, a
regulator would be able to limit the choice of risky mortgages by requiring -
in this case - the relevant online choice architects to implement ABS
technologies. Evidently, these speculations rest on the assumption that our
results are externally valid. Therefore, a critical follow-up question is to
investigate the robustness of the derived results outside the laboratory by
testing our hypotheses in the field.

The rest of the paper is organised as follows. Section 2 reviews the related
literature; Sections 3 and 4 present experiments 1 and 2, respectively;
Section 5 offers an interpretation of the results; Section 6 concludes. The
supplementary material (available upon request) contains the instructions,
further details pertaining to the experimental design, further robustness
checks, and three short videos aimed at illustrating the information-search
technologies.

##  2 Related Literature

This paper relates to multiple strands of literature. First, experimental
economists have investigated how people make decisions in choice problems
involving multi-attribute alternatives. For instance, Gabaix, Laibson,
Moloche, and Weinberg (2006) use the Mouse-Tracing paradigm to experimentally
investigate how experimental subjects acquire information. Sanjurjo (2017)
utilises Gabaix, Laibson, Moloche, and Weinberg (2006)’s data to examine
whether subjects search optimally, and find that subjects search too much
within an alternative and fail to optimally switch to the next alternative to
be investigated. On the other hand, Arieli, Ben-Ami, and Rubinstein (2011)
employ eye-tracking to analyse whether the subjects’ eye movement is
consistent with either an ABS or a CBS model when they choose between binary
lotteries. They find that when the calculation of the expected value is
relatively difficult (resp., simple) subjects’ eye movement is consistent with
a CBS (resp., a mixture of ABS and CBS) procedure. Unlike these studies, this
paper adopts a different approach by exploring the effects of inducing
individuals to use certain procedures.

As far as the latter approach is concerned, there are two related studies
(Reeck, Wall, and Johnson, 2017; Mittone and Papi, 2020). On the one hand,
Reeck, Wall, and Johnson (2017) conduct an an experiment in which subjects are
induced to use integrative vs comparative search strategies when making
intertemporal choices. They find that encouraging subjects to search in
different ways affects their choices over time. Unlike their work, this study
examines risky choices. On the other hand, Mittone and Papi (2020) find that
inducing subjects to use CBS procedures (as opposed to ABS procedures) in
lottery choice problems makes them to choose riskier lotteries. Their main
focus is to study how the exposure to different heuristics relates with the
complexity of the choice problem (measured in terms of attribute-based and
alternative-based complexity) and, importantly, their design involves
lotteries whose outcomes are gains only. In contrast, this study considers
mixed lotteries and explores the interplay between the heuristic subjects are
induced to use and the lottery-outcome domain, while holding complexity
constant.

Third, a number of studies have investigated specific aspects that are
relevant to digital nudging.141414See also Waldman (2020), who discusses how
cognitive biases are exploited by online platforms to induce individuals to
disclose information. For instance, Samek, Hur, Kim, and Yi (2016) examines
the effects of different sorting technologies on subjects’ choices by using
the ‘choice-process’ method, whereby not only final but also provisional
choices are recorded. There are three main differences with this study. First,
Samek, Hur, Kim, and Yi (2016)’s objects of choice are not lotteries, but
vectors of numbers. Second, the interactive technologies used in Samek, Hur,
Kim, and Yi (2016) are different from those used in this paper. Third, unlike
Samek, Hur, Kim, and Yi (2016), this paper does not utilise the ‘choice-
process’ method, but employs a variant of the Mouse-Tracing paradigm. On the
other hand, motivated by the widespread use of pressure-selling techniques,
Klimm, Kocher, Opitz, and Schudy (2023) explore the effects of perceived
urgency and regret in a sequential search task. In contrast, our study
investigates a different research question. The closest study to our work is
Aimone, Ball, and King-Casas (2016) who - following up on Arieli, Ben-Ami, and
Rubinstein (2011)’s findings - examine the effects of manipulating how
information is acquired in a lottery-choice experiment. This study differs
from ours in several respects: (i) the information-acquisition technologies
are different from ours151515For instance, unlike the CBS technology utilised
in this paper, the ‘CCorder’ technology employed in Aimone, Ball, and King-
Casas (2016) enables a subject to view either the outcome or the corresponding
probability at any point in time.; (ii) unlike Aimone, Ball, and King-Casas
(2016), this study considers lotteries that have the same expected value and
belong to the gain-loss lottery-outcome domain; and (iii) unlike in this
study, in Aimone, Ball, and King-Casas (2016) all subjects are shown - just
before making a decision - all lottery attributes at once, regardless of the
information-acquisition technology they are initially assigned to.
Interestingly, although for the reasons outlined above their study is not
comparable to ours, Aimone, Ball, and King-Casas (2016) also find that
exposing subjects to different information-acquisition formats has an effect
on the outcome of their decisions.

Fourth, in the judgment and decision-making literature, an open question
pertains to whether individuals are more likely to use holistic procedures in
risky choices (Glöckner and Herbold, 2011), or whether - instead - they tend
to consider attributes separately (Brandstätter, Gigerenzer, and Hertwig,
2006). Although not conclusive, the results of this study seem to provide
support in favour of the former view.

##  3 Experiment 1

As discussed above, in an earlier study (Mittone and Papi, 2020), we find
that, when lottery outcomes comprise only gains, inducing subjects to use CBS
procedures (as opposed to ABS procedures) makes them to choose riskier
lotteries. Motivated by these findings, our first pre-registered hypothesis is
that these results extend to mixed lotteries, i.e., lotteries whose outcomes
are gains and losses. The purpose of experiment 1 is to test this
hypothesis.161616The pre-registration contains an additional hypothesis
(hypothesis 2) pertaining to the interplay between the heuristic subjects are
induced to use and the classical preference-reversal phenomenon (Lichtenstein
and Slovic, 1971). Such additional hypothesis and the resulting analysis will
not be discussed here, but in a separate follow-up paper.

