[cbx@textcite]nameyeardelim

# Can LLMs Capture Human Preferences? ††thanks: Email addresses<EMAIL_ADDRESS><EMAIL_ADDRESS>
Ali Goli
University of Washington Amandeep Singh
University of Washington

###### Abstract

We explore the viability of Large Language Models (LLMs), specifically
OpenAI’s GPT-3.5 and GPT-4, in emulating human survey respondents and
eliciting preferences, with a focus on intertemporal choices. Leveraging the
extensive literature on intertemporal discounting for benchmarking, we examine
responses from LLMs across various languages and compare them to human
responses, exploring preferences between smaller, sooner, and larger, later
rewards. Our findings reveal that both GPT models demonstrate less patience
than humans, with GPT-3.5 exhibiting a lexicographic preference for earlier
rewards, unlike human decision-makers. Though GPT-4 does not display
lexicographic preferences, its measured discount rates are still considerably
larger than those found in humans. Interestingly, GPT models show greater
patience in languages with weak future tense references, such as German and
Mandarin, aligning with existing literature that suggests a correlation
between language structure and intertemporal preferences. We demonstrate how
prompting GPT to explain its decisions, a procedure we term “chain-of-thought
conjoint,” can mitigate, but does not eliminate, discrepancies between LLM and
human responses. While directly eliciting preferences using LLMs may yield
misleading results, combining chain-of-thought conjoint with topic modeling
aids in hypothesis generation, enabling researchers to explore the
underpinnings of preferences. Chain-of-thought conjoint provides a structured
framework for marketers to use LLMs to identify potential attributes or
factors that can explain preference heterogeneity across different customers
and contexts.

Keywords: Large language models, Intertemporal preferences, Decision making,
Chain-of-thought, Conjoint

> ##  1 Introduction

The rapid development of Large Language Models (LLMs), exemplified by models
like GPT-3.5 and GPT-4, signifies a transformative moment in both artificial
intelligence and the social sciences. These models hold the promise of
potentially understanding and emulating a wide spectrum of human behaviors,
emotions, and preferences. As LLMs become increasingly integrated into our
daily experiences and products like recommender systems, it becomes crucial to
gauge their depth and accuracy in mirroring human decision-making. Such
understanding is not only essential for discerning their potential
applications in business and market research but also vital for informed
product development.

In this study, we seek to assess whether LLMs, such as GPT-3.5 and GPT-4, can
be used for market research and understanding consumer preferences. This
investigation prompts three key questions: (i) Can LLMs “accurately” mimic
human preferences and decision-making? (ii) If unable to accurately mimic
absolute human preference levels, can LLMs capture any meaningful
heterogeneity across customer segments? and (iii) Does eliciting LLMs’
underlying reasoning, by prompting them to explain their choices, better align
their choices with human subjects and provide insight into factors and
mediators that help explain preference heterogeneity?

To examine whether LLMs can accurately mimic human responses, we focus on
intertemporal preferences - choices between immediate and delayed rewards.
This domain offers a robust testbed for assessing LLM preference elicitation
for two key reasons. First, such financial decisions are foundational to
consumption and thus to understanding broader consumer behavior [94]. In fact,
a vast body of literature in marketing and economics has sought to understand
time preferences [68] and its interplay with consumer behavior across
different domains, including credit card debt [72], mortgage choice [71],
retirement savings [56], and educational attainment [75]. Second, there is a
substantial literature dedicated to quantifying discount rates. Such extensive
groundwork offers a robust benchmark against which we can assess LLMs’
reliability in mirroring human preferences [48, 51, 52, 53, 55, 59, 64].

To understand, LLMs’ capability to recognize heterogeneity and correlational
structures in preferences across customer segments, we will specifically look
at their ability to capture the heterogeneity in discount rates across
languages, especially those with weak and strong future tense references (FTR)
[57, 70, 84]. Languages differ in their grammatical expression of future
events through weak or strong FTR. For instance, German, a weak FTR language,
can express future events without a specific future marker by using the
present tense and a temporal adverb, like “Ich gehe morgen ins Kino” (I go to
the cinema tomorrow). Alternatively, an explicit future tense can be created
using “werden” as an auxiliary verb: “Ich werde morgen ins Kino gehen” (I will
go to the cinema tomorrow). In comparison, English, a strong FTR language,
generally requires using “will” or “going to” to indicate future actions, as
in “I will go to the cinema tomorrow.” In weak FTR languages, verbs don’t need
explicit markers for future time, whereas strong FTR languages require
distinct markers to convey the future. Extant research has demonstrated that
speakers of weak FTR languages, like Mandarin and German, display more future-
oriented behaviors such as saving and long-term planning, compared to strong
FTR languages like English and Spanish. [57, 70, 84]. By comparing LLMs’
decisions across languages with weak and strong future-time referencing, we
can evaluate if LLMs are able to capture heterogeneity in intertemporal
preferences across languages.

We find that both GPT-3.5 and 4 are very impatient in our experiments.
Specifically, we find that GPT-3.5 exhibits lexicographic preferences over
time and rewards (in this specific order). This means that the likelihood of
choosing larger, delayed rewards does not shift with changes in interest
rates, which is inconsistent with the intertemporal preferences documented in
human subjects [64]. On the other hand, GPT-4, while showing responsiveness to
interest rate changes, exhibits a pronounced level of impatience compared to
humans. When prompted to explain its decision-making process [81], a procedure
we refer to as “chain-of-thought conjoint”, GPT-4 displays increased patience,
although it still remains more impatient than human decision-makers [48, 51,
52, 53, 55, 59, 64]. Overall our results show that the elicited preferences
are significantly influenced by both the model and the approach used for data
collection. Having said that, we find some evidence that both models may have
the ability to identify relevant language structures across different
languages and possibly among customer segments. For instance, both GPT-3.5 and
GPT-4 display a greater degree of patience in languages with weak FTR compared
to those with strong FTR, aligning with existing literature [57, 70, 84].

While the results from all our studies, including the standard conjoint with
GPT-3.5, GPT-4, and the chain-of-thought conjoint, suggest that using these
models to directly elicit preferences might be misleading, there is potential
for combining the chain-of-thought conjoint outputs with topic modeling
techniques [61]. This combination could be a useful approach for understanding
the underlying factors that explain heterogeneity in preferences. We document
that the topics GPT touches upon vary based on the context and language. For
example, the probability of discussing topics related to risk and uncertainty
increases systematically as the time gap between the smaller-sooner and
larger-later choice increases. Some of these factors, such as the role of risk
and uncertainty in intertemporal preferences, are already discussed in
existing literature [62]. In our view, rather than being a direct tool for
preference elicitation, LLMs can be a valuable resource for identifying
potential factors or mediators that can explain preference heterogeneity
across different contexts. This approach can be used for generating hypotheses
that can then be tested with human subjects.

