Factors of Religiosity and Loss Aversion

by

Brian Howatt

A Thesis Presented in Partial Fulfillment of the Requirements for the Degree

Master of Science

Approved April 2017 by the Graduate Supervisory Committee:

Elias Robles-Sotelo, Chair

Perla Vargas Tess Neal

ARIZONA STATE UNIVERSITY

May 2017

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ABSTRACT

Loss aversion manifests as a decision bias in which avoiding losses is preferred

over acquiring rewards and can drastically alter an individual’s decision-making by

overweighting potential losses relative to gains of equal magnitude. Consequently,

individuals may require greater positive compensation to offset potential losses, exhibit

contradictory choice preferences, or even avoid the decision entirely; and this behavior

may be ascribed to an over-reliance on automatic, unconscious (intuitive) judgments

rather than initiating analytic reasoning more capable of objectively evaluating outcomes.

Religion (specifically Christianity) is the topic of focus, as preliminary evidence

suggests an individual’s intuitive inclinations positively correlate with and predict

religious beliefs. Moreover, self-reported religious beliefs significantly differed as a

function of inducing either intuitive or reflective mindsets. Therefore, the purpose of this

experiment was to test the hypothesis that religious participants will display significantly

greater levels of loss aversion than nonreligious participants.

This hypothesis extends from a previous study relating large-scale cultural and

religious differences with loss aversion. While their results revealed religious orthodoxy

strongly influenced loss aversion, the parameters elicited may be less stable as only two

lottery questions were asked and religion was determined by cultural demographics. This

study used the same design, but with a total of ten lotteries and a more detailed

investigation into individual religious factors.

While loss aversion coefficients replicated the overall behavioral effect (Median θ

= 2.6), independent sample, Mann-Whitney U tests did not yield any significant

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differences between Christian and Nonreligious participants (p > 0.05); nor did any of the

religious factors examined account for a significant amount of variability.

This study attempted to add to current knowledge by further conflating the

relationship between religiosity and adaptive decision strategies susceptible to errant and

inconsistent behavior. While the hypotheses were unsupported, a null finding is still

important, and future research re-testing this association or introducing causational

designs may prove more fruitful in understanding these complex relationships.

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ACKNOWLEDGMENTS

The author would like to express gratitude to his thesis committee chair and

members, Drs. Elias Robles, Perla Vargas and Tess Neal for their invaluable assistance

and guidance during the formulation, carrying-out and completion of this project, as well

as Psychology faculty and students at Arizona State University for providing helpful

comments and questions.

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TABLE OF CONTENTS

Page LIST OF TABLES…………………………….………………….....……………….….vii LIST OF FIGURES…………………………………………………..…...…………….viii LIST OF EQUATIONS…………………………………………………………………..ix DEFINITIONS…………………………………………………………………………….x CHAPTER 1 INTRODUCTION…………………………………………………..……………. 1 Risk Preferences………………………….…………………..…………....1 Religion………………………..………………..…………..………..........2 Present Study………………………..……………………….……………3 2 RISK PREFERENCES…………………………………………….……………... 4 Prospect Theory………………………..………………………………….4 Alternative to Expected Utility Theory………………..…………..4 Framing Effects……………………………….…..……………….7 Forecasting…………………………...………………….………...……....8 Delay Discounting………………………………………………………...9 Behavioral Parameterization……………………..…….………….……..11 Risk Aversion………………..………………………....….……..12

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CHAPTER Page Loss Aversion………………………………..…....……………..13 Summary…………………………………………………………………14 3 DUAL-SYSTEM FRAMEWORK OF COGNITION………………...………… 15

Dual-System Models…………………...………………………………...15 Sloman (1996)................................................................................15 Kahneman (2003)...........................................................................16

Heuristics……………………………………...……...….18 Critical Review: Evans (2008)...................................................................22 Summary…………………………………………………………………23 4 CRITICISMS…………………………………………...……………………….. 24 Heuristics……………………...…….………..………………………….24 Rebuttals…………………….………………….…….………….26 Semantic Inference.....................................................................................27 Prospect Theory……………………………………...…..………..……..29 Rebuttal………………………………………………………..…30 Loss Aversion………………………………..…………….…………….31 Reconciliation…………………………..…………..……………….…...32 5 RELIGION………………………………………………………………………. 33

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CHAPTER Page Religiosity and Risk Preferences…………………………..…………….33

Delay Discounting……………………………………………….34

Risk Aversion……………………………………………….……35 Gambling………………………….…………………………………..….36 6 PRESENT STUDY………………………………..………………………..…… 38 Methods…………………………………………………………………..38 Participants……………...………………………………….…….38 Design/Procedure…………………...……….……………….…..39 Results………………………………………………..…………………..41 Data Analysis…………………………………………………….41 Religious Identity………………………………………………...42 Religious Statements Responses…………………………………46 7 DISCUSSION…………………………………………………………………… 47 REFERENCES…………………………………………………………………………. 50 APPENDIX

A DATA COLLECTION AND REDUCTION……………………………… 60 B SUPPLEMENTARY DATA RESULTS………………………………….. 62 C IRB APPROVAL………………………………………...………………... 66

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LIST OF TABLES Table Page

1. Median Gain/Loss Ratios by Religious Identity………………………………... 43 2. Correlation Table of Gain/Loss Ratio and Religious Factors…………………... 45

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LIST OF FIGURES Figure Page 1. Prospect Theory Utility Function………………………………………...…………… 5 2. Delay Discount Functions……………………………………………………………. 11 3. Dual-Systems Framework of Cognition…………………………...…………….…... 17 4. Lottery Table Design………………….…………...………………………………… 39 5. Loss Aversion Coefficients by Religious Identity………………….………………... 44 6. Distribution of Gain/Loss Ratios by Religiosity……………………………………... 46

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LIST OF EQUATIONS

Equation Page 1. Relative Risk Premium………………………………………………………………. 13

x

DEFINITIONS

Expected Value (EV) – the average payout of a gamble over repeated trials, but can be

applied to single-event likelihoods. This is calculated as summing the products of every

outcome’s probability and quantitative value. This value is then multiplied by the number

of times the gamble is offered. If a coin is flipped 10 times to win either $10 or $0, the

EV is ((.5 * $10) + (.5 * $0)) * (10) = $50. A single coin-flip would therefore yield an EV

of $5.

Certainty Equivalent (CE) – a guaranteed payout that acts as a deterrent to a

probabilistic outcome. Instead of accepting the above coin-flip gamble, an individual may

prefer a certain $6 reward instead. The expected value of a CE is the given amount

multiplied by the number of times it is offered: ((1.0 * $6) * (n)) = $6 * n. The expected

values of the gamble and CE are then compared to determine which choice is statistically

optimal.

Indifference Point – The point at which an individual switches their preference between

choices; the options are of roughly equal value. If an individual prefers the guaranteed

outcome when the CE is $6, but prefers the gamble when the CE is $4, the indifference

point is about $5.

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CHAPTER 1

INTRODUCTION RISK PREFERENCES

Individuals often make decisions involving degrees of uncertainty in the

outcomes, the consequences of which are unbeknownst prior to their manifestation.

While much of what an individual risks in daily decisions is tolerable (not bringing an

umbrella, transportation, indulging in a scratch-off lotto ticket), empirical evidence has

revealed the aversive qualities of risk-taking in pursuit of large rewards when a

guaranteed, lesser reward may appeal as an alternative. Conversely, individuals may

avoid guaranteed outcomes when presented as losses/punishments (Kahneman &

Tversky, 1979, 1984; Tversky & Kahneman, 1981). Moreover, decision-makers may

show a general reluctance to engage in 50-50 mixed-frame gambles unless the expected

gains are roughly twice as much as potential losses (Tversky & Kahneman, 1991;

Kahneman, 2003; Tom, Fox, Trepel, & Poldrack, 2007). These behavioral phenomena

intending to reduce uncertainty and negative outcomes, referred to as ‘risk aversion’ and

‘loss aversion’ respectively (Kahneman & Tversky, 1984), are illustrated by a subjective

overweighting of the dissatisfaction derived from forgoing guaranteed gains, or

experiencing losses relative to gains of equivalent magnitudes.

An important distinction must be made here between two different types of

uncertainty in judgments and choices - risk and ambiguity. Although these terms are

often linguistically interchangeable, they diverge semantically. Risky outcomes are those

with clearly-defined, measurable probabilities (e.g., a 50% chance of success: coin-flip)

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while ambiguity refers to outcomes with vaguely defined or even undefined likelihoods

(e.g., “some” chance of success) that requires individuals to make subjective probability

estimates (Knight, 1921). Because behavioral decision research primarily concerns the

analysis of judgments and choices under risk, one must be careful in how results are

interpreted within more ecological, ambiguous contexts. Nonetheless, models of

decision-making strive to generalize observed behavior and have effectively

demonstrated how these choice dynamics can fundamentally influence social and

economic processes, such as marketing and consumption preferences, negotiations, and

politics (Novemsky & Kahneman, 2005; Carnevale, 2008; McDermott, 2004).