###  3.1 Experimental Design

Subjects. A total of 181 subjects were recruited from the Cognitive and
Experimental Economics Laboratory (CEEL)’s subject pool of the University of
Trento.171717Most subjects were undergraduate students in economics. Further
details about the subjects’ characteristics can be found in the supplement. A
total of 64 subjects were assigned to the ABS treatment, 60 subjects to the
CBS treatment, and 57 subjects to the Baseline treatment. Experiment 1 was
between-subject, and took place online.181818The relevant dates are 19th
(CBS), 20th (ABS), and 21st (Baseline) of October 2021, 23rd (CBS), 24th
(ABS), and 25th (Baseline) of November 2021, and 12th (ABS and CBS) and 13th
(Baseline) of April 2022. The software used in this experiment was designed by
the authors of the paper and the CEEL manager Mr Marco Tecilla.

Lottery-Choice Task. The experiment comprises: a lottery-choice task and a
number of control tasks. While - as discussed below - some features of the
lottery-choice task are treatment-specific, the control tasks are identical
across treatments.

The lottery-choice task consists of a sequence of binary lottery choice
problems. In all treatments of this experiment, a choice problem consists of
two lotteries: a safe lottery $s$ and a risky lottery $r$. Every choice
problem is presented in one screenshot, and subjects are asked to make a
decision by choosing the lottery that they prefer the most within the time
limit, which is 40 seconds. Table 1 lists the safe and the risky lotteries
that have been constructed for this experiment, which are common across
treatments and whose outcomes are expressed in experimental points (1 point =
0.35 euros).191919Observe that the safe lotteries can be interpreted as a
$P$-bets and the risky lotteries as $\$$-bets (Lichtenstein and Slovic, 1971).
The lotteries have the properties that (i) they all have an expected value of
6 experimental points and (ii) every risky lottery is a mean-preserving spread
of every safe lottery.202020A key property of lotteries that can be ordered by
the mean-preserving spread relation is as follows: a lottery $L^{\prime}$ is a
mean-preserving spread of a lottery $L$ if and only if a risk-averse decision-
maker prefers $L$ over $L^{\prime}$, irrespective of their degree of risk
aversion (Rothschild and Stiglitz, 1970).

$\\#$ | Prob. | Gain | Prob. | Loss
---|---|---|---|---
| Safe Lotteries
$s_{1}$ | 0.80 | 7.60 | 0.20 | -0.40
$s_{2}$ | 0.70 | 8.70 | 0.30 | -0.30
$s_{3}$ | 0.60 | 10.40 | 0.40 | -0.60
| Risky Lotteries
$r_{1}$ | 0.40 | 17.22 | 0.60 | -1.48
$r_{2}$ | 0.30 | 23.15 | 0.70 | -1.35
$r_{3}$ | 0.20 | 35.00 | 0.80 | -1.25

  * •

Gains/losses are expressed in exp.currency (1 point = 0.35 euros).

Table 1: Lotteries used in experiment 1

We constructed a total of 9 binary lottery choice problems by matching each of
the three safe lotteries with each of the three risky lotteries. Throughout, a
choice problem will be denoted as an ordered pair $\left(s_{k},r_{l}\right)$,
where $k,l\in\\{1,2,3\\}$, and $s_{k}$ and $r_{l}$ denote a safe and risky
lottery, respectively, of table 1. In every treatment, the order according to
which the choice problems is presented to subjects is random. Within each
screenshot, the safe and risky lotteries are arranged side by side and their
position (left or right) is randomised as well. In all treatments of this
experiment, the outcome-probability pairs of each lottery are arranged on top
of each other, with the property that - from the top to the bottom - the gain-
probability pair is listed first and the loss-probability pair is listed
second. At the end of the experiment, a lottery choice problem is selected at
random, the lottery that the experimental subject chose at that particular
choice problem is played, and the subject is paid accordingly. If subjects do
not choose any lottery within the time limit at a particular choice problem,
then a total of $1.5$ experimental points are deducted from the subject’s
earnings in the event that at the end of the experiment the choice problem
under consideration is extracted for payment.

In order to induce subjects to use different procedures, we designed three
treatments: ABS, CBS, and Baseline. These treatments are identical (and as
described above), except for the technology that subjects use for exploring
the lotteries available at each choice problem.

ABS Technology. At every choice problem subjects are faced with in the
lottery-choice task, information is initially hidden. In particular, subjects
are faced with two buttons at the top of the screen corresponding to the two
lotteries available at that particular choice problem. To discover the
outcomes and the corresponding probabilities of a lottery, subjects click on
the button corresponding to the lottery that they want to explore, and, at the
bottom of the screen, the experimental software shows the outcomes and the
corresponding probabilities of the selected lottery. Next to the discovered
lottery, a ‘pie chart’ whose slices graphically represent the probabilities of
the different outcomes is also displayed. By clicking on the other button, the
experimental software automatically hides the outcomes and corresponding
probabilities of the lottery they initially clicked on, and shows the outcomes
and corresponding probabilities of the lottery they have subsequently clicked
on. Subjects are free to explore the lotteries as they like, even by
discovering the same lottery more than once. The supplement contains a video
(‘ABS$\\_$Treatment.mp4’) demonstrating how subjects can explore information
when they are administered the ABS technology. The ABS treatment is meant to
induce an ABS procedure, as it encourages subjects to explore all the
characteristics of one lottery, before exploring the next lottery.

CBS Technology. Like in the ABS treatment, at every choice problem subjects
are faced with in the lottery-choice task, information is initially hidden.
Unlike in the ABS treatment, subjects explore information by discovering one
outcome-probability pair at a time. In particular, by clicking on a gain-
probability (resp., loss-probability) pair, the software automatically shows
the gain-probability (resp., loss-probability) pairs of both lotteries
available at a particular choice problem. Next to each lottery, a ‘pie chart’
whose slices graphically represent the probability of the corresponding gain
(resp., loss) is also displayed. By clicking on the other outcome-probability
pair, the software automatically hides the outcome-probability pairs
previously displayed and shows the outcome-probability pairs they have
subsequently clicked on. Subjects are free to explore the outcome-probability
pairs as they like, even by discovering the same outcome-probability pair more
than once. The supplement contains a video (‘CBS$\\_$Treatment.mp4’)
demonstrating how subjects can explore information when they are administered
the CBS technology. The CBS treatment is meant to induce a CBS procedure, as
it encourages subjects to look up the value that an outcome-probability pair
takes across both lotteries available, before exploring the next outcome-
probability pair.