This study’s findings indicate a pathway for enhancing accuracy in capturing
consumer preference heterogeneity in future systems, though optimally
leveraging LLMs to understand consumer preferences remains a distant prospect.
Our research not only contributes to understanding LLM capabilities at the
intersection of language, time preferences, and decision-making but also
fosters discussions for future research aiming to leverage the continual
evolution of LLMs to enrich and broaden consumer behavior understanding and
predictions across diverse linguistic and cultural landscapes. Moreover, this
research adds to the burgeoning literature on the applications of LLMs in
social science research, providing a new perspective on understanding and
analyzing consumer preferences and decision-making. Complementing studies by
[88], [92], [85], [91], [90], and [83], our findings further investigate the
potential of LLMs in generating responses to economic scenarios, estimating
willingness-to-pay, and mimicking response distributions among various human
subgroups. Although we show that LLMs capture useful heterogeneity across
languages and offer means to enhance elicited preferences through planning
(chain-of-thought), the variability in preferences across models and prompts
suggests LLMs may not imminently replace traditional data collection methods,
such as human subject conjoint studies. Overall, our study advances our
understanding of LLMs’ reasoning abilities, forming a foundation for more
advanced, contextually adept AI systems [87].

##  2 Research Design

###  2.1 Data Collection

In our research, we utilized two models from OpenAI - “GPT-3.5-turbo” and
“GPT-4” - as state-of-the-art representatives of LLMs. For reproducibility, we
used the GPT-3.5-turbo snapshot from March 1, 2023 and the GPT-4 snapshot from
June 13, 2023. GPT-3.5-turbo has an extensive 175 billion parameters, while
GPT-4 represents a significant advancement with 1.7 trillion parameters. We
accessed these models using the OpenAI API in Python which enables users to
interact with the model and collect its responses to specific prompts. The API
also has a “temperature” parameter that varies between 0 and 2 and controls
the stochasticity of the output. Across all our studies, we retained the
default value for this parameter, which is 1, to ensure we get enough
variation across responses.

We conducted two sets of experiments. The first set, involving both GPT-3.5
and 4, encompasses straightforward conjoint-like studies where we ask the
models to choose between two options: one with a smaller, sooner reward and
another with a larger, later reward. Our analysis, detailed subsequently,
reveals that GPT-3.5 exhibits a lexicographic preference; the probability of
choosing the larger, later reward doesn’t change with the reward amounts and
is solely a functions of the distance (time delay) between the two
options.111In the online Appendix, we show that if both options are in the
same timeframe, then GPT-3.5’s choices change as a function of rewards, which
shows that GPT-3.5 has lexicographic preferences over time and rewards. This
behavior is incongruent with documented intertemporal preferences among
humans. Consequently, in the second set of studies that involve chain-of-
thought [81], we focus on GPT-4. Instead of merely requesting a choice from
GPT, we ask it to first elucidate its thought process, which has been
demonstrated to enhance its reasoning in other contexts through “planning”.
Below, we first outline the experiment design for the standard conjoint
experiments and then transition to using chain-of-thought prompting [81] to
collect conjoint data.

###  2.2 Experimental design

This study aims to assess the decision-making abilities of GPT by presenting
it with choices between smaller, sooner rewards and larger, later rewards. To
ensure consistency and avoid currency differences across languages, we frame
the rewards as “tokens” similar to [69]. Also, to ensure the word “token” is
not leading to any unexpected behavior in GPT, we also conduct our study with
currency DKK (for the Danish language) and USD (for the English
language).222This is to compare the results with [64, 59] that conducted their
studies with Danish DKK and those studies performed in English using USD such
as [51, 52]. Each experiment involves querying GPT in a specific language
$\ell$ and asking it to select between two options, $(t_{1},r_{1})$ and
$(t_{2},r_{2})$. Here, $t_{1}$ and $t_{2}$ represent the time until the reward
is received, while $r_{1}$ and $r_{2}$ represent the respective reward amounts
in tokens. Note that $t_{2}>t_{1}$ and $r_{2}>r_{1}$, that is the second
option offers a larger reward to be obtained at a later time, while the first
option presents a smaller reward to be obtained sooner.

In our experiments, we set $t_{1}$ to one month from the present and assign
$r_{1}$ a value of 1000 tokens.333Across all our conditions we set the time of
the sooner, smaller option to one month from now in order to avoid potential
issues arising from present bias [54]. We vary the duration of $t_{2}$ to be
2, 3, 4, 5, 7, 13, 25, or 37 months from now. To calculate the value of
$r_{2}$, we use the formula $r_{1}\cdot(1+i)^{\frac{d}{12}}$, where $d$
represents the time difference between $t_{2}$ and $t_{1}$, and $i$ (interest
rate) takes on one of seven values: 0.05, 0.1, 0.25, 0.5, 0.75, 1, or
2.444[48, 51, 52, 53, 55, 59, 64] report the elicited yearly discount rates
across a number of studies on human subjects, and the estimated discount rates
were all below 100%; therefore, we believe the current range is large enough
to generate enough variation for estimating discount rates. In total, we have
63 cells per language, representing 9 delay and 7 interest conditions. The
values of $r_{2}$ for each cell are presented in Table 1.

Table 1: Values of $r_{2}$ across experimental cells, represented by the time difference between the options in months ($d=t_{2}-t_{1}$) and the yearly interest rate ($i$). Note that the first reward is always delivered in a month from now ($t_{1}=1$), and its value is fixed at $r_{1}=1000$ tokens. Interest ($i$) (% per year) | Difference ($d$) between $t_{2}$ and $t_{1}$ (Months)
---|---
| 1 | 2 | 3 | 4 | 6 | 12 | 18 | 24 | 36
5 | 1004 | 1008 | 1012 | 1016 | 1024 | 1050 | 1075 | 1102 | 1157
10 | 1007 | 1016 | 1024 | 1032 | 1048 | 1100 | 1153 | 1210 | 1331
25 | 1018 | 1037 | 1057 | 1077 | 1118 | 1250 | 1397 | 1562 | 1953
50 | 1034 | 1069 | 1106 | 1144 | 1224 | 1500 | 1837 | 2250 | 3375
75 | 1047 | 1097 | 1150 | 1205 | 1322 | 1750 | 2315 | 3062 | 5359
100 | 1059 | 1122 | 1189 | 1259 | 1414 | 2000 | 2828 | 4000 | 8000
200 | 1095 | 1200 | 1316 | 1442 | 1732 | 3000 | 5196 | 9000 | 27000

We survey GPT across 22 languages555Each time we communicate in a language
other than English, we create a new instance of GPT to translate the prompts
from English into that language.: Arabic, Bengali, Danish, English, Estonian,
Finnish, French, German, Hindi, Indonesian, Italian, Japanese, Korean, Malay,
Mandarin, Norwegian, Portuguese, Russian, Spanish, Swedish, Thai, and
Vietnamese. The list comprises the top 10 languages with the largest number of
native speakers, such as English, Mandarin, Hindi, Spanish, and French, as
well as a set of languages with weak FTR, including German, Indonesian,
Norwegian, and Japanese. We use the categorization in [70] to classify
languages as weak or strong FTR, and in total, we have 10 weak FTR languages,
including Danish, Estonian, Finnish, German, Indonesian, Japanese, Malay,
Mandarin, Norwegian, and Swedish. In the next section, we provide a detailed
account of the prompts submitted to GPT across the different languages.