Additionally, some have established religion as a framework for guiding such

dispositions, perceptions and choices in life (Hommel & Colzato, 2010; Hui, Chan, Lau,

Cheung, & Mok, 2014).

RELIGION

Religion has played an integral role in human existence and development over

thousands of years and holds an almost ubiquitously entrenched presence across human

civilizations, with approximately 80% of people worldwide (Pew Forum Research, 2012)

and 78% of U.S. residents (Pew Forum Research, 2014) identifying with a religious

group. While some researchers have argued for the emergence and evolution of religion

within a cultural context (Henrich, 2009; Gervais, Willard, Norenzayan & Henrich, 2011;

Norenzayan et al., 2016), others have asserted a purely biological origin stemming from

the evolutionary adaptations of cognitive machinery (Bloom, 2007; Boyer & Bergstrom,

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2008), such as executive functioning (Friedman et al., 2008), that may motivate

intuitively causational ascriptions (Baumard & Boyer, 2013) to terrestrial events

(Kelemen, 2004; Kelemen & Rosset, 2009), assuaging the anxiety of environmental

uncertainty (Preston & Epley, 2005, 2009). Regardless of religion’s exact genesis, it

persists as a prevalent belief structure shaping one’s behavior through, but not limited to,

increased self-control and regulation, and prescribing intrinsically oriented goals that

temper hedonistic pursuits (McCullough & Willoughby, 2009).

PRESENT STUDY

Research aimed at studying religiosity has revealed significant relationships

between religious behavior - comfort, importance, prayer frequency and service

attendance, and increased risk aversion (Miller, 2000; Noussair, Trautmann, Kuilen, &

Vellekoop, 2013). Moreover, Rieger, Wang and Hens (2011) found preliminary evidence

suggesting Christian orthodoxy exerts a significantly stronger influence on loss aversive

behavior. However, the scope of Rieger and colleagues’ study was a large-scale, cross-

cultural and economic analysis of risk preferences, and their results were not intended to

be used on an individual level. Therefore, the purpose of this research project is a

modified replication and extension of their work, but with individual metrics of

religiosity.

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RISK PREFERENCES

PROSPECT THEORY

Prospect Theory (PT; Kahneman & Tversky, 1979) was introduced as an

alternative to the normative economic model of Expected Utility Theory (Bernoulli,

1738/1954), which had largely dominated the study of decision-making under risk.

Expected Utility Theory (EUT) posited that risk aversion resulted from subjectivity when

assessing [dis]utility (the [dis]satisfaction derived from the acquisition or loss of valued

stimuli) of choices, and proposed a set of axioms aiding in the objective analysis of

probabilistic judgments and choices. Satisfying these axioms will then, on average, lead

to statistically optimal outcomes and utility maximization, and mathematicians John Von

Neumann and Oskar Morgenstern (1944) later rigorously proved a series of conditions

under which these axioms hold.

The three primary conditions of Von Neumann and Morgenstern’s theorem, as

well as those challenged by PT are: completeness, transitivity, and independence.

Completeness assumes economic agents have well-defined preferences; Transitivity

assumes these preferences will remain stable across a series of choices (i.e., if A > B, and

B > C, then A > C); and Independence assumes this order of preferences will remain

stable, even when the first two are presented independently of the third (i.e., A>B>C and

A>B; although this axiom is controversial because its application can actually sometimes

lead to B>A - Allais, 1953). The seminal paper of Prospect Theory, as well as their work

surrounding it (Tversky, 1969; Tversky & Kahneman, 1974, 1981), sought to

demonstrate inconsistencies in these axioms and offer explanations for them. By

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providing participants with probabilistic scenarios and gambles, they were able to elicit

choices violating statistical intuitions and how risk-averse behavior could lead to

preference reversals.

alternative to EUT

The main conclusions of PT supplanted EUT as the predominant, descriptive

explanation for decision-making under risk, asserting the disutility of losses was a

significantly stronger force on behavior than originally accredited (Kahneman &

Tversky, 1979). Additionally, utility was no longer derived from purely an agent’s

overall status (i.e., total wealth) the outcome of a gamble contributed to; rather, it was

based on localized reference points (i.e., how much has been currently gained or lost) and

[dis]utility was judged by deviations from those baselines. This created an S-shaped

function (Figure 1) where an individual’s subjective value of a loss is greater than a gain

of equivalent magnitude.

Figure 1. - A hypothetical value function proposed by Kahneman & Tversky, 1979

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This judgment of potential losses exerting a more potent disutility was theorized

to lead individuals to avoid engaging in statistically optimal behavior involving

uncertainty, or decision outcomes with similarly valued rewards and losses, ‘risk’ and

‘loss’ aversion, respectively. Risk aversion can be characterized by accepting a lower,

guaranteed value over the potential to gain a probabilistic choice with a greater expected

value (the average payout of a decision over repeated trials, but is also used to describe

single-event values). And contextual conditions such as the magnitude of outcomes, the

type of gamble played, and the likelihood of an outcome may all play an important role in

judgments and choice dynamics by altering one’s propensity to accept guaranteed

amounts or take risks.

First, the magnitude of an outcome may significantly affect an individual’s

preferences by decreasing risk behavior as the stakes rise or increasing risk-taking in

minute stakes (Harinck, Van Dijk, Van Beest, & Mersmann, 2007). Next, the type of

gamble, or frame in which the decision is presented, significantly impacts risk

preferences, illustrated in the now classic ‘Asian Disease Problem’ presented below

(Tversky & Kahneman, 1981; percentage of respondents favoring the choice in

parentheses):

Problem 1 (N = 152): Imagine that the U.S. is preparing for the outbreak of an unusual Asian disease, which is expected to kill 600 people. Two alternative programs to combat the disease have been proposed. Assume that the exact scientific estimates of the consequences of the programs are as follows:

If Program A is adopted, 200 people will be saved. (72%)

OR

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If Program B is adopted, there is a one-third probability that 600 people will be saved and a two-thirds probability that no people will be saved. (28%)

Now consider another problem in which the same cover story is followed by a different

description of the prospects associated with the two programs:

Problem 2 (N = 155):

If Program C is adopted, 400 people will die. (22%)

OR

If Program D is adopted, there is a one-third probability that nobody will dies and a two-thirds probability that 600 people will die. (78%)

framing effects

This research by Tversky and Kahneman has demonstrated how different frames

can yield preference reversals - gain frames dampen risk-taking, while loss frames tend to

promote risk-taking - and they suggest that gains and losses are processed differently,

according to the aforementioned reference points. Despite the statistical equivalency of

the decision scenarios, the gain condition is focused on saving lives and therefore

processed as a reward by increasing the reference point; the loss condition is focused on

losing lives, evoking a much more emotional process that seeks to maintain the current

reference point.

An interesting wrinkle in framing effects arises though when the probabilities of

outcomes are manipulated. For gain frames, the propensity to take risks increases for

lower likelihood outcomes, while higher likelihood outcomes decrease risk. This effect

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tends to reverse for loss frames - greater risk-taking in high likelihood outcomes and

reduced risk-taking in low likelihood outcomes. This pattern is referred to as the

“fourfold pattern of risk attitudes” (Tversky & Kahneman, 1992, p. 308) and is of special

interest to the decision research community, in that risk attitudes are flipped simply by

the types of outcomes that may occur (see Kuhberger, Schulte-Mecklenbeck, & Perner,

1999, for a review confirming the efficacy of framing effects).

This cognitive distinction between rewards and punishments often leads to “losses

looming larger than gains” (Kahneman & Tversky, 1979), where the negative feelings

anticipated from potential losses are much greater than the positive feelings aroused by a

potential reward. It is crucial though to make point of the wording and stress that “losses

looming larger than gains” does not necessarily equate to “losses are actually stronger

than gains”. Accordingly, Prospect Theory postulates asymmetric psychophysical

properties between ‘Decision’ Utility (anticipated utility - Kahneman & Tversky, 1984)

and ‘Experienced’ Utility, in that how an agent feels a decision will affect him/her may

not match the actual hedonic experience.

FORECASTING

When the precise nature of decision outcomes is unknown, an individual’s choice

is often predicated upon the outcome anticipated to yield the greatest affectual return

(Mellers, Schwartz, & Ritov, 1999; Mellers & McGraw, 2001). Loss aversion can

interfere with this process if the asymmetry between gains and losses in decision utility is

not appropriately reflected in one’s experienced utility. If, however, these utilities of

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gains and losses are inherently different, the justification to forgo a $15 reward in lieu of

possibly incurring a $10 loss is rationally admissible (Tversky & Kahneman, 1991).

Previous research has suggested this may not be the case though, as participants tended to

overestimate the duration and intensity of their reactions to negative scenarios, such as

the dissolution of relationships, or denial of tenure and employment (Gilbert, Pinel,

Wilson, Blumberg, & Wheatley, 1998; Gilbert, Morewedge, Risen, & Wilson, 2004).