Baseline Technology. Unlike in the ABS and CBS treatments, in the Baseline
treatment the outcome-probability pairs of both lotteries available at a
choice problem are immediately visible. As such, the Baseline treatment is not
meant to induce any specific procedure, and will be used as a standard of
comparison. The supplement contains a video (‘Baseline$\\_$Treatment.mp4’)
demonstrating how subjects can explore information when they are administered
the Baseline technology.

We do not claim that assigning a subject to the ABS (resp., CBS) treatment
forces them to use an ABS (resp., a CBS) procedure. Rather, we believe that
the ABS technology makes the use of an ABS procedure more natural than the CBS
technology. Likewise, the CBS technology makes the use of a CBS procedure more
natural than the ABS technology.

Controls and Implementation . In order to minimise the disruptions directly or
indirectly caused by Covid (e.g. sudden imposition of restrictions that
prevent the use of the laboratory), the experiment was conducted online by
following a modification of Zhao, López Vargas, Friedman, and Gutierrez
(2020)’s protocol. In particular, the day before the experiment, the subjects
were sent an email containing a link to a Zoom meeting and a link to the
actual experiment that was operational only at the time in which the sessions
were scheduled. On the day of the experiment, at the scheduled time subjects
were asked to connect to the Zoom meeting with an experimentalist. They were
instructed to keep their cameras on for the entire duration of the experiment.
In this way the experimentalist was able to communicate with the subjects, and
monitor their activities (e.g. check that no individual other than the
experimental subject took part to the experiment). Subjects read the
instructions, and then an experimentalist read them loudly. Before undertaking
any task and after reading the instructions, subjects had to answer a number
of control questions aimed at verifying whether they have understood the
instructions.212121The instructions as well as the control questions can be
found in the supplement in both Italian (original language) and English. They
were allowed to proceed only if they answered all the questions correctly.

Subjects began by undertaking the lottery-choice task described above. After
completing the lottery-choice task, they were asked to undertake an extended
cognitive reflection test (CRT7) developed by Toplak, West, and Stanovich
(2014).222222As indicated in the first pre-registration, after the lottery-
choice task and before undertaking the CRT7, subjects were also asked to
express their willingness to pay for the lotteries encountered in the lottery-
choice task by using the Becker, Degroot, and Marschak (1964)’s method (BDM).
This task was included in the experimental design to test an additional
hypothesis included in the pre-registration that relates the heuristic
subjects are induced to use with the classical preference-reversal phenomenon
(Lichtenstein and Slovic, 1971). Like for the other tasks, feedback was given
at the end of the experiment. However, as discussed above, the combined
analysis of the lottery-choice task and BDM will not be discussed here, but in
a separate follow-up paper. In any case, for completeness, in the supplement
we include a detailed description of the BDM and corresponding instructions.
Subjects were rewarded a total of 0.07 points for every correct answer they
provided to the CRT7 questions. Then, subjects went through the Bomb Risk
Elicitation Task (BRET) developed by Crosetto and Filippin (2013).232323For a
detailed description of the BRET, see the supplement. After completing the
BRET, subjects were administered an anonymous questionnaire aimed at recording
their demographics. To have an indication of subjects’ level of attention in
the experiment, we included in the questionnaire a 7-point scale introspective
attention question, where 1 (resp., 7) corresponded to minimal (resp.,
maximal) attention. Furthermore, we added an additional multiple-choice
introspective salience question aimed at asking subjects whether the aspect
that mattered the most to them in making lottery decisions was: (1) the
outcomes, (2) the probabilities, (3) both the outcomes and the probabilities,
or (4) neither the outcomes nor the probabilities of the lotteries. We then
asked subjects to guess what was the most popular answer to the introspective
salience question by the other experimental subjects in the same session by
rewarding a correct guess with a total of 3 experimental points.242424Due to
an unintended mistake in the experimental software, the introspective salience
question and the corresponding guessing question were recorded in the second
and third sessions of experiment 1 (those taking place in November 2021 and
April 2022), but not in the first session (that taking place in October 2021).
As a result, the number of observations for these two questions in experiment
1 are: 37, 41, and 36 in the ABS, CBS, and Baseline, respectively.

Subjects were given feedback at the end of the experiment and were informed
about their total monetary payoff, inclusive of the show-up fee (10
experimental points), and were paid accordingly via a bank transfer. Subjects
earned on average 9.07, 9.14, and 8.63 euros in the ABS, CBS, and Baseline
treatment, respectively.

Figure 1: Average Riskiness $R^{t}$ with standard error bars; Exp.1

###  3.2 Results

Choice Analysis. Throughout, let $\mathcal{N}_{t}$ denote the set of
experimental subjects assigned to treatment $t$, where
$t\in\\{ABS,CBS,Base\\}$. Recall that a choice problem is denoted by an
ordered pair $(s_{k},r_{l})$, where $k,l\in\\{1,2,3\\}$, and $s_{k}$ and
$r_{l}$ denote a safe and risky lottery, respectively, of table 1. We being by
investigating the extent to which subjects made risky choices in the lottery-
choice task. To do so, for every subject $i$ facing a choice problem
$(s_{k},r_{l})$ in treatment $t$, we construct a riskiness index
$R_{i}^{t}(s_{k},r_{l})$ as follows.

$R_{i}^{t}(s_{k},r_{l}):=\left\\{\begin{array}[]{ll}0&\mbox{, if subject $i$
chose $s_{k}$ at problem $(s_{k},r_{l})$}\\\ 1&\mbox{,
otherwise.}\end{array}\right.$ (1)

That is, the riskiness index $R_{i}^{t}(s_{k},r_{l})$ is equal to $0$ (resp.,
$1$) if subject $i$ in treatment $t$ chose the safe (resp., risky) lottery.
Recall that in our design every risky lottery is a mean-preserving spread of
every safe lottery. As such, the riskiness index satisfies the property that
it is increasing in the riskiness of the chosen lottery.