###  2.3 Standard conjoint (GPT-3.5 and 4)

For every query to Open AI one has to send the entire history of previous
conversations for GPT to understand the context of the conversation. Every
query is treated as a fresh instance and the conversation history is the only
way GPT model understands context [93]. For our study, we first initialize the
Chat GPT model with the following prompt:

“Assuming you are a survey participant and you are paid in tokens, please wait
for my prompt and tell me whether you prefer option (1) or option (2). There
is no need to explain your choice, simply answer with (1) or (2).”

Due to the stochastic nature of generative models, GPT may or may not comply
with a given prompt. It might respond by stating its readiness for input or
mention that, as an AI language model, it does not have preferences, as shown
in the left panel of Figure 1. GPT keeps track of the conversation by
maintaining the context in a list called “conversation history,” which records
both user prompts and its own responses. To prevent instances where GPT
declines to participate in the survey and to eliminate dependence across
samples through the conversation history, we consistently reset its history
and obtain samples by initializing the first prompt presented above.
Additionally, we modify GPT’s response to our first prompt in the conversation
history list to:

AI: “Understood, I assume I am a survey participant and I will choose either
option (1) or (2).”

In essence, our approach involves initiating a conversation that always begins
with these two prompts, as seen in the right panel of Figure 1. This strategy
enables us to sample from the distribution of choices _conditional_ on GPT
agreeing to participate in the survey, thus reducing the likelihood of it not
making a choice in subsequent questions. To acquire each sample, we reset the
history, provide only the first two prompts as displayed in Figure 1, and then
present the question asking GPT to choose between sooner, smaller rewards and
larger, later rewards.

Figure 1: Comparison of the standard prompting method without modifying AI
history on the left, versus our approach that involves passing an edited AI
history and the subsequent questions presented to GPT on the right.

Choice Order Sensitivity: GPT is known to be order sensitive [80, 89, 85, 86],
exhibiting a higher likelihood of choosing the first-listed option when
presented with multiple choices. To account for this across all our
experimental cells, we shuffle the order of the options such that the sooner,
smaller option appears as (1) half of the time and as option (2) during the
other half.

###  2.4 Chain-of-Thought Conjoint (GPT-4)

Given the complexities involved in intertemporal trade-off decision-making, we
also try using a chain-of-thought conjoint approach using GPT-4. This involves
prompting GPT-4 to generate a chain of reasoning steps elucidating its thought
process when choosing between smaller, sooner rewards and larger, later
rewards. Drawing inspiration from the research by [81], which posits that
chain-of-thought prompting can significantly enhance the reasoning
capabilities of LLMs, we incorporate this technique to evaluate its potential
impact on GPT-4’s intertemporal choices.

Here, GPT-4 is queried to make an intertemporal trade-off decision and provide
a brief chain of thought explaining its reasoning. Our prompt becomes:

“Assuming you are a survey participant and you are paid in tokens, please wait
for my prompt and tell me whether you prefer option (1) or option (2). Think
step by step, and explain your decision”

We also accordingly modify the GPT’s response to our first prompt in the
conversation history list to:

“Understood, I assume I am a survey participant and I will explain my decision
and then choose either option (1) or (2).”

This serves two goals: First, it provides insights into the decision-making
process and attributes presented in response to a prompt. Specifically, it
helps us examine the reasons and attributes that GPT lists across different
contexts and languages. Second, it enables us to evaluate the impact of
generating a reasoning chain (similar to priming in human subjects) on GPT’s
final decision. In this approach, GPT typically lists a set of reasons before
deciding to choose either the smaller, sooner option or the larger, later one
(see Figure 5 for an example). It is important to recall that LLMs
fundamentally sample from a conditional distribution. Our approach allows GPT
to initially outline attributes that matter for this decision, such as
uncertainty and opportunity cost, and then make a decision conditional on the
conversation history which now includes attributes that are likely relevant to
this choice. This technique has been shown to assist GPT in solving puzzles
and enhancing its decision-making, as illustrated by [81, 87]. Given the
complex nature of the output in this exercise, we employ GPT itself to extract
the answer. After GPT presents its initial response, we query it again,
prompting it to choose either option (1) or (2) and print the selection.

This querying method is more expensive than the standard conjoint as GPT-4
bills based on both input and output tokens. The chain-of-thought conjoint
substantially increases the length of printed tokens. To keep the experiment’s
cost manageable, we collect 10 samples for each of the 63 experimental
conditions described in section 2.2 across the 22 languages studied, which
amounts to $63\times 22\times 10=13860$ samples. Since the introspection or
listed reasons by GPT could provide insights into drivers of heterogeneity
across languages and contexts, we translate GPT’s responses from these
languages into English for analysis of the underlying reasons.666We use
another instance of GPT to translate responses into English. We do not expect
a new instance to alter the meanings in translations; however, we acknowledge
that one may want to use another service, such as Google Translate, to ensure
the results are robust. Similar to our approach in section 2.3, we shuffle the
order of the options such that the sooner, smaller option appears as option
(1) half of the times and as option (2) in the other half within each
experiment cell.

##  3 Empirical Analysis

Our experimental conditions involve variations in model, language, delay, and
interest rate levels. In this section, we present results from three sets of
studies: (1) standard conjoint with GPT-3.5, (2) standard conjoint with GPT-4,
and (3) chain-of-thought conjoint using GPT-4.777Our analysis of standard
conjoint, which we report below, revealed that GPT-3.5 is lexicographic in
time delay and rewards, inconsistent with human decision-makers. We chose to
experiment with the chain-of-thought approach using the more advanced GPT-4
model, which is not lexicographic. For studies (1) and (2), we follow the
steps outlined in section 2.3, and for study (3), we follow section 2.4. For
each of these studies, we submit queries across 22 distinct languages, 9 delay
conditions, and 7 interest rate values. For GPT-3.5, we draw 100 samples per
condition, while for studies involving GPT-4, we draw 10 samples due to cost
and query limits.888GPT-4 has lower query limits and costs about 30 times more
than GPT-3.5 as it bills based on both input and output tokens’ length. This
results in a total of $22\times 9\times\ 7=1386$ experimental cells, with 100
samples for GPT-3.5 and 10 samples for GPT-4 per cell. In this section, we
examine the heterogeneity in choices across different studies (standard
conjoint with GPT-3.5, GPT-4, and chain-of-thought conjoint with GPT-4),
language, and interest rate. Subsequently, we investigate whether the choices
made by GPT mirror those of real-life human decision-makers and evaluate if
using chain-of-though methods [81] affects the outcomes.

The subsequent sections aim to answer the following: (i) Can LLMs “accurately”
reflect human intertemporal preferences and decision-making? (ii) If they
cannot perfectly emulate absolute human preference levels, can LLMs discern
meaningful heterogeneity across languages, especially across strong or weak
FTR languages? and (iii) Does prompting LLMs to explain the reasoning (chain-
of-thought conjoint) better align their choices with human subjects and
provide insights on factors and mediators that could explain preference
heterogeneity?