In addition, participants also displayed a significant hedonic and temporal

asymmetry of monetary losses only in the predictive stages of a decision (Kermer,

Driver-Linn, Wilson & Gilbert, 2004). Experienced losses were significantly less potent

than initially estimated, and statistically equivalent to experienced rewards. Thus, this

confluence of misjudgments may lead a person to believe that most, if not all negative

events hold a greater affectual impact relative to themselves and gains than they actually

do, though this relationship is not immutable.

DELAY DISCOUNTING

As a brief aside that will be relevant to religious behavior and the subsequent

section on cognition, it is helpful to discuss another important type of probabilistic

decision-making, notably when consequences will occur in the future. Delay discounting

is a behavioral phenomenon illustrated by an agent’s subjective value of a reward or

punishment decaying as a function of time (Chung & Herrnstein, 1967). That is, gaining

[losing] $100 today is weighted much more heavily than gaining [losing] $100 next

week, thereby promoting gains with immediate payoffs or neglecting future punishments.

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But, because future stimuli are important to plan for, our behavior accounts for this by a

willingness to accept larger amounts of compensation as the temporal distance from the

present also increases. For example, in order to forgo a $100 reward today, the future

reward may need to be at least $150, and the larger the value of the delayed stimuli, the

greater the rate of discounting (i.e., the less future stimuli are subjectively valued). This

discount rate can then be compared within or between-subjects in myriad ways, whether

as a function of the outcome type, their value, delay, or likelihood of attainment (Rachlin,

Raineri, & Cross, 1991).

This suggests immediate behaviors and consequences are more highly prioritized,

and generally for good reason. Until recent scientific and medical advances, one’s

lifespan was often more susceptible to the volatile fluctuations of the environment, be it

resource competition, medicinal/health quality (e.g., infant mortality rate) or natural

disasters that could prematurely end a lifespan. To the extent that it afforded an

opportunity to consume resources or reproduce, it was clearly advantageous not to wait.

However, analogous to probabilistic gambles where risk aversion can lead to over-

favoring certainty, rates of future discounting can fall into a similar pattern. Instead of a

future stimuli’s value decaying equally (exponentially) across time points, there is an

extremely rapid decrease in its value over the short-run, followed by a flattening of the

value for more distant time steps (i.e., a hyperbolic function - Mazur, 1987; Figure 2 -

Green & Myerson, 1996). And behavior following this hyperbolic model often leads to

greater impulsivity in choices, spurning optimal, future outcomes in favor of immediate,

lesser ones. These behaviors can also be empirically connected to risk aversion, with

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Frederick (2005) suggesting individuals who display steeper discount rates will also

display more pronounced risk aversion patterns in monetary choices. Ioannou and Sadeh

(2016) did not share this conclusion for either monetary or environmental risks, but

theorized this discrepancy as possibly resulting from incentivized tasks.

Figure 2 – Exponential and Hyperbolic Discount Functions

BEHAVIORAL PARAMETERIZATION

While Kahneman and Tversky were not the first researchers to recognize and

record empirical violations of economic axioms of decision-making (Markowitz, 1952;

Allais, 1953; Ellsberg, 1962; Lichtenstein & Slovic, 1971), their pioneering work on

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formulating a rigorous descriptive model of behavior was instrumental for a deeper

comprehension of the nuances and lability of judgments and choices. Although the theory

in a general sense helped to explain misjudgments and choice inconsistencies, perhaps its

greatest contribution was laying the foundations for a formal parameterization of risky

behavior above and beyond binary choice sets. Despite Tversky and Kahneman’s

rejection of within-subjects designs, by eliciting an indifference point (or a participant’s

point of preference reversal between two choices) through repeated measures designs, an

individual’s precise specifications can be determined and compared across choices in

other tasks, participants and studies. To contextualize this, monetary gambles are a

common methodology as they offer a quantitatively standardized scale to measure

degrees of risk and loss aversion.

risk aversion

Gambles measuring risk aversion (Kahneman & Tversky, 1979) typically consist

of a choice between two alternatives: A) either a probabilistic outcome between a reward

[loss] and a null outcome ($0), or B) a guaranteed reward [loss] - also called a Certainty

Equivalent (CE), which acts as a deterrent to the gamble - illustrated below.

Which of the following would you prefer?

A: 50% chance to win $1000 and 50% chance to win nothing

OR

B: $450 for sure

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Winning $1000 is enticing, but walking away with $450 is also quite appealing and

forgoing this reward in lieu of potentially losing the bet might sting. By having

participants clearly define their CE with an explicit value, or by scaling the amounts

through repeated choices, their ‘Relative Risk Premium’ (RRP - Eq 1; Rieger et al., 2011)

can be calculated to determine rates of risk tolerance.

Eq. 1) 𝑅𝑅𝑃 = !" ! !"!"

The lower an individual’s CE, the more positive their RRP and the more risk-averse they

are, relative to the expected value of the gamble presented (smaller and smaller amounts

of guaranteed outcomes are not enough to prefer taking the gamble). Conversely, the

higher the CE, the more negative their RRP and the more risk-taking they are, relative to

the EV of the gamble (they will continue declining higher guaranteed amounts in pursuit

of the gamble).

loss aversion

While risk and loss are similar in nature, they are also clearly different - risk does

not always entail loss, and loss can be exhibited in riskless, or non-probabilistic,

scenarios (Tversky & Kahneman, 1991). That being said, utilizing monetary gambles

similar to risk aversion is still the most effective method of parameter estimation; only in

this case by directly pitting rewards against losses without null or certain outcomes.

Suppose Kahneman and Tversky’s (1979) original gamble was presented again, but

collapsed into a single 50-50 chance of either winning or losing $100. This parameter can

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be estimated similarly to the RRP: calculating it through a series of accept/reject choices

of gambles with varying gain and loss amounts, or specifically defining the necessary

rewards to offset potential losses. The latter method is referred to as the Gain/Loss Ratio

(G/L - Tversky & Kahneman, 1991) and derives its name from the estimation technique,

dividing the specified gain amount by the loss amount. For example, if a participant

required $150 to offset a $100 loss, their loss aversion coefficient would be 1.5

(150/100). Lower G/L ratios imply less loss aversion; larger G/L ratios imply greater loss

aversion. There are other, more intricate ways of measuring this parameter, but the G/L

ratio is simple and can reliably differentiate behavioral patterns in a between-subjects

paradigm, like in the present project.

SUMMARY

Risk preferences stemming from aversion to uncertainty and loss can lead to

interesting violations of statistically optimal decision-making in a given scenario. And

research has shown that the asymmetry between estimating the impact of an outcome and

its actual experience can be ascribed to the subjectivity of the behavioral process.

Moreover, many of these violations can be ameliorated under objective analysis,

following a set of axioms developed to maximize one’s output that are accessible but

often neglected. The question is then, why does this occur? If individuals possess the

necessary cognitive aptitudes to overcome errors in thinking and aversion to beneficial

situations, why is it so difficult to tap into?

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CHAPTER 3

DUAL-SYSTEM FRAMEWORK OF COGNITION

DUAL-SYSTEM MODELS

Sloman (1996).

A critical element of risk preferences is the formulation of these judgments in

relation to the mechanisms of differential, yet complementarily functioning cognitive

systems. Conceptually, the roots of this notion can be traced back to Ancient Greek

philosophy (Aristotle - cited in Sloman, 1996), with Plato comparing these processes to

controlling a chariot with two horses, one well-trained and the other wild. More recently,

psychologists and philosophers such as William James (1890/1950; cited in Sloman,

1996) have also attested to a general cognitive capacity of both parallel and serial

processing mechanisms.

However, it wasn’t until Steven Sloman (1996), that a formal, empirically

oriented theory of a dual-system model of categorization and reasoning was proposed.

Although Sloman’s own work at the time was in its nascent stages, the foundation of his

arguments encompassed an extensive literature on human language processing,

reasoning, judgments and choice. Theory and data compiled from these research domains

yielded evidence distinguishing between two modes of cognition, which he labeled the

Associative System and the Rules-based System. The associative system is characterized

as judgments governed by principles of automaticity, speed, similarity and contiguity,

and Sloman illustrates these functions as: intuition, creativity, associative memory and

visual recognition. These cognitive mechanics provide an agent with the ability to

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quickly draw rough statistical inferences from one’s environment, based on similarity and

generalization from personal experiences that serve as flexible guidelines with soft

constraints.

Conversely, the rules-based cognitive system is primarily portrayed as a symbol

manipulator, derived from one’s culture, language and formal systems. The

computational procedures in this system are slow, but engender deliberative, logical

interpretations of causality and purpose from environmental information collected. Its

processing is productive and systematic, in diametric opposition to the automaticity of the

associative system, and applies hard constraints to the reasoning strategies utilized and

judgments rendered. Sloman suggests the rules-based cognitive mechanisms must be

initiated when greater processing is required, or to monitor, and correct if necessary, the

associative system’s encoding and conclusions. However, he also notes the application of

the rules-based system to reasoning does not guarantee optimal solutions. It is merely a

process-oriented approach to behavior.