In addition, define
$R_{i}^{t}:=\frac{1}{9}\sum_{k}\sum_{l}R_{i}^{t}(s_{k},r_{l})$ as subject
$i$’s average riskiness index across choice problems in treatment $t$, and
$R^{t}:=\frac{1}{|\mathcal{N}_{t}|}\sum_{i\in\mathcal{N}_{t}}R_{i}^{t}$ as the
average riskiness index in treatment $t$. Figure 1 displays the average
riskiness index $R^{t}$ in each treatment $t$ with standard error bars.

Figure 2: Average Number of Clicks in the ABS Treatment; Exp.1

By looking at figure 1, three observations can be drawn. First, the average
riskiness index $R^{t}$ is in absolute value significantly smaller than $0.50$
in all treatments. Given that in this experiment every risky lottery is a
mean-preserving spread of every safe lottery, subjects’ choices reveal that
their propensity towards risk tends to be on average of aversion to risk.
Second, the subjects assigned to the ABS and Baseline treatment chose in a
similar way in terms of riskiness. Third - and most importantly - the subjects
assigned to the CBS treatment systematically chose in a safer way compared to
the subjects assigned to the ABS and Baseline treatment. We run a Mann-Whitney
test for independent samples and find that the difference in average riskiness
between ABS-CBS and Baseline-CBS is statistically significant at conventional
levels (standard test statistics are $2.383^{**}$ and $2.601^{***}$,
respectively). Robustness checks consisting of a bootstrap analysis for
independent samples t-test confirm these results (estimated p-values are
$0.015^{**}$ and $0.009^{***}$, respectively).252525In conducting each
bootstrap procedure for this experiment, a total of 9,999 bootstrap samples
were generated (Moffatt, 2016).

Figure 3: Average Number of Clicks in the CBS Treatment; Exp.1

Information-Search Analysis. We begin the information search analysis by
investigating the average number of times subjects looked up the safe and
risky lottery in the ABS treatment. As illustrated in figure 2, subjects
clicked on average 1.70 times on the safe and 1.51 times on the risky lottery.
Although the averages are not too far apart, a Wilcoxon signed-rank test for
dependent samples confirms that the number of clicks on the safe and risky
lottery are significantly different at conventional levels (test stat.=
$4.635^{***}$).

Panel Probit Regression on the riskiness index in the ABS treatment (Exp.1)
---
Riskiness index | Model 1 | Model 2 | Model 3 | Model 4
$\\#$safe lott.clicks |  -2.596471∗∗∗ |  -2.604038∗∗∗ |  -3.154586∗∗∗ |  -3.109959∗∗∗
| (.313102) | (.3360061) | (.4571613) | (.4478019)
$\\#$risky lott.clicks |  2.806335∗∗∗ |  2.695346∗∗∗ |  3.011842∗∗∗ |  2.957496∗∗∗
| (.3149929) | (.3305261) | (.4295831) | (.4202122)
Clicked on both lott. | -.0745059 | .4866022 | .70863 | .8485965
| (1.900412) | (3.937476) | (5.477841) | (6.076832)
Time on safe lott.($s$) |  | -.0201542 | .0182827 | .0146173
|  | (.0243167) | (.0280446) | (.028186)
Time on risky lott.($s$) |  |  .0522189∗ |  .0944618∗∗∗ |  .0910314∗∗∗
|  | (.0270158) | (.0320183) | (.0317932)
Controls | No | No | Yes | Yes
Demographics | No | No | No | Yes
Constant | -.7806593 | -1.384203 | -4.684561 | -1.892109
| (1.89635) | (3.937924 ) | (5.558398) | (6.254942)
Log likelihood | -180.81086 | -178.75117 | -159.47795 | -156.69288
Akaike inf.crit. | 371.6217 | 371.5023 | 370.9559 | 369.3858
Observations | 576 | 576 | 576 | 576

  * •

Standard errors in parentheses, ∗ $p<0.10$, ∗∗ $p<0.05$, and ∗∗∗ $p<0.01$.
Controls: period at which choice was made, choice problem, number of collected
boxes (BRET), 7-item CRT score, and player declared attention (7-point scale,
where 7 means ‘maximum attention’). Demographics: age and gender. Lottery
outcomes are gains and losses.

Table 2: Choice and Information-Search in the ABS Treatment($n=64$); Exp.1

We next examine the average number of times subjects explored the gain-
probability pair and the loss-probability pair in the CBS treatment. As shown
in figure 3, subjects clicked on the gain-probability pair an average of 1.77
times and on the loss-probability pair an average of 1.10 times. These results
provide clear evidence that subject systematically explored more often the
gain-probability pair than the loss-probability pair (Wilcoxon signed-rank
test stat.= $6.445^{***}$).

Information-Search and Choice Analysis. We next combine the information-search
and choice analysis, in order to shed light on how subjects’ clicking
behaviour is related with their choices in the ABS and CBS treatments. We do
so by running a set of random-effects panel probit regressions. In particular,
as far as the ABS treatment is concerned, the riskiness index
$R_{i}^{ABS}(s_{k},r_{l})$ (equation 1) has been regressed on the number of
times subjects have looked up the safe and risky lottery, a dummy variable
capturing whether or not they have explored both lotteries, the amount of time
(in seconds) they have spent on looking up the safe and risky lottery, and
additional control variables. Results are displayed in table 2. As one
expects, the number of times subjects have clicked on the safe (resp., risky)
lottery is negatively (resp., positively) related to the probability that the
risky lottery is chosen. The corresponding average marginal effects are
-.4279682 ($z=-9.16^{***}$) and .4069875 ($z=9.29^{***}$), respectively. The
only other regressor that has a statistically significant coefficient is the
time spent on the risky lottery, although the corresponding marginal effect is
relatively small ($<0.02$).