###  3.1 Heterogeneity across models and languages

First, we analyze the variation in decision-making across languages by
examining the probability of selecting the larger, delayed reward for each
language across all experimental cells, as seen in Figure 2. The patterns in
Figure 2 reveal that:

  1. (a)

GPT selects the larger, later reward only $22\%$ of the time on average in
standard conjoint studies using GPT-3.5 and $16\%$ for GPT-4. However,
employing the chain-of-thought approach increases this rate to $34.5\%$ for
GPT-4.

  2. (b)

There is significant heterogeneity across languages. For instance, the
probability of opting for the larger, delayed reward ranges from $37.2\%$
(GPT-3.5) and $29\%$ (GPT-4) for Malay to a mere $6.6\%$ (GPT-3.5) and $4.9\%$
(GPT-4) for Russian. However, across most languages, the probability of
choosing the larger, later reward increases when using the chain-of-thought
approach.

The rank ordering of preferences across languages differs significantly
depending on the method used to elicit intertemporal preferences. This
variation is somewhat anticipated when contrasting the standard conjoint with
the chain-of-thought conjoint, as the latter can act as a form of priming,
potentially influencing heterogeneity across languages. Even in human
subjects, introspection has been shown to impact decision-making [50, 49, 67,
77]. Nonetheless, the discrepancy in elicited preferences between the standard
conjoint approaches of GPT-3.5 and GPT-4 is concerning for researchers seeking
to elicit preferences using LLMs. In the following section, we delve deeper
into these findings, ensuring they adhere to some regularity conditions before
employing them to estimate discount factors.

Figure 2: Share of delayed reward choices across languages. The displayed
intervals correspond to the 95% confidence intervals, clustered at the
experimental cell (language-delay-interest) level. Languages with strong FTR
are displayed in bold font and clustered on top.

###  3.2 Heterogeneity across model and interest $(i)$ conditions

Above, we examined how GPT choices vary across languages and different model.
In this section, we explore how GPT choices change as the interest rate
increases. Recall that GPT is presented with a choice between a smaller,
sooner reward of $r_{1}=1000$ tokens at time $t_{1}$ (a month) from now, and a
larger, later reward of $r_{2}=1000\cdot(1+i)^{\frac{d}{12}}$, where
$d=t_{2}-t_{1}$ and $i$ represents the interest rate. Holding all other
factors, including the delay $d$, constant, the larger, later reward becomes
(weakly) more attractive as the interest rate $(i)$ increases. Figure 3
depicts the propensity to choose the larger, later reward as a function of
different interest rate ($i$) levels.

The patterns in Figure 3 offer two key insights. First, the choices recorded
using the chain-of-thought conjoint method are more responsive to changes in
the interest rate, i.e., the probability of choosing the larger later reward
as a function of interest rate ($i$) increases more rapidly with the chain-of-
thought conjoint compared to the standard GPT-4 conjoint. Second, our results
underscore a significant difference between GPT-3.5 and GPT-4. While the
probability of choosing the larger, later option increases as the interest
rate rises in experiments (2) and (3), which were run on GPT-4, this
probability does not change as a function of the interest rate in experiment
(1), which was run on GPT-3.5.

For GPT-3.5, the probability of choosing the larger, later reward remains
relatively stable across a wide range of interest rate conditions, varying
from 5 to 200% per year. This behavior is peculiar, as human decision-makers
do alter their intertemporal choices when they are offered higher interest
rates, as evidenced by, for example, [64]. The patterns in Figure 3, along
with our analysis in the online Appendix, reveal that GPT-3.5 is lexicographic
across time and rewards, and does not respond to changes in interest rates
offered (which affects the gap in reward sizes).999In the online Appendix, we
show that GPT-3.5’s choices do change as a function of rewards if both options
are presented within the same timeframe, indicating that GPT-3.5 exhibits
lexicographic preferences in time and rewards (in this specific order). This
finding implies that GPT-3.5’s choices are not consistent with exponential,
hyperbolic, or any other well-known random utility model where utility changes
as a function of the offered interest rate. For that reason, from this point
forward, we will focus only on responses provided by GPT-4.

Figure 3: Proportion of larger, delayed reward selection across different
interest rate $(i)$ conditions. The displayed intervals correspond to the 95%
confidence intervals, clustered at the level of experimental cells (language-
delay-interest).

###  3.3 Identifying discount rate

Now, instead of looking at the proportion of later reward choices, we will
examine the discount rates implied by GPT’s choices. To estimate these
discount rates, we will use the discounted random utility model from [60] and
[64] to specify the likelihood of GPT’s choices given the model. This model
assumes that the probability of choosing, say, the sooner option is equal to
the associated net present value of the expected payoff, raised to the power
of $\frac{1}{\mu}$, denoted as
$\left(\mathbb{E}U_{\mathrm{sooner}}\right)^{\frac{1}{\mu}}$, divided by the
sum of the expected payoffs raised to the power of $\frac{1}{\mu}$,
$\left(\mathbb{E}U_{\mathrm{sooner}}\right)^{\frac{1}{\mu}}$ and
$\left(\mathbb{E}U_{\mathrm{later}}\right)^{\frac{1}{\mu}}$, for the two
options:

$Pr(\text{choose option
sooner})=\frac{\mathbb{E}U_{\mathrm{sooner}}^{1/\mu}}{\left(\mathbb{E}U_{\mathrm{sooner}}^{1/\mu}+\mathbb{E}U_{\mathrm{later}}^{1/\mu}\right)},$

where $\mu$ is a structural “noise parameter” that captures the sensitivity of
choice probabilities to differences in payoffs. For instance, if
$\mu\rightarrow 0$, then decisions are deterministic as a function of
differences in payoffs, and the option with a higher net present value gets
picked with probability 1. Conversely, as $\mu\rightarrow\infty$, the decision
to pick each option becomes 50% and is insensitive to differences in payoffs.
The net present payoff of an option that delivers reward $r$ in $d$ months
from now is equal to:

$\mathbb{E}U(r,d)=\frac{r}{(1+\delta)^{(\frac{d}{12})}},$

where $\delta$ is the discount rate, and $\frac{1}{1+\delta}$ is the implied
yearly discount factor. Given estimates of $\delta$ and $\mu$, along with the
observed choices between sooner and later monetary options, the likelihood
function for the model can be written as:

$\ln L(\delta,\mu;\text{data})=\sum_{i}\biggl{[}y_{i}\log Pr_{i}(\text{choose
option sooner})+(1-y_{i})\log(1-Pr_{i}(\text{choose option
sooner}))\biggr{]},$

where $y_{i}=1$ if GPT chose the sooner option for instance $i$, and 0
otherwise. The likelihood sums the log probability of the observed choices
across all GPT instances conditional on the model parameters. We estimate the
parameters $\delta$ and $\mu$ by choosing the ones that maximize the log-
likelihood of the observed choices.