Kahneman (2003)

Daniel Kahneman (2003) built upon Sloman’s and others’ theories (Stanovich &

West, 2000; Kahneman & Frederick, 2002), primarily driven by his and Amos Tversky’s

research on judgments and heuristics investigating errors of intuitive thinking (Sloman’s

associative system was now labeled colloquially as either ‘System 1’ [Stanovich & West,

2000] or ‘intuition’ [Kahneman & Frederick, 2002]; the rules-based system was changed

to either ‘System 2’ [S&W, 2000] or ‘Reflective’/’Reasoning’ [K&F, 2002]). Figure 3

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below shows this framework, and now includes perceptions in the model, suggesting that

while the perceptual and intuitive processes are similar, the nature of their respective

content evaluated differs. Between intuitive and reflective cognition, this relationship is

reversed, in that the content evaluated is similar but their respective processes through

which that content is evaluated are quite different.

Figure 3. - Process and Content in Two Cognitive Systems proposed by Kahneman, 2003

Kahneman then adds further dimensions to each cognitive structure, suggesting

System 1’s proficiency may be due to ‘attribute substitution’ (Kahneman & Frederick,

2002), a method of breaking down complex problems into smaller, simpler and more

manageable pieces. However, he also cautions this system can be prone to emotional

reactivity in judgments and are governed by habits, making them difficult to control or

alter. Moreover, because cognitive capacitance is limited, System 2’s effortful application

to judgments can be laborious to initiate and sustain, thus potentially causing interference

between concurrent effortful tasks, or permitting System 1 to run amok. Kahneman

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reaffirms Sloman’s proposed cognitive hierarchy of System 2 monitoring and suppressing

System 1’s initial judgments (for neurological evidence, see De Martino, Kumaran,

Seymour, & Dolan, 2006; for integration into the dual-system framework, see Kahneman

& Frederick, 2007), as well as asserting task-interference designs can reliably demarcate

the invocation of each system between judgments, tasks and choices.

HEURISTICS

Kahneman’s (2003) dual-system model of cognition delineated between

perceptions and intuitions. This was very important, as intuition is not constrained by

immediate information as perceptions are; rather, it is a cognitive function fully capable

of integrating past information into judgments an agent will make in the future, by

forming “impressions of the attributes of objects or perception and thought” (p. 699).

However, System 1 sits (metaphorically, of course) in an interesting position then,

sharing its processing and content of evaluation with two mutually exclusive cognitive

functions. It has the capacity to rapidly filter through massive amounts of information and

come to generally accurate conclusions of the past, present and future, sans the

metabolically taxing effort and temporality of System 2. How might it accomplish such

feats?

A heuristic is a method of problem solving employed by an agent through which,

by trading off optimality for efficiency, an adequate solution can be discovered and

recalled for future utilization. Its application to cognition originated from Herbert Simon

(1955), who coined the term ‘satisficing’, judgments and choices an individual makes

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that are “good enough” despite lacking statistical optimality. Recalling back to the

previous section on Prospect Theory, where subjects exhibited behavioral inconsistencies

that systematically violated normative models, it may come as little surprise that Tversky

and Kahneman’s empirical exploration of heuristics (Kahneman & Tversky, 1972;

Tversky & Kahneman, 1973) paved the way for Prospect Theory as a descriptive model

of choice behavior.

Their foray into pitting the statistical intuition of experts and laypeople alike

against normative calculations led to the development of a number of specific heuristics

used to expedite the cognitive process, most notably availability and representativeness.

The availability heuristic is a memory-based evaluation of content, and

representativeness is a method of assessing or organizing similar stimuli according to a

general prototype. To conceptualize these, consider the following decision vignettes and

their respective results:

Availability:

In four pages of a novel (about 2,000 words), how many words would you expect to find that have the form “ _ _ _ _ i n g” (seven-letter words ending with “ing”)? Indicate your best estimate by circling one of the values below: 0 1-2 3-4 5-7 8-10 11-15 16+

A second form of this problem asked subjects the same question, but with seven-

letter words consisting of the form “ _ _ _ _ _ n _”. Tversky and Kahneman (1983) found

that the median estimate for words ending with “ing” was 13.4, while the median

estimate for words with the form only “n” as the 6th letter was 4.7. However, because

any seven-letter word ending with the form of “ing” has ‘n’ as the 6th letter, it is

20

statistically impossible for there to be more cases of it than seven-letter words with only

‘n’ as the 6th letter. Tversky and Kahneman argued the ability to recall words ending

with “ing” is much easier than words with only ‘n’ as the 6th letter visible, leading to the

inverted results and violation.

Representativeness:

Linda is 31 years old, single, outspoken and very bright. She majored in Philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.

○ Linda is a teacher at an elementary school ○ Linda is active in the feminist movement (F) ○ Linda is a psychiatric social worker ○ Linda is a bank teller (T) ○ Linda is an insurance saleswoman ○ Linda is a bank teller and is active in the feminist movement (T&F)

Tversky and Kahneman (1983) asked participants to rank-order which choice is

more probable, or provide probability estimates, given the personality sketch. They found

that 82-85% of subjects believed “Linda is a bank teller and is active in the feminist

movement” (T&F) as more likely than “Linda is a bank teller” (T), violating the

conjunction axiom of probability theory (they ranked Linda as a feminist (F) as more

likely than both (T) and (T&F) though). “Conjunction” in probability theory is the

likelihood that two (or more) events will occur - e.g., the chance that it is cloudy and

windy today - but without one necessarily depending on the other (which is called

conditional probability). The corollary of this axiom is that the likelihood of both events

occurring cannot exceed the likelihood of one of the single events - i.e., there cannot be a

greater chance it is both cloudy and windy today, than only cloudy or only windy.

21

Tversky and Kahneman argued these results fit representativeness, with

participants believing that because Linda resembles the prototype of a feminist, she will

be more likely to fit a conjunction comprised of the target characterization (feminist) and

a neutral target (bank teller), above and beyond an option with just the neutral target.

Base-Rate Neglect:

While base-rate neglect is not a heuristic, it serves as a salient example of how brushing

over details of single-event likelihood estimates can skew judgments. Consider the

scenario (Casscells, Schoenberger, & Graboys, 1978):

If a test to detect a disease whose prevalence is 1/1000 has a false positive rate of 5%, what is the chance that a person found to have a positive result actually has the disease, assuming no prior knowledge? Casscells and colleagues originally found that the modal response was 0.95, the

average was 0.56, and only 18% of subjects correctly responded 0.02. Cosmides and

Tooby (1990) replicated this effect, with only 12% of subjects correctly responding

(although in the next section, they show how to reduce this effect). The reason this is

called ‘base-rate neglect’ is because subjects tended to assess the likelihood of a positive

test if the patient does have the disease, and not the likelihood of the patient having the

disease (which is unknown) given a positive test, the latter of which uses the base-rate

1/1000 in its likelihood calculations.

Additionally, Slovic, Finucane, Peters and MacGregor (2007) put forth another

heuristic, affect, wherein the emotionality of judgments and outcomes may significantly

influence behavioral processes using the “pain principle” - pursue pleasure and avoid

pain. Altogether, these cognitive shortcuts aim to drastically reduce the time and effort of

22

judgments/decisions by boiling down relevant information to the essentials and

processing them in a parallel manner, through which the most satisfactory conclusion can

be made.

CRITICAL REVIEW: EVANS (2008)

To rein in the surfeit dual-system models proposed after its initial inception, each

with similar yet distinguishable qualities, Jonathan Evans (2008) collated an extensive

review and weighed in on the manner. Although generally agreeing with the overall

notion of dual-processes of cognition, Evans suggests it does not necessarily imply a

general dual-system framework, which he calls “oversimplified and misleading” (p. 270).

Because the operations and underlying architecture of each purported system are not

mutually exclusive, and both “systems” may consist of overlapping elements of

preconscious and conscious processes, it is difficult to wholly map onto independent

mechanisms. He attempts to resolve these inconsistencies by offering a key distinction -

“type 2 processes are those that require access to a single, capacity-limited central

working memory resource” (p. 270), and that the overload and interference of working

memory can disrupt slow, sequential processing.

Other researchers have taken this a step further and argued that a uni-system

model of cognition is superior (Gigerenzer & Regier, 1996; Keren & Schul, 2009;

Kruglanski & Gigerenzer, 2011), as the evidence that ostensibly supports dual-system

theories actually lacks adequate power in explaining and predicting behavior. Gigerenzer

and Regier (1996) claim both intuitive and reflective judgments are rule-based, and

23

through a “routinization” of shared rules, deliberative judgments can become intuitive

(Kruglanski & Gigerenzer, 2011). Moreover, Keren and Schul (2009) assert that System

2 relies on System 1’s input or else it would fail, clearly signaling interdependence

between the two alleged systems.