Panel Probit Regression on the riskiness index in the CBS treatment (Exp.1)
---
Riskiness index | Model 1 | Model 2 | Model 3 | Model 4
$\\#$ gain clicks | .0087717 | -.0387183 | -.0312628 | -.0306694
| (.0960892) | (.122487) | (.1343821) | (.1341742)
$\\#$ loss clicks | -.0263597 | -.0893256 | -.1675496 | -.1637419
| (.1074184) | (.1430135) | (.1592626) | (.1596865)
Clicked on both |  .4041006∗ |  .3758542∗ | .3889483 |  .3985032∗
| (.210637) | (.2142926) | (.2377372) | (.2395036)
Time on gains($s$) |  |  .0276693∗ |  .0647531∗∗∗ |  .064431∗∗∗
|  | (.0158024) | (.0189068) | (.0189098)
Time on losses($s$) |  | .0260843 |  .0486575∗∗ |  .0480832∗∗
|  | (.0189092) | (.0215103) | (.0215431)
Controls | No | No | Yes | Yes
Demographics | No | No | No | Yes
Constant |  -1.089952∗∗∗ |  -1.238329∗∗∗ |  -2.653098∗∗∗ | -2.299955
| (.1521088) | (.1681951) | (.7629245) | (1.465449)
Log likelihood | -270.88113 | -268.06494 | -242.04729 | -241.95995
Akaike inf.crit. | 551.7623 | 550.1299 | 536.0946 | 539.9199
Observations | 540 | 540 | 540 | 540

  * •

Standard errors in parentheses, ∗ $p<0.10$, ∗∗ $p<0.05$, and ∗∗∗ $p<0.01$.
Controls: period at which choice was made, choice problem, number of collected
boxes (BRET), 7-item CRT score, and player declared attention (7-point scale,
where 7 means ‘maximum attention’). Demographics: age and gender. Lottery
outcomes are gains and losses.

Table 3: Choice and Information-Search in the CBS Treatment ($n=60$); Exp.1

A similar random-effects panel probit regression has been performed for the
CBS treatment. In particular, the riskiness index $R_{i}^{CBS}(s_{k},r_{l})$
has been regressed on the number of times subjects have looked up the gain and
the loss (and corresponding probabilities), a dummy variable capturing whether
or not they have explored both outcomes and corresponding probabilities, the
amount of time (in seconds) they have spent on the gain and the loss (and
corresponding probabilities), and additional control variables. Results are
displayed in table 3.

Unlike one would expect, the number of times subjects clicked on the gains or
losses (and corresponding probabilities) does not seem to be related to the
probability of choosing the risky lottery. To the contrary, the extent to
which subjects explore both the gain and the loss (and corresponding
probabilities) appears to be a significant factor, in the sense that when
subjects happen to explore both outcomes (and corresponding probabilities),
they are more likely to choose the risky lottery in the CBS treatment. An
analysis of the marginal effects reveals that doing so increases on average
the probability of choosing the risky lottery by 8.6 percentage points
($z=1.64^{*}$). Consistently with the latter, the time spent on both gains and
losses (and corresponding probabilities) is also positively related with the
probability of choosing the risky lottery.

Controls. Evidence indicates that female subjects tend to be more risk-averse
than male subjects (Croson and Gneezy, 2009). For this reason, we made sure
that all our treatments are balanced in terms of gender.262626Overall, we
recruited 96 female and 85 male subjects by allocating them as follows: 35 and
29 in the ABS, 33 and 27 in the CBS, and 28 and 29 in the Baseline, female and
male subjects, respectively. Another potential issue is that our results could
be driven by systematic differences in risk attitudes across treatments. In
the supplement, we demonstrate that in our experiment there is no difference
in the distribution of subjects’ risk preferences elicited via BRET across
treatments, and conduct additional robustness checks.

###  3.3 Summary of the Results

The results of experiment 1 indicate that, contrary to our initial hypothesis,
when lottery outcomes comprise gains and losses, inducing subjects to use a
CBS procedure makes them choose safer options. Specifically, the information-
search analysis indicates that in the ABS treatment subjects tend to look up
the safe lottery a little more often than the risky lottery. By combining the
information-search and choice analysis, we find that the probability that the
risky lottery is chosen in the ABS treatment is positively (resp., negatively)
related with the number of times subjects click on the risky (resp., safe)
lottery. On the other hand, in the CBS treatment subjects systematically look
up the gains (and corresponding probabilities) more often than the losses.
Interestingly, although the subjects assigned to the CBS treatment choose on
average in a safer way, we find that whenever they happen to look up both
outcomes, the probability that they choose the risky lottery increases, which
results in their behaviour being more in line with that of the subjects
assigned to the other treatments.

##  4 Experiment 2

After conducting experiment 1 and analysing the resulting data, we concluded
that our first hypothesis is falsified. The first hypothesis states that
inducing subjects to use a CBS procedure makes them choose riskier lotteries.
In contrast, unlike we expected, we found that in experiment 1 inducing
subjects to use a CBS procedure made them choose safer lotteries. These
unexpected results have led us to formulate an alternative explanation: it is
the presence of losses amongst the lottery outcomes that produces a
discrepancy between the first hypothesis and the derived results. This
conjecture is supported by the fact that it is well-known that individuals
treat gains and losses differently in various choice settings ranging from a
choice-from-description (Kahneman and Tversky, 1979) to a choice-from-
experience setup (Wulff, Mergenthaler-Canseco, and Hertwig, 2018).272727See
also Bateman, Dent, Peters, Slovic, and Starmer (2007) for a study that
investigates the effects of introducing small losses.

To test this explanation, we pre-registered a second experiment that is
identical to experiment 1, except that to all outcomes of the lotteries used
in experiment 1, the same positive constant is added, in order to turn the
losses into (small) gains. This transformation produces lotteries that, from
the point of view of a standard expected utility maximiser, are ordered in the
same way as the original ones. We hypothesize that running a second experiment
using the transformed lotteries reverses the results found in experiment 1.
That is, consistently with Mittone and Papi (2020), we expect that inducing
subjects to use CBS procedures makes them choose riskier lotteries.282828Like
the first pre-registration, also the second pre-registration contains a
further hypothesis pertaining to the interplay between the heuristic subjects
are induced to use and the classical preference-reversal phenomenon. As
mentioned above, this additional hypothesis and the resulting analysis will
not be discussed here, but in a separate follow-up paper. The purpose of
experiment 2 is to test this second hypothesis.