For each of the 22 languages in our data, we follow the described procedure to
estimate $\mu$ and $\delta$. Figure 4 displays the estimated $\delta$ values
across these languages. A lower discount rate $(\delta)$ indicates greater
patience. Recall that the yearly discount factor is given by
$\frac{1}{1+\delta}$. Hence, a discount rate $\delta$ of 2 (200%) implies that
the value of a dollar or token a year from now equates to
$\frac{1}{1+\delta}=33$ cents in today’s terms.

Figure 4: Estimates for $\delta$ across different languages using both
standard (red circles) and chan-of-thought conjoint (blue triangles). The
intervals are 95% confidence intervals. Languages with strong FTR are
displayed in bold font and clustered on top.

The discount rate ($\delta$) reflects the extent to which intertemporal
choices are influenced by changes in the implied interest rate. Our findings
in Figure 4 reveal substantial heterogeneity across languages. Many
researchers have demonstrated that consumers who speak languages with a weak
FTR exhibit more patience (smaller $\delta$) compared to those who speak
languages with a strong FTR [57, 70, 84]. Of the 22 languages studied here, 10
(Danish, Estonian, Finnish, German, Indonesian, Japanese, Malay, Mandarin,
Norwegian, and Swedish) are weak FTR, while the rest are strong FTR languages.
We pool the data from strong and weak FTR languages and estimate a pooled
$\delta$ and $\mu$ for each of these groups for the standard conjoint GPT-4
and the chain-of-thought conjoint GPT-4. For the standard conjoint, the
estimated 95% confidence interval for $\delta$ was [1.715, 1.948] for the weak
FTR language pool and [1.948, 2.210] for the strong FTR language pool. These
figures for the chain-of-thought conjoint were [1.206, 1.367] and [1.301,
1.470], respectively. Interestingly, across both studies, GPT displayed more
patience (smaller $\delta$) when queried in weak FTR compared to strong FTR.

While the results above are encouraging and suggest that GPT might indeed
capture intriguing heterogeneities across languages, the estimated discount
rates are notably larger than those documented in previous literature. For
example, [48, 51, 52, 53, 55, 59, 64] have run experiments in similar time
frames, and in all of these studies, the estimated discount rate $\delta$ is
below one. Notably, all $\delta$ values obtained using the standard conjoint
with GPT-4 exceed 1.101010To make it comparable with studies that used dollars
instead of say token, we also ran additional experiments where we used US
Dollars instead of tokens in English, and the estimated $\delta$ was 1.188
(0.018) compared to a range of 0.04 to 0.3 discount rates reported in [51,
52]. We also used Danish Kroner (DKK) in Danish, and our estimate of $\delta$
was 1.287 (0.114) compared to 0.28 and 0.252 in [59, 64]. For many languages,
these values continue to exceed 1 even when considering the chain-of-thought
conjoint results. However, our findings suggest that preferences elicited
using the chain-of-thought conjoint more closely align with those documented
in the literature for human subjects [48, 51, 52, 53, 55, 59, 64]. Given that
a prompting procedure similar to the chain-of-thought can also influence
decisions in human participants, as evidenced by [50, 49, 67, 77], one must
exercise caution when directly comparing $\delta$ values from the chain-of-
thought conjoint method to studies that only present participants with
“smaller, sooner” and “larger, later” options. Nonetheless, our results
suggest that the chain-of-thought approach reduces the disparity between the
$\delta$s measured in this study and those observed in human subjects. In the
subsequent section, we demonstrate that the chain-of-thought conjoint method,
when used with LLMs, offers an additional benefit: the LLM first lists a set
of attributes or features relevant to the decision and then makes a decision.
This insight is valuable as it provides a window into which attributes or
features are of greater importance for each decision. Additionally, it is
worth noting that even if LLMs are not directly useful for eliciting
preferences, variations across languages and choices could provide insights
into the underlying differences across attributes considered in different
decisions. Below we discuss these points in greater detail.

###  3.4 Analyzing responses in chain-of-thought conjoint

In the chain-of-thought conjoint method, GPT is prompted to “think step by
step.” Below, in Figure 5, we present an example where GPT is tasked with
choosing between 1000 tokens in a month and 1562 tokens in 25 months from now.
Multiple factors are discussed. Firstly, there is a brief discussion on the
immediacy or urgency of needs. This is followed by a discussion on the time
value of money, or opportunity cost (alternative investment opportunities).
Our objective is to determine if the topics discussed vary systematically
across different delay, interest rate, and language conditions. This
examination is important as it can offer insights into the deliberations of
human decision-makers across different choices. It might also help explain
certain observations, such as why discount rates tend to vary over different
time horizons [58, 62], suggesting that the weight of factors and attributes
that decision-makers might consider could change as the time horizon shifts.

Figure 5: An example response from GPT-4 Using Chain-of-Thought conjoint
prompting.

s

To investigate the text, we use Latent Dirichlet Allocation (LDA) topic
modeling [61]. We follow these steps: First, we translate all responses to
English. Second, we tokenize the text into individual words and convert them
to lowercase for consistency. We eliminate standard English stopwords,
context-specific stopwords, numerics, and words shorter than three characters.
Then we employ the PorterStemmer, a well-established algorithm, to condense
words to their root form, ensuring that various morphological variations of a
word are treated as a single entity. Third, we utilize a bag of words model
and apply LDA, a probabilistic model designed to discover a predetermined set
of latent topics in text corpora. In this context, it is set to identify 4
topics.

Subsequently, we extract the top words associated with each identified topic
along with their respective probability values to discern the primary themes
of each topic. Table 2 presents the top 20 words for each topic. It is
noteworthy that the PorterStemmer yields the roots of words, leading to terms
like “uncertainti”, “valu”, and “immedi”. Topic 1 primarily centers on risk
and uncertainty, topics 2 and 4 delve into opportunity cost and alternative
investment options, while topic 3 concerns urgent or immediate needs. We have
also created an interactive web-based visualization that allows one to explore
the topics discovered by the LDA model, their prominence, and relationships in
a more intuitive way. It can be reached at this anonymous link https://mksc-
llm.tiiny.site/. One can for instance click on the word “risk”, and that
highlights the topics (topic 1) with the highest association with the word.

Topic 1 | Topic 2 | Topic 3 | Topic 4
---|---|---|---
valu | risk | option | receiv | need | option | money | valu
receiv | option | wait | month | valu | choos | receiv | invest
may | time | choos | time | month | immedi | time | futur
month | futur | use | one | wait | receiv | month | potenti
consid | choos | addit | invest | consid | factor | option | amount
chang | factor | consid | therefor | howev | decis | use | worth
one | prefer | earlier | offer | futur | make | earn | one
wait | chip | may | although | urgent | increas | choos | due
uncertainti | decreas | get | two | depend | financi | opportun | prefer
also | immedi | reason | prefer | time | n’t | consid | decis
Table 2: Top 20 words for each topic.