SUMMARY

Kahneman and Tversky’s (and others) ‘Heuristics and Biases Program’ (HBP;

Kahneman, Slovic, & Tversky, 1982; Tversky & Kahneman, 1974, 1983) swept through

the research world, demonstrating instances of cognitive deficiencies in rapid

probabilistic judgments and risky decisions. And this was attributed to a reliance on

intuitive cognition and failure to initiate reflective reasoning that can override automatic

judgments. Despite their acknowledgments on the efficacy of these routine mental

faculties, the evidence was as damning as it was alarming - systematic deviations from

normative probabilistic judgments were observed, even when the correct answers were

seemingly right in the decision vignettes themselves, in both laypeople and expert

statisticians alike (Tversky & Kahneman, 1972). Man as an “intuitive statistician” was in

severe jeopardy. How could one’s judgment so crassly neglect fundamental probabilistic

principles (i.e., base-rates, conjunction) built into the scenarios? More importantly

though, was what if these conclusions were wrong?

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CHAPTER 4

CRITICISMS

While there exists literature debating Prospect Theory’s accuracy as a descriptive

utility function of decision-making under risk (Levy & Levy, 2002a, 2002b; Baltussen,

Post, & Van Vliet, 2006; Nwogugu, 2006), many focus on the specific mathematical

parameterizations of the function (as opposed to the general estimates described earlier).

Although that scope is not the focus of this review, their methodological qualms as to

why Kahneman and Tversky’s findings may be invalid, unreliable or merely a

“transitional stage” (Gigerenzer, 1991, p. 3) are, as an entire body of past, current and

future research may be based on misleading foundations and incorrect conclusions.

Therefore, an analysis of criticisms and counterarguments is necessary to understand the

efficacy of risk preferences; if loss aversion does not hold water, then any results of this

current project are suspect.

HEURISTICS

Spearheading the opposition to Kahneman and Tversky’s ‘Heuristics and Biases

Program’ (HBP) was Gerd Gigerenzer and his formulation of a theoretical framework

called ‘Probabilistic Mental Models’ (Gigerenzer, Hoffrage, & Kleinboelting, 1991). This

work sought to properly describe and explain probabilistic judgments within a formal,

frequentist model, a manner he argued HBP lacked. Gigerenzer’s primary critiques of

HBP (Gigerenzer, 1991) were two-fold: 1) the conjunction axiom of probability theory

cannot be rigorously applied to single-event judgments/choices. Instead, frequentist-

25

framed scenarios were more appropriate. 2) HBP lacked a coherent description of what

cognitive heuristics entailed from a mechanistic perspective. He also questioned how

“biases were actually biases” when they could be reduced and even perform optimally in

many ecological situations and within-subjects presentations.

To illustrate these differences, recall the Linda Problem and how Tversky and

Kahneman argued violations of the conjunction axiom could be explained by

representativeness. Gigerenzer disagreed with this supposition, contending that Tversky

and Kahneman’s heuristics are, “largely undefined concepts and can post hoc be used to

explain almost everything” (1991, p. 102). Moreover, he condemns using single-event

probabilities with distracting fillers between ‘Bank Teller’ and “Bank teller and is active

in the Feminist Movement” as a legitimate methodology, opting instead for frequency-

based judgments with response contiguity that are much easier to understand:

There are 100 persons who fit the description above (i.e., Lindas). How many of them

are:

A) Bank tellers

B) Bank tellers and active in the feminist movement

He cites Fiedler's (1988) results, showing that only 22% and 17% of participants violated

the conjunction axiom in this context. Gigerenzer then cites Cosmides and Tooby (1990),

who showed how this type of presentation also reduced ‘base-rate neglect’, with 76% and

92% of participants properly identifying 0.02 as the statistically correct likelihood of a

patient with a positive test actually having the disease.

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rebuttals

Kahneman and Tversky (1996) responded to Gigerenzer’s critiques, arguing that

they themselves initially found that frequentist and within-subjects methods can reduce

these biases (Tversky & Kahneman, 1983), but this effect is not as stable as Gigerenzer

insists (Tversky & Kahneman, 1974; Slovic, Fischhoff, & Lichtenstein, 1982). They

claimed this de-legitimizes his criticisms as ignoring counterevidence, and that within-

subjects presentations aren’t ecologically valid and can too obviously cue participants to

correct their responses. They further claim the development of a theoretical model of

heuristic analyses is moot and the lack of such does not discredit the role of

representativeness in intuitive prediction:

This objection misses the point that representativeness (like similarity) can be

assessed experimentally; hence it need not be defined a priori. Testing the

hypothesis that probability judgments are mediated by representativeness does not

require a theoretical model of either concept. The heuristic analysis only assumes

that the latter is used to assess the former and not vice versa (1996, p. 585)

They also found his criticism of single-event conjunctive probabilities problematic,

suggesting it is highly improbable he disregards an individual’s subjective probability,

and more so to consider them devoid of meaning and normative rigor - individuals simply

must be able to assign an appropriate likelihood to a decision without necessarily

considering their behavior in repeated trials. They further state that the dissipation of

cognitive illusions is not the only aspect of interest to them, but rather their very

27

existence - “The Mueller-Lyer Illusion, for example, “disappears” when the two figures

are embedded in a rectangular frame, but this observation does not make the illusion less

interesting” (p. 586).

Gigerenzer (1996) responded to Kahneman and Tversky (1996), echoing PMM as

a well-founded theoretical framework of heuristic judgments and his original critiques of

HBP: principles of probability theory cannot be so strictly applied to single-event

outcomes; definitions alone cannot describe mental processes - testable and falsifiable

models must be instantiated; and within-subjects testing is a viable and ecological

research methodology. However, he does make an important clarification, in that

frequentist formats are not necessarily an end-all solution to misjudgments; only that they

aid in making proper evaluations, in part by simplifying complex single-event probability

calculations. Regardless of their disagreement, Gigerenzer stresses “understanding how

people reason under a bewildering variety of circumstances” (1996, p. 595), and implores

Kahneman and Tversky to do the same for his recommendations on researching not just if

these biases disappear, but why or why not.

SEMANTIC INFERENCE

One additional theme that arose in Gigerenzer’s (1996) reply concerning the

dichotomy between probabilistic and frequentist judgments was the linguistic aspects of

the Linda Problem. Take for example, “We invited friends and colleagues to the party”

(Mellers, Hertwig, & Kahneman, 2001). Here, the ‘and’ operator can denote membership

in one or both classes (a party attendee can be either a friend, a colleague, or both).

28

Gigerenzer argued that the semantic ambiguity of “Linda is a bank teller and is active in

the feminist movement”, coupled with the use of the word ‘probable’ when ranking

choices, could possibly lead participants to believe if ‘Linda is a bank teller” then it

excludes her activity in a feminist movement, Linda being in either of the categories

satisfies the conjunction, or interpreting it as a conditional - i.e., if Linda is a bank teller,

then she is also active in the feminist movement. Because of this he claims the behavior

observed cannot be evaluated under normative standards. Since the word ‘probable’

evokes plausibility, or having the appearance of truth, this loosens the hard constraints of

probabilistic conjunction.

Linguistic analyses (Hertwig & Gigerenzer, 1999) substantiated this claim,

yielding significant differences in how participants interpreted ‘probability’ and

‘frequency’. Participants consistently inferred non-mathematical interpretations from

‘probability’ - i.e., “possibility”, “correspondence”, “applicability” and “conceivability” -

and overwhelmingly exhibited conjunction effects (83%). Conversely, participants

consistently interpreted ‘frequency’ as mathematical - i.e., “how often”, “number”,

“percentage” and “proportion” - and “never violated the conjunction rule” (p. 288). And

this effect was then replicated without using the word ‘frequency’, demonstrating the

context, and not just the terminology, is important.

Further dispute regarding the ‘and’ operator in the Linda Problem culminated

with an “adversarial collaboration” between Hertwig and Kahneman, mediated by

Mellers (Mellers et al., 2001), attempting to reduce conjunction effects by using “and

are”, “who are” and “feminist bank teller” in lieu of “and is”. However, these results were

29

not so equivocal, showing that although conjunction effects disappeared when the filler

items were removed for “and are”, “who are” and even “and is”, only “who are”

significantly reduced conjunction effects in the presence of filler options. Ultimately,

Hertwig and Kahneman still had some different perspectives on the matter regardless of

the results (as was expected). Nonetheless, some progress was made, as Hertwig

conceded that the semantic ambiguity of “and” was not the only influence of conjunction

effects, while Kahneman accepted representativeness could be lessened in different,

equally likely linguistic contexts.

Gigerenzer (2008) neatly summarizes his work as an alternative to Kahneman,

Tversky and Slovic’s HBP, proposing common misconceptions of heuristics and an

“adaptive toolbox” likely comprised of, but not limited to 10 processes (unsurprisingly

lacking availability, representativeness, or affect) that instead promote efficacious

ecological behavior: satisficing, recognition, take the best, or default (status quo).

Gigerenzer states: “the goal of a [darwinian] organism is not to follow logic, but to

pursue objectives in its environment” (p. 25) and provides evidence these methods can

reliably outperform mathematical optimization techniques in practical scenarios. He

concludes his arguments calling for a deeper understanding of heuristics in the

environment and how to mitigate errors by altering their usage or the environment itself.