###  4.1 Experimental Design

Subjects. A total of 129 subjects were recruited from the CEEL’s subject pool
of the University of Trento.292929Most subjects were undergraduate students in
economics. A total of 42 subjects were assigned to the ABS treatment, 42
subjects to the CBS treatment, and 45 subjects to the Baseline treatment. Like
experiment 1, experiment 2 was between-subject and took place online.303030The
relevant dates are 9th (ABS and CBS) and 10th (Baseline) of November 2022, and
7th (ABS and CBS) and 8th (Baseline) of March 2023.

Figure 4: Average Riskiness $R^{t}$ with standard error bars; experiment 2

Design. The design of experiment 2 is identical to that of experiment 1,
except for the lotteries used. In particular, the lotteries used in experiment
2 have been obtained by adding the same positive constant (i.e., 2.00
experimental points) to all outcomes of the lotteries used in the experiment
1, while holding the probabilities constant.313131The resulting transformed
lotteries can be found in the supplement. Observe that, in order to make sure
that subjects would earn approximately the same amount of money in the two
experiments, the exchange rate of experiment 2 has been decreased to ‘1 exp.
currency = 0.30 euros’. In this way, all outcomes of the resulting lotteries
are gains, and the resulting lotteries continue to have the properties that
(i) every lottery has the same expected value, (ii) every transformed risky
lottery is a mean-preserving spread of every transformed safe lottery.
Furthermore, letting $s_{k}$ and $r_{l}$ denote a safe and a risky lottery
used in experiment 1 and letting $\tilde{s}_{k}$ and $\tilde{r}_{l}$ denote
the corresponding transformed lotteries used in experiment 2, a risk-averse
decision-maker prefers lottery $s_{k}$ over lottery $r_{l}$ in experiment 1 if
and only if a risky-averse decision-maker prefers transformed lottery
$\tilde{s}_{k}$ over transformed lottery $\tilde{r}_{l}$ in experiment 2.

In experiment 2, subjects earned on average 8.87, 8.97, and 9.02 euros in the
ABS, CBS, and Baseline treatment, respectively.

Figure 5: Average Number of Lookups in the ABS Treatment; experiment 2

###  4.2 Results

Choice Analysis. Figure 4 displays the average riskiness index $R^{t}$ along
with standard error bars. On the one hand, we find that - like in experiment 1
- average $R^{t}$ is smaller than 0.5 across treatments, revealing a tendency
of subjects to be averse to risk. On the other hand, we find that that, in
sharp contrast to the results of experiment 1, the subjects assigned to the
CBS treatment choose riskier options compared to the subjects assigned to the
ABS treatment. A Mann-Whitney test for independent samples and a bootstrap
analysis for independent samples t-test confirm that the difference is
statistically significant at conventional levels (the corresponding standard
test statistics is $-1.815^{*}$ and the estimated p-value is $0.059^{*}$,
respectively). As far as the CBS-Baseline comparison is concerned, although
figure 4 indicates that the average riskiness index of the Baseline treatment
is smaller than that of the CBS treatment and greater than that of the ABS
treatment, we do not detect any statistically significant difference.

Figure 6: Average Number of Lookups in the CBS Treatment; experiment 2

A natural follow-up question is to investigate whether there are systematic
differences within treatments by transitioning from the gain-loss lottery-
outcome domain (experiment 1) to the gain lottery-outcome domain (experiment
2). Interestingly, as far as the ABS treatment is concerned, there is no
statistically significant difference in the average riskiness index $R^{t}$
between experiment 1 and experiment 2 (average $R^{t}$ is 0.31 and 0.28,
respectively). The same pattern occurs in the Baseline treatment (the
corresponding average $R^{t}$ is 0.31 and 0.34, respectively). In contrast, in
the CBS treatment, experiment 1’s average $R^{t}$ is markedly smaller than
experiment 2’s average $R^{t}$ (0.22 and 0.37, respectively). A Mann-Whitney
test for independent samples and a bootstrap analysis for independent samples
t-test confirm that this difference is statistically significant at
conventional levels (the corresponding standard test statistics is
$-3.807^{***}$ and the estimated p-value is $0.000^{***}$, respectively).

Information-Search and Choice Analysis. Figure 5 shows the average number of
times subjects clicked on the safe and risky lottery in the ABS treatment
(1.81 and 1.58 times, respectively). Figure 6, on the other hand, displays the
average number of times subjects looked up the high prize and the low prize
and corresponding probabilities in the CBS treatment (1.80 and 1.22 times,
respectively). Results are analogous to those of experiment 1: (i) subjects
tend to click on the safe lottery a little more often than on risky lottery
and (ii) subjects systematically look up more often the high prize than the
low prize (and corresponding probabilities) in the CBS treatment. The
differences in the number of clicks are statistically significant at
conventional levels (the corresponding Wilcoxon signed-rank test statistics
are $4.035^{***}$ and $5.054^{***}$, respectively).

Just like we did for experiment 1, we run a set of random-effects panel probit
regressions - whose details can be found in the supplement - in order to gain
further insights into how subjects’ information-search behaviour is related
with their choices in the ABS and CBS treatments. As far as the ABS treatment
is concerned, we similarly found that the number of times subjects have looked
up the safe (resp., risky) lottery is negatively (resp., positively) related
to the probability that the risky lottery is chosen. The corresponding average
marginal effects are -.3079823 ($z=-11.42^{***}$) and .3684556
($z=17.01^{***}$), respectively. As far as the CBS treatment is concerned,
like in experiment 1, the extent to which subjects explore both outcomes (and
corresponding probabilities) tends to be a significant factor. However, in
sharp contrast to the results of experiment 1, when subjects happen to explore
both outcomes (and corresponding probabilities), they are less likely to
choose the risky lottery. In particular, an analysis of the corresponding
average marginal effect indicates that exploring both outcomes and
corresponding probabilities decrease the chances of choosing the risky lottery
by about $18\%$ ($z=-2.45^{**}$).

Just like we did for experiment 1, we made sure that all treatments of
experiment 2 are balanced in terms of gender, and conducted additional
robustness checks, which can be found in the supplement.