In the following, we use the label “risk and uncertainty” for topic 1. We
create an umbrella topic by merging topics 2 and 4 and labeling it “investment
and opportunity cost,” and we name topic 3 “urgent and immediate needs.” Using
the trained LDA model, we can assign each of the descriptions generated by
GPT-4 to a mix of these three topics. That is, each description will be
assigned a vector of three probabilities, reflecting the mix of topics
discussed. In Figures 6-7, we display the probability of each topic across
different interest and delay conditions. A few interesting patterns emerge.
First, when a larger interest is offered (Figure 6), the probability of
discussing opportunity cost or alternative investments decreases, with
discussions about urgent and immediate needs taking their place. Notably,
throughout different ranges of interest rates, the probability of the “risk
and uncertainty” topic remains flat. Second, as the time delay between the two
options increases (Figure 7), the share of the “risk and uncertainty” topic
goes up, suppressing discussions on opportunity cost without affecting
discussions of urgency.

These patterns are intriguing and parallel how human decision-makers might
allocate priorities or mental resources across various factors, including
urgency, uncertainty, and opportunity cost. For instance, these results can be
used to understand the role of risk and uncertainty and why humans have
different discount rates over different time horizons [58, 62]. They can also
explain why consumers opt for choices with a higher variety for later periods
[66]. This suggests that even if chain-of-thought conjoint analyses might not
be directly useful for eliciting preferences, they could help formulate
hypotheses for testing with human subjects, thus aiding in understanding the
underpinnings of preferences. The patterns in Figures 6-7 can be generated for
other decisions or conjoint exercises to propose hypotheses for
factors/mediators that might influence decisions.

((a)) Risk and Uncertainty

((b)) Opportunity cost

((c)) Urgency

Figure 6: Probability of each topic across different interest conditions. The
displayed intervals correspond to the 95% confidence intervals, clustered at
the level of experimental cells (language-delay-interest).

((a)) Risk and Uncertainty

((b)) Opportunity cost

((c)) Urgency

Figure 7: Probability of each topic across different delay conditions. The
displayed intervals correspond to the 95% confidence intervals, clustered at
the level of experimental cells (language-delay-interest).

We can repeat this exercise across various languages. In Figure 8, we display
the propensity of each topic across the 22 languages studied here. Significant
heterogeneity is observed across languages. These patterns highlight how GPT
discusses or considers different sets of topics across languages in the
context of intertemporal choices. Likely, these differences arise from
variations in topic co-occurrences across different cultures and languages
when discussing intertemporal choice. To demonstrate why this information
might be valuable to researchers, let’s identify which topic varies the most
between weak and strong FTR languages. To achieve this, consider the following
specification:

$\mathbf{Y}_{k}=\alpha\cdot\mathbbm{1}_{\ell_{k}\in\mathcal{S}}+\eta_{d_{k}i_{k}}+\epsilon_{k},$
(1)

where $k$ indexes the sample, and $\ell_{k}$ is the query language used for
drawing sample $k$. The interest rate and the delay for the experiment
condition corresponding to sample $k$ are represented by $i_{k}$ and $d_{k}$,
respectively. $\mathcal{S}$ is the set of languages with strong FTR in our
dataset. $\mathbf{Y}_{k}$ is the normalized propensity of a given topic which
is calculated as the probability of a given topic in the query response
divided by the average probability of that topic across all queries. This
helps us normalize for differences in the overall prevalence of different
topics, and the coefficient $\alpha$ can be interpreted as the percentage
difference in the prevalence of a given topic in weak relative to strong FTR
languages. Finally, $\eta_{d_{k}i_{k}}$ represents the interest-delay fixed
effects. By including these fixed effects in the regression, we are
essentially comparing different languages (those with strong and weak FTR) for
the same set of interest-delay conditions and investigating whether the
likelihood of choosing the larger, later option systematically differs between
languages with strong and weak FTR.

The results from specification (1) for each of the three topics-risk and
uncertainty, opportunity cost, and urgency-are displayed in Table 3. The
results indicate that the topic of risk & uncertainty is discussed 20% less
frequently than average in strong FTR languages. This figure is 13.8% for
opportunity cost and -8.3% for urgency. This suggests that the difference in
intertemporal preferences between strong and weak FTR languages might
primarily be due to differences in risk and uncertainty aversion.
Interestingly, the difference in risk-taking between weak and strong FTR
languages in corporates and banks has been documented in the corporate finance
literature [73, 78].

Our analysis above showcases that such variations might help researchers
identify factors or mediators that influence choices across different customer
segments or choice contexts. Given the role of language in our perception, we
believe our results underscore GPT’s potential to pinpoint areas and factors
that could explain differences in consumer preferences. However, we do not
believe that GPT can be used to directly elicit preferences.

((a)) Risk and Uncertainty

((b)) Opportunity cost

((c)) Urgency

Figure 8: Probability of each topic across different delay conditions. The
displayed intervals correspond to the 95% confidence intervals, clustered at
the level of experimental cells (language-delay-interest). Languages with
strong FTR are displayed in bold font.  Table 3: Differences in prevalence of
topics across strong and weak FTR languages.

| Dependent variable: Prevalence of topic (normalized)
---|---
| Risk & Uncertainty | Opportunity cost | Urgency
| (1) | (2) | (3)
Strong FTR |  $-$0.209∗∗∗ | 0.138∗∗∗ |  $-$0.083∗∗∗
| (0.025) | (0.015) | (0.021)
Observations | 13,860 | 13,860 | 13,860
R2 | 0.086 | 0.169 | 0.128
Adjusted R2 | 0.082 | 0.165 | 0.124
Residual Std. Error (df = 13796) | 1.146 | 0.600 | 0.762
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
All regressions include delay-interest fixed effects.
All standard errors are clustered at the experimental cell (language-delay-
interest) level.

##  4 Discussion and Conclusions

Arguably, one of the most notable advancements in AI research in recent years
has been the emergence of LLMs. Built on the Transformer architecture [74],
these models focus on predicting subsequent words, enabling LLMs to generate
“plausible” text based on extensive training data. LLMs have demonstrated
exceptional performance in tasks such as coding, music, and abstraction [87].
The vast size of LLMs could lead to the development of “neural circuits” that
specialize in certain tasks or reasoning within specific contexts [79, 82].

Owing to the capacity of LLMs to mimic humans across various contexts and
their inherent stochastic nature, social scientists have explored their use in
producing survey samples. They achieve this by employing different contexts,
such as prompting GPT to emulate responses generated by distinct demographic
groups [88, 85, 92, 83]. These prompts enable LLMs to draw response samples
conditional on the given context, like sociodemographic groups. To test this
capability, we use GPT-3.5 and 4 to measure intertemporal preferences. The
focus on intertemporal preferences is due to (a) the existence of a large body
of literature that can be used for benchmarking and understanding properties
of such preferences, (b) the literature that documents systematic differences
in intertemporal preferences across languages, and (c) the potential of LLMs
to recommend products or educate users on products involving intertemporal
trade-offs such as mortgages, investments, and insurance services. This
potential prompts us to investigate if LLMs are indeed able to make such
trade-offs.