PROSPECT THEORY

While the preceding counterarguments primarily focused on the efficacy of

judgments leading to putative violations of normative models of decision-making, this

30

section presents some methodological counters to the actual implemented designs of risk

preferences (Kahneman & Tversky, 1979). Recall the S-shaped value function of

Prospect Theory (PT) - risk aversion in gains and risk-seeking in losses. These results

derived from asking participants to select between binary choice sets with congruent

outcomes in the frames, i.e., none of the gambles matched a reward against a loss. Levy

and Levy (LL - 2002a, 2002b) argued this methodology is intractable given the complex

nature of investments, involving both positive and negative consequences. To support

this claim, they ran a series of experiments that included mixed-frame gambles and results

strongly suggested participants’ choices in this respect significantly deviated from PT;

single-frame gambles replicated PT’s original results. This lead LL to adamantly reject

PT as an accurate descriptive model of decision-making under uncertainty.

rebuttal

Soon after LL’s reports came out, Wakker (2003) re-analyzed their data and fired

back, asserting their results actually do support PT and that LL had failed to properly

incorporate their data into Tversky and Kahneman’s updated (1992) model. When the

data are modeled correctly, their results agree with PT and their interpretations are

rendered asinine; Baucells and Heukamp (2004) replicated this rebuttal as well (although

Baltussen, Post, & Van Vliet, 2006 argue in favor of LL). Additionally (and this is my

argument), they explicitly state PT only uses single frame outcomes. And yet, though

they cite Tversky and Kahneman’s 1992 article, they completely ignore their use of

mixed gambles leading to the conclusions in that very article.

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LOSS AVERSION

Despite the literature criticizing heuristics and PT, the general notion of loss

carrying a greater psychophysical weight than gains seems stable (Tom et al., 2007).

While some research has sought to define its boundaries (Novemsky & Kahneman, 2005)

or pointed out instances of reversal (Harinck et al., 2007), this phenomenon marched on.

Recently however, more poignant research has begun to show weaknesses in loss

aversion as a domain-general behavior (Ert & Erev, 2013), or an explanation of status

quo biases and risk bet premiums (Gal, 2006). Walasek and Stewart (2015) took this

criticism a step further, claiming loss aversion is merely a product of research designs

and ran a modified replication of the results from Tom and colleagues’ (2007) article,

who found a loss aversion rate of about 2:1 in their study. Their criticism of this article

came from Tom and colleagues using gain values ranging from $10-$40 and loss values

ranging from $5-$20, which they argued artificially creates a 2:1 loss aversion ratio.

To amend this asymmetry, they compared this range with a balanced range, but

also included ranges with greater loss values. Results from the condition congruent with

Tom and colleagues’ study replicated their original results, but loss aversion in the

balanced condition largely disappeared. Interestingly, risk seeking was slightly increased

in the condition with larger loss ranges. The authors conclude by acknowledging loss

aversion as a behavior phenomenon that can arise as a result of “an asymmetry in the

distribution of gains and losses...reflected in people’s memory” (e.g., small but frequent

bank withdrawals, and large but fewer bank deposits - p. 10), but restate their claim that it

can be largely elicited as a product of design.

32

RECONCILIATION

This contradicting body of research is naturally of great importance. Given that

the direction of this research project concerns the behavioral aspects of loss aversion in

single-event choices, due caution must be urged regarding the validity and reliability of

any results found and interpretations made. Nonetheless, there exist other loss aversion

paradigms that are currently still methodologically credible, along with a dual-process

cognitive framework.

Thus, the manner in which judgments are generated, whether intuitively or

reflectively (Kahneman & Frederick, 2002), is crucial to decision-making, as an over-

reliance on heuristics or failure to properly initiate corrective reasoning may cause the

retention of intuitively compelling, but discordant or false responses. Frederick’s (2005)

‘Cognitive Reflection Test’ (CRT), a three item assessment of these cognitive styles

suggests participants who respond more intuitively to the questions display risk

preferences with greater loss aversive tendencies and steeper rates of delay discounting

(replicated by Hardisty & Weber, 2009; Shenhav, Rand, & Greene, 2017). Furthermore,

research has shown how cognitively intuitive proclivities are not only linked with greater

propensity to hold paranormal/religious beliefs (Aarnio & Lindeman, 2005, 2007), but

that inducing intuitive or reflective mindsets, in both positive and negative frames, can

also significantly alter these beliefs (Shenhav, Rand, & Greene, 2012).

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CHAPTER 5

RELIGION

The reach and strength of religion’s influence on people and cultures around the

world is profound. Whether it is an individual engaging in religious practices or societal

gatherings to partake in rites and customs, these beliefs permeate through one’s

perspectives about the world and affect the decisions they make in the environment.

Hommel and Colzato (2010) offer a slightly more provocative framework of this

relationship though: religions can act as a cognitive control-guide permanently altering

perceptual and attentional processing of information, and that re-directing attention to or

away from important states helps individuals follow the principles of their belief. The

reinforcement of these values may instill them as deeply ingrained, long-lasting default

control styles, facilitating judgments and choices when faced with uncertainty.

In a review analyzing religious identification and behaviors, this sentiment seems

to be well supported, with religiosity strongly relating to self-control and regulation but

not necessarily self-monitoring (McCullough & Willoughby, 2009). These relationships

present an interesting case then. Most doctrines encourage moderation (or abstinence) of

resource consumption, charitable donations, sexual reticence, et cetera. And all of these

behavioral modulators have a clear purpose: some form of eternal salvation or karmic

reward meant to trump any immediately pleasurable activities an individual may engage

in. By not indulging in immediate, smaller rewards, they maximize future rewards.

Connecting this with risk preferences, will there be observable differences in discount

rates, future planning and risk aversion as a function of religiosity?

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RELIGIOSITY AND RISK PREFERENCES

delay discounting

Indeed, previous research has demonstrated how participants with greater

religious beliefs (or fundamentalism) and conviction tend to be more future oriented

(Oner-Ozkan, 2007) and discount future rewards less than non-religious participants

(Carter et al., 2012). However, Paglieri and colleagues (2013) studied Dutch Calvinists (a

highly conservative Protestant sect), Italian Catholics and Atheists from both countries,

and found that while Calvinists were significantly more future oriented than Catholics

and Atheists, Catholics were significantly less future oriented than Atheists. The authors

attribute this disparity to Calvinists believing in predestination and the permanence of

actions across their lifespan, while Catholics believe in confession, permitting more

flexibility in short-term behavior. These denominational differences are vital to

understanding and disentangling between-subjects from within-subjects variability, as

observed differences may be incorrectly ascribed to the general ideology rather than the

intensity of individual factors. For example, Shenhav and colleagues’ (2017) studies

contrast this general notion, showing a steeper discount rate for individuals who self-

identify as more religious and with greater conviction, although religious demographics

were not recorded. These differences are quite stimulating and serve as a reminder of the

complexities of constructs under examination, wherein a multi-perspective approach must

ultimately be the goal. However, these nuanced analyses demand greater sample sizes

and are therefore more time consuming and expensive.

35

risk aversion

With empirical evidence observing these tentative relationships between

religiosity, cognitive styles and delay discounting that warrants credence, will similar

associations exist with risk aversion? First, in a cross-cultural analysis (Miller, 2000),

there was a tendency for both Western and Eastern cultures to display risk-averse

behavior, although significant differences were present. Participants from traditional

western cultures (U.S. & Italy) with a greater proportion of Christians, and Turkey (Islam

- Turkey is difficult to classify as it straddles Eurasia) displayed significantly stronger

negative correlations between levels of religiosity and risk-taking than traditional eastern

cultures (Japan [Buddhist and Shinto] and India [Hindu]). Moreover, between these

countries, regression coefficients were significantly stronger for the U.S. compared to all

other countries, stronger for Italy compared to India and Japan, and stronger for Turkey

compared to Japan.

Next, Noussair and colleagues (2012) measured the relationship between risk

propensity and Christian denominations, Catholic or Protestant, and initial tests

demonstrated a positive association between religiosity and risk aversion. However,

results showed no significant differences between these groups in either hypothetical or

real stake games. Furthermore, religious factors such as frequency of church attendance

and praying were significantly correlated with risk aversion, but religious belief and

conviction were not. So overall, while mixed results are present, there seems to be at least

a general trend as to how particular religions, their denominations and elements of belief

or practices may or may not play a role in risk-based behavior. But these studies were

36

largely confined to lab-based testing of surveys and designs; do these results hold in an

ecological context?

GAMBLING

While the previous studies primarily utilized general self-report and lab-based

designs, there is a closely related economic and social behavior individuals may

frequently entertain: gambling. Gambling consists of staking portions of one’s own (or

another’s) money (or objects of value) for a probabilistic chance to win greater amounts.

Gambling can take many forms, from sports/track betting to games of luck (roulette,

slots) or skill (poker), but the prevailing notion is the same. Recalling back that most

religions tend to encourage familial responsibilities and moderation of resource

consumption, and recognize that the excessive pursuit of material wealth can interfere

with these, do major religions then have explicit stances regarding gambling?

According to Kevin King (2013), they do, and negatively so. He states that

Hinduism and Buddhism frown upon gambling as non-virtuous and leading to moral and

financial destitution, by placing far too much intrinsic value on external conditions.