###  4.3 Summary of the Results

In line with our second hypothesis, we find that, when lottery outcomes
comprise only gains, the main result of experiment 1 is reversed, i.e.,
inducing subjects to use a CBS procedure makes them choose riskier options. In
the ABS treatment we find that - like in experiment 1 - (i) subjects tend to
look up the safe lottery a little more often than the risky lottery and (ii)
the probability that the risky lottery is chosen in the ABS treatment is
positively (resp., negatively) related with the number of times subjects click
on the risky (resp., safe) lottery. Likewise, in the CBS treatment, our
results indicate that subjects systematically look up the high prize (and
corresponding probabilities) more often than the low prize. However, although
the subjects assigned to the CBS treatment choose on average in a riskier way,
we find that whenever they happen to look up both outcomes, the probability
that they choose the risky lottery decreases, which results in their behaviour
being more in line with that of the subjects assigned to the other treatments.
Interestingly, while in experiment 1 the probability that the risky lottery is
chosen increases when both outcomes are looked up, in experiment 2 the
probability that the risky lottery is chosen decreases when both outcomes are
looked up.

##  5 Discussion

By jointly considering experiment 1 and experiment 2, we find that subjects’
choice behaviour in the ABS and Baseline treatment is not influenced by the
lottery-outcome domain. In fact - as demonstrated above - by transitioning
from the gain-loss lottery-outcome domain (experiment 1) to the gain lottery-
outcome domain (experiment 2), we do not detect any statistically significant
difference in average risky choice within these two treatments. In contrast,
we find that in the CBS treatment the lottery-outcome domain does have an
impact on subjects’ choices. In particular, on the one hand, when the lottery-
outcome domain comprises gains and losses (experiment 1), inducing subjects to
use a CBS procedure makes them choose safer lotteries. On the other hand, when
the lottery-outcome domain comprises gains only (experiment 2), inducing
subjects to use a CBS procedure makes them choose riskier lotteries. Why do
subjects exhibit this switch in behaviour when they are induced to use a CBS
procedure? And why do they not exhibit any switch in the other two conditions?

These findings were unexpected and turned out to be more interesting than we
initially conjectured. We indeed obtain preference reversals by simply
exposing subjects to certain information-search technologies, while holding
both the outcomes and the probabilities of the lotteries available constant.
In this section we propose an ex-post rationalisation of our results that is
based on prospect theory. Specifically, we argue that, at the core of the
matter, is the combined effect on the formation of the reference point of, on
the one hand, the heuristic subjects are induced to use and, on the other
hand, the lottery-outcome domain.

In prospect theory decision-makers evaluate the lottery outcomes with respect
to a reference point, which defines the domains of gain and losses, with the
property that in the gain (resp., loss) domain subjects are risk-averse
(resp., risk-lover) (Kahneman and Tversky, 1979). A key aspect of the ‘coding
phase’ is therefore that of the formation of the reference point. Although in
the early formulations of prospect theory the reference point is exogenously
determined, in many cases there is a natural candidate for the reference
point, such as the status-quo option and an individual’s current asset
position. In other scenarios, the reference point may be given by a decision
maker’s expectation or aspiration (O’Donoghue and Sprenger, 2018).323232See
Kőszegi and Rabin (2006) as a prominent study aimed at endogenising the
reference point by assuming it to coincide with the decision-maker’s
expectations. As such, it is worth bearing in mind that the reference-point
position is subjective and cannot be mechanically traced back to an intrinsic
objective nature.

Turning to our experiments, it is reasonable to assume that, when lottery
outcomes involve gains and losses (experiment 1), subjects consider any
positive amount as a gain and any negative amount as a loss, by implicitly
setting the reference point at zero. On the other hand, when lottery outcomes
involve gains only (experiment 2), it is plausible to expect that the
reference point is given by some function of the lottery attributes, that has
the property that it is nondecreasing in the lottery outcomes. In the latter
case, examples of the candidate reference point include the average lottery
outcome, the maxmin payoff, and the expected value.333333Baillon, Bleichrodt,
and Spinu (2020), for instance, investigate which reference point, such as
expected value, maxmin payoff, and most likely outcome, subjects use in a
lottery-choice experiment in which the lottery-outcome domain involves gains
only. Amongst others, see also Hack and von Bieberstein (2015) who provide an
in-depth look at reference point formation mainly by investigating the
expectations’ role. Specifically, they suggest an ‘integrated mechanism’
whereby people’s expectations are based on the average outcomes rather than
any single potential outcome. Therefore, by transition from a lottery-outcome
domain consisting of gains and losses (experiment 1) to a lottery-outcome
domain involving only gains (experiment 2), the reference point is likely to
shift to the right by taking on a value that is strictly greater than zero.

The key question then becomes: why should a rightward shift of the reference
point cause the subjects that are exposed to the CBS heuristic to exhibit a
preference reversal? And why does this phenomenon not occur to the subjects
that are assigned to the other conditions? Although only speculative, one
possible explanation of this preference reversal is that the CBS treatment -
which forces subjects to view an outcome at a time - makes the ‘high-prize’
attribute relatively more salient. As evidenced by the information-search
analysis, we indeed observe that subjects systematically click more often on
the high prize (and corresponding probability) than on the low prize.343434An
analysis of subjects’ modal response to the introspective salience question
indicates that - in both experiment 1 and experiment 2 - the aspect that
mattered the most to them in making lottery choices was ‘both the outcomes and
the probabilities’ for the subjects assigned to the ABS and Baseline treatment
and ‘the probabilities’ for the subjects assigned to the CBS treatment
(details can be found in the supplement). Retrospective protocols do not
appear to be a valid instrument for inferring the underlying cognitive
processes (Russo, Johnson, and Stephens, 1989). As such, subjects’ responses
to the introspective salience question should be used with caution, and are
not incompatible with the proposed interpretation of the results. Assuming, as
we have just done, that the reference point is taken to be a non-decreasing
function of the lottery outcomes, it follows that focusing on the high-prize
attribute (by paying relatively little attention to the associated probability
of occurrence and the other lottery attributes) translates into a further
right-ward shift of the reference point.353535According to the interpretation
proposed in Mittone and Papi (2020), it is also assumed that - to the subjects
that are exposed to the CBS heuristic - the high prize becomes relatively more
salient. This is equivalent to saying that the domain of losses prevails over
the gain domain, which ultimately results in subjects exhibiting relatively
more risky choice behaviour in experiment 2.