In this paper, we document that GPT’s choices in intertemporal trade-offs
change systematically when it is queried across different models (GPT-3.5
versus 4), different ways to query (chain-of-thought versus standard
conjoint), and across languages. We show that GPT-3.5 displays lexicographical
preferences when confronted with intertemporal trade-offs, favoring immediate
rewards but struggling to effectively trade off smaller, sooner rewards with
larger, later ones. This pattern changes for GPT-4, but we still document
larger discount rates than those measured among human subjects. We propose an
alternative to the standard conjoint with LLMs, which we call “chain-of-
thought conjoint.” We show that GPT exhibits more patience when queried using
the chain-of-thought conjoint approach. Given the extent of changes across
different ways of eliciting preferences, we argue that eliciting preferences
directly using GPT responses could be misleading. Interestingly, however, we
show that by using a combination of topic modeling and chain-of-thought
conjoint one can generate a set of topics or mediators that play a role in
decision-making and then test them in human subjects. Furthermore, across our
experiments, GPT exhibits greater patience in languages with weak FTR, such as
German and Mandarin, compared to those with strong FTR, like English and
French. These results are consistent with prior literature on the impact of
language on intertemporal preferences and suggest that GPT can be a useful
tool for understanding how language or other factors might influence consumer
behavior. These results indicate that, while using GPT to directly elicit
preferences could be misleading, GPT can play an important role in generating
hypotheses that can help researchers understand the underpinnings of
heterogeneity in preferences across context and customer segments.

## Funding and Competing Interests Declaration

All authors certify that they have no affiliations with or involvement in any
organization or entity with any financial interest or non-financial interest
in the subject matter or materials discussed in this manuscript. The authors
have no funding to report. [sorting=nty]

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## Online Appendix: Further Investigation of GPT-3.5 Choices

The findings presented in section 3.1 demonstrate that GPT-3.5’s choices do
not vary as a function of different interest rates offered. This pattern is
strange and is not consistent with a discounted utility decision maker or
humans [64]. In this online appendix, we delve deeper into decisions made by
GPT-3.5, first by investigating differences across strong and weak FTR
languages, and then by formally showing that GPT-3.5 exhibits lexicographic
preferences in terms of time and rewards.

### Strong versus weak FTR languages (GPT-3.5)

The observations in Figure 2 emphasize the potential role of language in time
preferences, consistent with previous findings by [70] and others [57, 65,
84]. Our results in Figure 3 show that GPT-3.5 decisions are not consistent
with any discounted utility decision models (see above) or decision-making by
humans. Therefore, the data from GPT-3.5 decisions are not suitable for
estimating a discount rate in a discounted utility model. However, we now
examine whether GPT-3.5 is more likely to choose the larger, later reward in
languages with strong FTR compared to those with weak FTR. We consider the
following specification:

$\mathbf{Y}_{k}=\alpha\cdot\mathbbm{1}_{\ell_{k}\in\mathcal{S}}+\eta_{d_{k}i_{k}}+\epsilon_{k},$
(2)

where $k$ indexes the sample, and $\ell_{k}$ is the query language used for
drawing sample $k$. The interest rate and the delay for the experiment
condition corresponding to sample $k$ are represented by $i_{k}$ and $d_{k}$,
respectively. $\mathcal{S}$ is the set of languages with strong FTR in our
dataset. $\mathbf{Y}_{k}$ is a dummy variable that equals one if the larger,
later option was selected. Finally, $\eta_{d_{k}i_{k}}$ represents interest-
delay fixed effects. By including these fixed effects in the regression, we
are essentially comparing different languages (those with strong and weak FTR)
for the same set of interest-delay conditions and investigating whether the
likelihood of choosing the larger, later option systematically differs between
languages with strong and weak FTR.

We display the estimates for equation (2) in Table 4. The first column
presents the estimates without any fixed effects, and we progressively include
additional fixed effects as we proceed to the third column. The standard
errors are all clustered at the experimental cell (language-delay-interest)
level. Our findings remain consistent as we include more fixed effects. Our
preferred specification with Delay-Interest fixed effects shows that GPT-3.5
is 2.8% less likely to choose the larger, later reward when queried in
languages with strong FTR, compared to its responses in languages with weak
FTR. These results are consistent with previous studies such as [70, 57, 76].
However, the patterns in Figure 3 indicate that GPT-3.5’s decisions do not
vary with changes in the interest rate and remain relatively stable across a
wide range of interest rate conditions, varying from 5 to 200% per year. These
patterns are peculiar, as human decision-makers do alter their intertemporal
choices when interest rates increase, as evidenced by, for example, see [64].
In the next section, we examine whether GPT-3.5’s choices satisfy simple
regularity conditions that one would expect human choices to adhere to.

Table 4: The difference in the propensity of selecting the larger, later
option between languages with strong and weak FTR.

| Dependent variable:
---|---
| Choosing the delayed reward
| (1) | (2) | (3)
Strong FTR |  $-$0.028∗∗∗ |  $-$0.028∗∗∗ |  $-$0.028∗∗∗
| (0.009) | (0.007) | (0.007)
Constant | 0.232∗∗∗ |  |
| (0.006) |  |
Delay FE |  | X |
Delay-Interest FE |  |  | X
Observations | 138,600 | 138,600 | 138,600
R2 | 0.001 | 0.050 | 0.059
Adjusted R2 | 0.001 | 0.050 | 0.059
Residual Std. Error | 0.412 (df = 138598) | 0.402 (df = 138590) | 0.400 (df = 138536)
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
All standard errors are clustered at the experimental cell (language-delay-
interest) level.

### Are GPT-3.5 choices consistent with a “proper” choice model?

The evidence documented in sections 3.1 and above highlights notable
heterogeneity in GPT-3.5 choices across languages. Our findings in section
3.2, however, suggest that the decision patterns do not seem to conform to an
exponentially discounted utility model since the likelihood of selecting the
larger, later reward changes in the interest rate. These patterns deviate from
human decision-making behavior. Motivated by this observation, in this
section, we first establish a set of straightforward regularity conditions
that various models of intertemporal choices, such as exponential, hyperbolic,
or quasi-hyperbolic models, fulfill. Next, we assess whether GPT-3.5 choices
adhere to these regularity conditions.

We start by defining a “proper” random utility function over tuples $(t,r)$,
where $t$ represents the time a reward is received, and $r$ denotes the value
of the reward.

######  Definition 1.

A random utility function $U:(\mathcal{T},\mathcal{R})\rightarrow\mathds{R}$
is “proper” if for $\forall t_{1},t_{2},r_{1}$ the probability
$v(r_{2})=P\left(U(t_{2},r_{2})>U(t_{1},r_{1})\right)$ is an increasing
function of $r_{2}$.