Abrahamic traditions (Judaism and Christianity) also discourage and even outright forbid

gambling (Islam), denouncing it as laborless or effort-free wealth acquisition and stealing

from those whom one wins against. However, different sects of these religions hold

varying gradations of attitudes towards behaviors, and therefore it is helpful to examine

gambling behavior across Christian sects.

37

Beginning with participants hailing from Las Vegas itself, Diaz’s (2000) analyses

between Christian denominations found significant negative relationships between

frequency of gambling and religious service attendance and importance of faith.

Gambling frequency also significantly differed across denominations, with Catholics

gambling the most often and Mormons the least often. Furthermore, the average amount

gambled was negatively related to service attendance and importance of faith, but did not

differ across denominations. However, Diaz states many of these correlations were only

weakly significant or of small effect size and could not substantially establish these

relationships. Additionally, Lam (2006), using data from the National Gambling Impact

Commission’s 1999 survey, found similarly consistent results. Gamblers were

significantly less likely to attend religious services than non-gamblers, and the number of

games an individual has played (0-4) emerged as a significant, negative predictor of

service attendance. However, importance of faith was not significantly different between

gamblers and non-gamblers; and while it significantly predicted gambling frequency,

only a small-moderate effect size was observed.

Ellison and McFarland (2011) did a denominational analysis of gambling

behaviors across Christian sects and found significant differences as a function of

religious conservatism. First, conservative Protestants were less likely to engage in mid-

high frequency gambling compared to mainline Protestants, Catholics and non-believers.

Furthermore, conservative Protestants had significantly stronger negative relationships

between gambling and service attendance and percentage of one’s social network

affiliated with their religious congregation - friendships with fellow members and a

38

religious leader acted as a stronger deterrent of gambling propensities than for mainline

Protestants, Catholics and Jews. Lastly, frequency of prayer was not related to gambling

behaviors.

Given the intriguing empirical connections (or lack thereof) between an

individual’s cognitive style, religiosity and risk preferences, little research has focused on

the individual behavioral components of loss aversion as it pertains to religiosity beyond

Rieger and colleagues’ (2011) initial reports on cultural dispositions. Therefore, the

purpose of this study was twofold: to further explore if Christian participants exhibit

greater levels of loss aversion across a series of hypothetical lotteries compared to

Nonreligious participants; and to examine if/which other factors of religiosity may play a

role in differential response patterns.

CHAPTER 6

PRESENT STUDY

METHODS

participants.

250 participants were initially recruited from Amazon’s Mechanical Turk

(mTurk) online survey platform and redirected to the tasks on Qualtrics via an

anonymous link. A power analysis estimated that to detect a moderate effect size (0.5)

with a power of 0.9 and significance level of 0.05 using independent samples, two-tailed t

tests, at least 86 subjects per group were necessary. More participants than recommended

were recruited to adjust for demographically asymmetric response rates and deletion of

39

poor quality data. The total sample used (reduction methods in Appendix A) in the final

analyses was 180 (50% Christian, 54.2% male, Mage = 33.97). Participants were drawn

from a U.S. population, aged 18+, who identified as either ‘Christian’ or ‘Nonreligious’,

and no restrictions on their mTurk worker status (master or non-master classification)

were used. The assessments lasted approximately 15 minutes and participants were

compensated $2.00. This study was approved by the Institutional Review Board at

Arizona State University (see Appendix C for approval documentation).

design and procedure

Participants were first presented with a series of 10 uniformly randomized,

hypothetical lottery tables (Figure 4). Each lottery table consisted of a 50-50 chance to

lose $5-$140 (intervals of $15) and asking the participants to state the minimum amount

they would require to potentially win, in order to make each lottery acceptable to play.

Figure 4. - An example lottery table presented to participants.

This specific method was used as it replicated Rieger and colleagues’ (2011)

design eliciting a simple, yet robust loss aversion coefficient termed the ‘Gain/Loss

Ratio’ (Tversky & Kahneman, 1991). Recall how the participant’s monetary value to

40

make the gamble acceptable is divided by the loss amount originally presented; and the

larger the quantitative coefficient, the greater the inferred loss aversion. G/L ratios of

each loss value and their overall average were calculated and log transformed to

normalize the data.

Next, participants were asked to provide demographic information pertaining to

their age, sex, education status and religious identification. Participants self-identifying as

‘Christian’ were then asked to provide their denomination, how often they attended

religious services, and their frequency of prayer, and then answered the

Intrinsic/Extrinsic (I/E) Religiosity Scale (Gorsuch & McPherson, 1989), three subscales

(Intrinsic, Extrinsic-Personal, Extrinsic-Social) measured on a Likert scale ranging from

0 (Strongly Disagree) to 4 (Strongly Agree). Participants who self-identified as

‘Nonreligious’ were only asked to state if they were ‘Atheist’, ‘Agnostic’, or

‘Unaffiliated’. Both groups of participants then took the nonreligious subscale of the

Nonreligious Nonspiritual Scale (NRNSS; Cragun, Hammer, & Nielsen, 2015), a

questionnaire measured on a Likert scale from 0 (Strongly Agree) to 4 (Strongly

Disagree), developed to validly and reliably measure observable differences of religiosity

and spirituality between religious and nonreligious individuals. As this study was only

interested in religiosity of participants, and for time/compensation purposes, the

spirituality subscale was not used.

The final task consisted of a series of 40 short, uniformly randomized and

individually presented statements sampled from Harris et al.’s (2009) experimental

41

stimuli, in which participants were asked to say whether they believed each statement to

be ‘True’, ‘False’, or ‘Unsure’. The statements were equally split into four categories:

Religiously True/Nonbeliever False - “Jesus really rose from the dead.”

Religiously False/Nonbeliever True - “The Biblical story of creation is false.”

Factually True - “Eagles really exist.”

Factually False - “Superman really exists.”

For reasons of time/compensation, we used this abridged version of their original

240 statements. As all of the religiously oriented statements were confirmed to

significantly differ by religious identity by Harris and colleagues in a pilot study prior to

their main experiment, and these statements do not comprise a conglomerated larger

scale, this subset can be acceptably included for exploratory purposes in relation to the

certainty of ideological affirmation without sacrificing validity or reliability. In addition

to the statement responses, response times were measured to assay whether religious and

nonreligious participants differed in how quickly they affirmed or rejected, or were

unsure of, doctrinal statements [in]congruent with their religious identity.

RESULTS

data analysis

As a manipulation check, a two-tailed t test for independent samples was run in

SPSS V.24 to determine if religious and nonreligious participants differed in their mean

42

responses to the NRNSS. The test revealed significant differences between religious (M =

1.62) and nonreligious (M = 3.48) participants in the expected direction, t(178) = -

13.539, p < .001, 95% CI [-2.14, -1.59].

Reliability analyses using Cronbach’s alpha were conducted for the ten log

transformed G/L Ratios (ɑ = .984), NRNSS (ɑ = .963), I/E Intrinsic subscale (ɑ = .855),

I/E Extrinsic-Social subscale (ɑ = .898), and the I/E Extrinsic-Personal subscale (ɑ =

.677). Because the I/E Extrinsic-Personal subscale is only three items, deletion of items to

improve reliability may cause issues with data analysis.

religious identity and loss aversion

Even after a log transformation correction and much more acceptable levels of

skewness and kurtosis, the Shapiro-Wilk test of non-normality was significant. Therefore,

independent samples Mann-Whitney U tests were used that yielded non-significant

differences between religious and nonreligious participants for every lottery, as well as

the overall averaged G/L Ratio, (p > .05). Table 1 and Figure 5 show the median values

of each lottery and the overall median, as a function of religious identity.

43

Table 1. - Median Loss Aversion Coefficients separated by Religious Identity.

Lottery Value Nonreligious G/L Ratio Religious G/L Ratio

$5 2.00 2.00

$20 2.50 2.50

$35 2.36 2.42

$50 3.00 3.00

$65 2.31 2.46

$80 2.50 2.50

$95 2.53 2.34

$110 2.49 2.73

$125 2.40 2.40

$140 2.50 2.47

Overall Median 2.49 2.47

44

Figure 5. – Median Loss Coefficients by Religious Identity.

Bivariate correlations (Table 2) assessing the relationship between loss aversion

and religious service attendance, frequency of prayer, intrinsic religiosity, extrinsic social

religiosity and extrinsic personal religiosity were all nonsignificant (p > .05). Figure 6

shows the distribution of log Gain/Loss ratios as a function of responding on the NRNSS,

separated by religious identification. These data were analyzed to ascertain if a quadratic

relationship existed, but the R-squared value was only 0.0014.