On the other hand, the subjects exposed to the ABS heuristics and the subjects
who left free to compare all lotteries simultaneously (Baseline treatment) do
not exhibit such a change in behaviour. The reason is that the subjects in the
ABS and Baseline treatments simultaneously view both outcomes and
corresponding probabilities of each lottery. As such, on the one hand, the
phenomenon at work in the CBS treatment whereby the high-prize attribute
receives relatively more attention is less likely to occur, and, on the other
hand, the ‘holistic view’ that is enforced in the ABS and Baseline treatments
acts as a moderator in the formation of the reference point, in the sense that
the other attributes (other than the ‘high prize’) gain relatively more
importance. This implies that the range of values that the reference point
takes on in the ABS and Baseline treatment is smaller than that of the CBS
treatment. In particular, when the lottery-outcome domain comprises gains and
losses (experiment 1), the reference point tends to be relatively higher, and
when the lottery-outcome domain comprises only gains (experiment 2), the
reference point tends to be relatively smaller, compared to that of the CBS
treatment. This implies that the subjects assigned to the ABS and Baseline
treatments choose in a relatively riskier (resp., safer) way in experiment 1
(resp., experiment 2).

On the basis of the offered interpretation, a key driver of the detected
preference reversal is the fact that in the CBS treatment subjects view one
outcome at a time. We indeed observe that the preference reversal phenomenon
is less likely to occur in the CBS treatment whenever CBS subjects happen to
look up both lottery outcomes. In fact, as demonstrated by the combined
information-search and choice analysis, while in experiment 1 the probability
that the risky lottery is chosen increases when both outcomes are looked up,
in experiment 2 the probability that the risky lottery is chosen decreases
when both outcomes are looked up. That is, in both experiment 1 and experiment
2, whenever CBS subjects happen to explore both outcomes, their choices tend
to be more similar to those of the respective ABS (and Baseline) subjects. We
argue that this result provides further support to the proposed
interpretation.

We conclude this section by linking our results to the literature. In standard
and behavioural models of risky choice, the way the decision-maker allocates
attention is a function of the lottery attributes. For example, while - to
calculate the expected utility - an expected-utility maximiser looks up all
lottery attributes (outcomes and corresponding probabilities) of all lotteries
available, a decision-maker using a ‘maxmin’ procedure looks up the lottery
outcomes only. On the other hand, while in prospect theory rare events are
over-weighted (Kahneman and Tversky, 1979), in salience theory a state of the
world $\tilde{s}$ is more salient than some other state $s$ whenever
$\tilde{s}$ stands out, i.e., the payoff range of state $s$ is contained in
the payoff range of state $\tilde{s}$ (Bordalo, Gennaioli, and Shleifer,
2012). In contrast, our findings are in line with the well-documented
principle whereby attention is not an output but an input of the decision
process, and plays a key role in determining the decision-maker’s choice
(Orquin and Mueller Loose, 2013). For example, Pachur, Schulte-Mecklenbeck,
Murphy, and Hertwig (2018) identify a systematic relationship between the way
in which attention is allocated to the lottery attributes and the prospect
theory’s preference parameters, such as loss aversion and probability
weighting. On the other hand, Hirmas and Engelmann (2023) demonstrate that
imposing a more extensive exposure to a lottery attribute increases its weight
on the final decision. We argue that the proposed interpretation of our
results is consistent with this strand of literature.

##  6 Conclusion

In this paper we study the effects of digital nudging by exposing individuals
to choice interfaces in a controlled laboratory setting. By suitably modifying
the Mouse-Tracing paradigm, we administer three information-search
technologies that are based on well-known heuristics, such as alternative-
based search (ABS) and characteristic-based search (CBS) (Payne, Bettman, and
Johnson, 1993), in two pre-registered lottery-choice experiments. Our findings
are three-fold. First, we identify an interplay between the heuristic subjects
are induced to use and the lottery-outcome domain. In particular, (i) when
lottery outcomes comprise gains and losses (experiment 1), inducing subjects
to use CBS procedures systematically makes them choose safer lotteries,
compared to the subjects that are exposed to the other technologies, and (ii)
when lottery outcomes comprise gains only (experiment 2), these results are
reversed: inducing subjects to use CBS procedures systematically makes them
choose riskier lotteries. Second, we propose an interpretation of our results
that is based on prospect theory, whereby, at the core of the matter, is the
combined effect on the formation of the reference point of, on the one hand,
the heuristic subjects are induced to use and, on the other hand, the lottery-
outcome domain. Third, experiment 2 constitutes a replication of our earlier
results documenting the effects of exposing individuals to information-search
technologies in risky choice.

We conclude by discussing several limitations of this study and outlining
potential extensions. First, this paper investigates the effects of exposing
individuals to several information-search technologies in two distinct
lottery-outcome domains: (i) mixed domain (experiment 1) and (ii) gain domain
(experiment 2). A natural follow-up question is to examine the very same
research question in a lottery-outcome domain consisting of only losses.

Second, on the basis the information-search and choice analysis, an
interpretation of the results has been proposed, according to which there is
an interplay between, on the one hand, the heuristic subjects are induced to
use, and, on the other hand, the level of attention that - in forming a
reference point - subjects pay to the different lottery attributes. It would
be interesting to run a replication study by complementing the (instrumental)
use of the Mouse-Tracing paradigm with an eye-tracker. Doing so would enable
the researcher to refine the information-search analysis, and as a result,
conduct a better test of the proposed interpretation.

Third, this paper demonstrates that, in a controlled laboratory setting,
administering certain information-search technologies can affect people’s
risky choices in specific ways. Our results are thus of significant importance
for the design and the framing of real-world digital choice platforms.
Therefore, a critical follow-up question is to investigate the robustness of
the derived results outside the laboratory by testing our hypotheses in the
field.

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