A proper random utility function essentially represents a utility function
where the probability of choosing the larger, later reward increases as the
size of the later reward grows. This condition is satisfied by exponential,
hyperbolic, quasi-hyperbolic, or any other standard discounted utility model.
This essentially implies that choosing the larger, later reward is positively
correlated with the gap in rewards, or in other words,
$cor(\mathbbm{1}_{\\{U(t_{2},r_{2})>U(t_{1},r_{1})\\}},r_{2}-r_{1})>0$. We now
examine whether GPT choices indeed fulfill this condition using the following
specification:

$\mathbf{Y}_{k}=\alpha\cdot(r_{2}-r_{1})+\eta_{\ell_{k}d_{k}}+\epsilon_{k},$
(3)

where $k$ indexes the sample, and $\ell_{k}$ is the query language used for
drawing sample $k$. The delay for the experiment condition corresponding to
sample $k$ is denoted by $d_{k}$. $\mathbf{Y}_{k}$ is a dummy variable that
equals one if the larger, later option was selected. $r_{2}-r_{1}$ is the
difference between the rewards, measured in increments of 1000 tokens.
Finally, $\eta_{\ell_{k}d_{k}}$ represents language-delay fixed effects. By
including these fixed effects in the regression, we are comparing different
interest rate conditions while holding language and delay fixed.

Table 5 presents the estimates from equation (3). The first column displays
the estimate for the regression without any fixed effects. The coefficient is
slightly negative and statistically significant. Note that we expect this
coefficient to be positive, as increasing $r_{2}$ should make choosing the
delayed reward option more likely. In column (2), we incorporate language
fixed effects, but the coefficient remains unchanged. Finally, in column (3),
we add language-delay fixed effects, and the coefficient shrinks in size and
becomes statistically insignificant. This analysis suggests that GPT-3.5
choices cannot be rationalized by any proper utility function. It is important
to emphasize once again that these results demonstrate GPT-3.5’s inability to
reasonably trade off larger, later rewards with smaller, sooner ones.

Table 5: Testing if GPT-3.5 choices are “proper”. Our results show that
increasing the larger, later reward does not increase the likelihood of
GPT-3.5 choosing the larger, later reward. Data for this study were sourced
from GPT-3.5, employing the experimental design described in section 2.2.

| Dependent variable:
---|---
| Choosing the delayed reward
| (1) | (2) | (3)
Difference in rewards (in 1000 tokens) |  $-$0.009∗∗∗ |  $-$0.009∗∗∗ | 0.001
| (0.001) | (0.001) | (0.001)
Constant | 0.227∗∗∗ |  |
| (0.004) |  |
Language FE |  | X |
Language-Delay FE |  |  | X
Observations | 138,600 | 138,600 | 138,600
R2 | 0.006 | 0.048 | 0.114
Adjusted R2 | 0.006 | 0.048 | 0.112
Residual Std. Error | 0.411 (df = 138598) | 0.402 (df = 138577) | 0.388 (df = 138401)
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
All standard errors are clustered at the experimental cell (language-delay-
interest) level.

#### Are GPT-3.5 choices consistent with lexicographic preferences over time
and rewards?

The findings above suggest that GPT-3.5 demonstrates lexicographic preferences
in relation to time and rewards, essentially ignoring reward differences when
the time periods are not the same. To examine this, we prompt GPT-3.5 across
the 22 languages in our dataset, but this time we ask GPT-3.5 to choose
between tuples $(t,r_{1})$ and $(t,r_{2})$, where $t$ is part of the set
${2,3,4,5,7,13,25}$, $r_{1}=1000$ tokens, and $r_{2}$ belongs to the set
${1041,1082,1401,1781,3174,5061,7376}$. In total, we have $22\times 7\times
7=1078$ experimental cells and gather 100 samples for each condition. Note
that these choices are essentially trivial, asking GPT-3.5, for example,
whether it prefers 1041 tokens in 2 months or 1000 tokens in 2 months from
now.

We plot the likelihood of choosing the larger option across different in
Figure 9. The average probability of selecting the larger option is equal to
$74\%$, which means that GPT-3.5 is able to compare the options when they are
presented in the same time frame.

Figure 9: Probability of selecting the larger option when both choices are
offered $t$ months from the present.

Comparing the average 22% probability of selecting the larger later reward
when there is a delay between time periods (as shown in Figure 2) with these
results suggests that GPT-3.5 is indeed exhibiting lexicographic preferences.
However, it is important to note that the choices mentioned above appear
trivial; GPT-3.5 should pick the higher reward with a probability of 1, given
that both rewards are offered in the same time period $t$. Yet, this is not
what we observe due to inherent randomness in the choice. Under a standard
lexicographic utility function, the preferences should be deterministic [63].
To address this, we now formally define a lexicographic random utility model
of rewards and the time at which they are received $(t,r)$, and present
additional evidence supporting the fact that GPT-3.5 demonstrates
lexicographic preferences (in the random utility sense).

######  Definition 2.

A random utility function $U:(\mathcal{T},\mathcal{R})\rightarrow\mathds{R}$
is lexicographical if for $\forall t_{1}\neq t_{2}$ and $\forall r_{1},r_{2}$
the random variable $\mathbbm{1}_{\\{U(t_{1},r_{1})>U(t_{2},r_{2})\\}}\perp
r_{1},r_{2}$, but for $\forall t$, we have
$\mathbbm{1}_{\\{U(t,r_{1})>U(t,r_{2})\\}}\not\perp r_{1},r_{2}$.

Our results in Table 5 indicate that when $t_{1}\neq t_{2}$,
$r_{2}-r_{1}\perp\mathbbm{1}_{\\{U(t_{1},r_{1})>U(t_{2},r_{2})\\}}$, which
aligns with the first part of Definition 2. We now illustrate that when the
time periods are the same ($t_{1}=t_{2}$), GPT-3.5 does systematically shift
its decisions as the gap in rewards increases, i.e.,
$cor(r_{2}-r_{1},\mathbbm{1}_{\\{U(t,r_{1})>U(t,r_{2})\\}})>0$. To investigate
this, we re-estimate specification (3) to examine if GPT-3.5 choices shift as
a function of differences in rewards when $t=t_{1}=t_{2}$. The results of this
analysis are presented in Table 6 and demonstrate that the probability of
choosing the larger option systematically changes as the gap between the
values increases. This finding indicates that GPT-3.5 is capable of discerning
between options’ reward sizes when they are presented within the same time
frame.

Table 6: The effect of changing the reward size on the probability of choosing
the option with the larger reward. This study involves choices that are
presented in the same time frame, that is $t_{1}=t_{2}$. The results show that
GPT-3.5 is more likely to pick the large options and the gap in reward
increases.

| Dependent variable:
---|---
| Choosing the larger reward
| (1) | (2) | (3)
Difference in rewards (in 1000 tokens) | 0.012∗∗∗ | 0.012∗∗∗ | 0.012∗∗∗
| (0.002) | (0.002) | (0.002)
Constant | 0.712∗∗∗ |  |
| (0.010) |  |
Language FE |  | X |
Language-Delay FE |  |  | X
Observations | 107,800 | 107,800 | 107,800
R2 | 0.004 | 0.092 | 0.110
Adjusted R2 | 0.004 | 0.092 | 0.108
Residual Std. Error | 0.440 (df = 107798) | 0.420 (df = 107777) | 0.416 (df = 107645)
Note: |  ∗p$<$0.1; ∗∗p$<$0.05; ∗∗∗p$<$0.01
All standard errors are clustered at the experimental cell (language-delay-
interest) level.