45

Table 2. - Correlation Table of Average Loss Coefficients and Religious Factors

Variable 1 2 3 4 5 6

1. Log G/L

Ratio

-

2. Service

Attendance

.00990 -

3. Freq. Prayer .06090 .33390** -

4. I/E Intrinsic .02490 -.34090** -.65190** -

5. I/E ext. social -.06690 -.50790** -.05890 .08590 -

6. I/E ext.

personal

.00390 -.06490 -.11390 .144 .15890 -

7. NRNSS avg. .033180 .31490** .46490** -.73490** -.08590 -.2790*

Pairwise N’s are provided in subscript

** Correlations significant at the .001 level (two-tailed)

* Correlations significant at the 0.05 level (two-tailed)

46

Figure 6. - Log Gain/Loss Ratio Religiosity and Identity.

religious statement responding

Pearson Chi-square difference tests in crosstabs analyses replicated Harris and

colleagues’ (2009) results of religious participants significantly affirming doctrinally true

statements and rejecting doctrinally false statements compared to nonreligious

participants. Both groups also correctly validated and rejected factually true and factually

false statements, respectively, at equivalent rates. Although Mann-Whitney U tests

showed no significant difference in the median response time, averaged across all

statements, between religious (Med. = 3.67s) and nonreligious participants (Med. =

3.40s), nonreligious participants responded significantly faster in 10 (50%) religiously

47

oriented statements, and three (7.5%) factual statements (p < .05; see Appendix B for

more details on chi-square and response time analyses).

DISCUSSION

Previous research using monetary gambles has reliably evinced a behaviorally

salient aversion to losses (Kahneman & Tversky, 1979, 1984; Tversky & Kahneman,

1981; Tom et al., 2007), the repercussions of which have been attributed to individuals

deviating from economic rationality in decision-making (Novemsky & Kahneman, 2005).

The reliance on, or slacked monitoring of, intuitive judgments susceptible to emotional

reflexivity (Kahneman, 2003) may lead to this overweighting of negative outcomes, and

has also been linked to the beliefs one holds, such as in the existence of supernatural

beings (Aarnio & Lindeman, 2005, 2007; Shenhav et al., 2012). Experiments testing the

reverse relationship of religiosity predicting risk preferences congruent with intuitive

thinking, while limited, have suggested a similar pattern (Rieger et al., 2011). Thus, the

present study set out to explore how religious identity and its corresponding factors might

relate specifically to loss aversion.

Despite replicating the overall nature of loss aversion within the sample collected

(Med. θ = 2.6), no significant main effect was found between religious and nonreligious

participants. Nor did religious factors significantly predict levels of this aversion. This is

a puzzling result; religious participants responded significantly different from their

nonreligious counterparts on the NRNSS and doctrinal statements, but actually tended to

show lower average loss coefficients. In addition, there was no quadratic relationship

48

between loss aversion and religious responding on the NRNSS present, an analogous

observation Kahan (2012) found when testing political ideology and cognitive style.

Kahan’s results suggested participants with greater political convictions (both

conservative and liberal) provided more reflective answers on Frederick’s (2005)

cognitive reflection test compared to political moderates, and he interpreted this as

ideologues being able to initiate deliberative cognition to rationalize one’s beliefs.

There appears to be no simple explanation for these results. Every study has a

likelihood of yielding null results based on the methods, sample, or merely as a

probabilistic blip, and this present study was not without its limitations. First, previous

studies have linked Christian orthodoxy (Rieger et al., 2011) and intuitive cognition

(Frederick, 2005) to increased loss aversion coefficients, and intuitive cognition to a

general religiosity (Shenhav et al., 2012), but this current experiment did not include

metrics of either religious fundamentalism or intuitive inclinations. Therefore, while the

factors of religiosity utilized did not elicit any significant predictive qualities, it may be

premature to speculate any further without understanding the cognitive strategies

participants implemented when performing this task. Second, a slight modification of the

wording used to present the lotteries was made to fit the constraints of Qualtrics’ API,

possibly leading to some participants interpret the task differently. Third, the overtness of

the recruitment script requiring a [non]religious identity could have also contributed to

this result.

Of course, it is also entirely possible that there are no practical differences

between these groups in terms of loss aversion. Therefore, more research is necessary to

49

either suggest this finding as an outlier or substantiate that the ideology and motivational

factors themselves are not predictive of loss aversion, but rather something the

fundamentalist mindset ideologies can shape. Future studies could incorporate response

times of decisions in the lottery or cognitive style items, as Pennycook, Cheyne, Koehler

and Fugelsang (2013) have shown lengthened response latencies and higher accuracy

rates in analytic reasoning tasks for religious skeptics. Finally, there are a multitude of

possible designs used in loss aversion literature, such as a dichotomous

acceptance/rejection of a gamble, and non-monetary (Asian Disease Problem) or riskless

scenarios, and integrating these along with cognitive attitudes into a religious context

may paint a better picture of this behavior.

50

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APPENDIX A

DATA COLLECTED OCTOBER 2016

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Data from 250 participants were initially collected. However, the final data

analyzed did not reflect this amount as attention tests were failed, and the unconstrained

lottery values were subject to extreme variability resulting in ratios approaching and

occasionally surpassing 100; other participants responded in values below a ratio of 0.50.

To combat this, while still maintaining an essence of the data collected and conforming to

Rieger et al.’s (2011) methodology and power analyses, participants with an average G/L

ratio greater than or equal to 100, or below 0.50 were entirely deleted, as well as any who

failed at least one of the two attention tests. Out of the 250 original participants, 228 were

retained. A second data reduction method was also run to balance religious affiliation

groups by randomly dropping Nonreligious subjects. After this round of deletion, 180 (90

each group) participants were used in the analysis.

Timing data for the affirmation statements were deleted on a case-wise basis. As

the average ‘page submit’ response time was typically around 5 seconds, any RT above

30 seconds will reflect instances above and beyond the required time to read and answer

the question, especially when the participants’ RT for other statements more closely

resembles the average. Overall, only less than 8% of timing data were deleted.

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APPENDIX B

STATISTICAL ANALYSES

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CHI-SQUARE DIFFERENCE TESTS

Examples of each of the four stimuli conditions showing the expected response

[in]congruency as a function of religious or factual statements:

Religiously True: “People who believe in God do so on good evidence”

Christians significantly more likely to affirm this statement, 𝜒2 = 58.397, p < .001

Religiously False: “Jesus really did not rise from the dead”

Christians significantly more likely to reject this statements, 𝜒2 = 109.515, p <

.001

Factually True: “Eating wrong foods can negatively affect health”

Both groups equally likely to affirm this statement, 𝜒2 = .994, p > .05

Factually False: “A high rate of crime is very good for society”

Both groups equally likely to reject this statement, 𝜒2 = 1.006, p > .05

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TIMING DATA

Significant results (medians reported; C = Christian, N = Nonreligious; **denotes a

religiously false statement):

Q16** - Humans are a product of the natural world, just like all other animals.

C = 4.76 N = 3.68 p < .001

Q25** - The Biblical story of creation is purely a myth.

C = 3.98 N = 3.10 p < .001

Q32 - Jesus Christ will literally save all human beings who accept his grace.

C = 4.41 N = 3.42 p < .001

Q43** - Jesus Christ is very unlikely to return to Earth in a Second Coming

C = 4.07 N = 3.64 p = .021

Q44 - A high rate of crime is very good for society.

C = 3.72 N = 3.10 p = .013

Q51 - The Bible is the most important book we have.

C = 3.55 N = 2.72 p < .001

Q52 - Some Christians will probably go to heaven after death.

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C = 3.96 N = 3.65 p = .032

Q54 - Superman is a fictional character.

C = 3.21 N = 2.67 p = .002

Q55 - The airplane is a human invention.

C = 3.04 N = 2.51 p = .001

Q61** - If Jesus existed, he was conceived naturally, like every other human being.

C = 5.11 N = 4.21 p = .005

Q62 - Human cultures are all exactly the same.

C = 3.66 N = 3.02 p = .002

Q65 - The Bible is free from error.

C = 3.38 N = 3.02 p =.042

Q68 - Jesus Christ really performed the miracles attributed to him in the Bible.

C = 3.67 N = 3.04 p = .017

Q73** - Original Sin is nothing more than a myth.

C = 3.54 N = 3.03 p = .011

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APPENDIX C

IRB APPROVAL

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EXEMPTION GRANTED Elias Robles-Sotelo Social and Behavioral Sciences, School of 602/543-4515 Elias.Robles@asu.edu Dear Elias Robles-Sotelo: On 10/6/2016 the ASU IRB reviewed the following protocol:

Type of Review: Initial Study Title: Factors of Religiosity and Loss Aversion Investigator: Elias Robles-Sotelo IRB ID: STUDY00005101 Funding: None Grant Title: None Grant ID: None Documents Reviewed: • Consent Form, Category: Consent Form;

• Stimuli, Category: Measures (Survey questions/Interview questions /interview guides/focus group questions); • Demographics, Category: Measures (Survey questions/Interview questions /interview guides/focus group questions); • mTurkRecruitmentScript.pdf, Category: Recruitment Materials; • Howatt-Robles 2016.docx, Category: IRB Protocol;

The IRB determined that the protocol is considered exempt pursuant to Federal Regulations 45CFR46 (2) Tests, surveys, interviews, or observation on 10/6/2016. In conducting this protocol you are required to follow the requirements listed in the INVESTIGATOR MANUAL (HRP-103). Sincerely, IRB Administrator