Canadian Economic Association · Annual Meeting · 2026

Do LLMs Have Utility Functions?

Insights from choice experiments with financial portfolios.

Joy BuchananBrock School of Business
Samford University

Joshua Foster (👋)Ivey Business School
Western University

PART 01

Introduction

LLMs as Economic Actors

01 · Introduction

Do LLMs need a utility function?

AI agents are being deployed as autonomous decision-makers.
These models are increasingly responsible for evaluating economic tradeoffs.
Knowing how economic tradeoffs are evaluated becomes critical for alignment.
However, the underlying preferences of these models remain largely unmapped.

Research Question

Do LLMs adhere to the rationality axioms of utility theory?

Why It Matters

Each principal deploying AI agents will want to understand their preferences, and potentially engineer alignment with the principal's preferences.

PART 01

How LLMs Work

Choices from Autoregressive Distributions

01 · Introduction

How LLMs Generate Text

Input Context

$x$

▶

LLM

▶

Logit Scores

$y_1$ $u_1(x) = -0.33$

$y_2$ $u_2(x) = 1.15$

$y_3$ $u_3(x) = 5.42$

$y_4$ $u_4(x) = -2.11$

$y_5$ $u_5(x) = 0.87$

$y_6$ $u_6(x) = -1.06$

⋮ all $i \in \mathcal{Y}$

▶

Softmax

$\color{white} \dfrac{e^{u_i / \tau}}{\sum_{j \in \mathcal{Y}} e^{u_j / \tau}}$

▶

Probabilities

$y_1$ $P_1 = 0.022$

$y_2$ $P_2 = 0.099$

$y_3$ $P_3 = 0.712$

$y_4$ $P_4 = 0.004$

$y_5$ $P_5 = 0.075$

$y_6$ $P_6 = 0.011$

⋮ sums to 1

$\tau$: temperature is the scale of the stochastic component.

01 · Introduction

A Typical Choice Experiment Prompt

Experimenter prompt:

You have two options for your annual financial portfolio.
Choose the portfolio you prefer and reply with A or B only.

Option A offers an expected return of 8% and
a standard deviation of 12%.

Option B offers an expected return of 10% and
a standard deviation of 5%.

Subject response:

I choose Option _______.

01 · Introduction

The Core Insight

The LLM's choice mechanism is McFadden (1974)'s conditional logit.

Input Context $x$

Which do you prefer?

Option A: $\mu=8$% and $\sigma=12$%

Option B: $\mu=10$% and $\sigma=5$%

I choose Option ____

▶

LLM

▶

Logits $u$

"A" 1.15

                    "B"
                    5.42
                  

"C" -2.11

... 100,000+ tokens

▶

Softmax

$\color{white} \dfrac{e^{u_i / \tau}}{\sum_{j \in \mathcal{V}} e^{u_j / \tau}}$

▶

Probability $P$

"A" 0.149

                    "B"
                    0.712
                  

"C" 0.004

... sums to 1

\underbrace{P(i \mid x, \tau) = \frac{\exp\!\bigl(u_i(x)/\tau\bigr)}{\displaystyle\sum_{j \in \mathcal{V}} \exp\!\bigl(u_j(x)/\tau\bigr)}}_{\text{Probability of Selecting Token $i$}} \quad \iff \quad \underbrace{U_i = u_i(x) + \tau\,\varepsilon_i, \quad \varepsilon_i \overset{\text{iid}}{\sim} \text{EV-I}}_{\text{Random Utility from Selecting Token $i$}}

01 · Introduction

Llama 3.1 8B Indifference Curve

Prefers grid bundle Prefers base bundle Empirical indifference curve (Δz = 0) Base bundle (σ=30, μ=10)

PART 01

Utility Axioms

Testing the Economic Rationality of LLMs

01 · Introduction

Utility Axioms

Complete: must express some preference or indifference.

The probability of selecting a choice label among the available options will be approximately 1.

$ P(A \mid x, \tau) + P(B \mid x, \tau) \approx 1 $

01 · Introduction

Utility Axioms

Reflexive: any bundle of goods is at least as good as itself.

When options are identical, their probability of selection will be the same.

$ P(A \mid x, \tau) = P(B \mid x, \tau) $

01 · Introduction

Utility Axioms

Continuity: there is a "tipping point" between being better than and worse than a given option.

Let $A\succ B\succ C$. There is a value $\epsilon\in [0,1]$ such that

$ (1-\epsilon)P(A \mid x, \tau) + \epsilon P(C \mid x, \tau) $

$ = P(B \mid x, \tau) $

01 · Introduction

Utility Axioms

Strong monotonicity: more (less) of a good (bad) is always better.

The probability of selecting a dominant option will always be higher than a non-dominant one.

$ P(A \mid x, \tau) > P(B \mid x, \tau) $

01 · Introduction

Utility Axioms

Transitive: if $A\succ B$ and $B\succ C$, then $A\succ C$.

The probability of selecting A will always be higher than B, and B higher than C.

$ P(A \mid x, \tau) > P(B \mid x, \tau) $

$ P(B \mid x, \tau) > P(C \mid x, \tau) $

PART 02

Experimental Design

A portfolio choice laboratory and a structural model of risk preference.

02 · Experimental Design

Portfolio choice laboratory

Binary menus over risky assets with known payoff moments.

Experimenter prompt:

You have two options for your annual financial portfolio.
Choose the portfolio you prefer and reply with A or B only.

Option A offers an expected return of [$\mu_A$]% and a standard deviation of [$\sigma_A$]%.

Option B offers an expected return of [$\mu_B$]% and a standard deviation of [$\sigma_B$]%.

Subject response:

I choose Option _______.

PART 03

Results

Rationality diagnostics, and inducing specific preferences.

03 · Results

Rationality diagnostics

Do LLMs satisfy the axioms of choice over risky portfolios?

Model	Complete	Reflexive	Continuity	Monotonicity	Transitive
Qwen 3 (14B)	0.9999	0.0002	1.0000	1.0000	0.9749
Qwen 3 (8B)	0.9999	0.0018	1.0000	1.0000	0.9923
Gemma 4 (31B Instruct)	0.9999	0.0000	1.0000	1.0000	0.9882
Ministral 3 (8B Instruct)	0.9995	0.0496	0.9667	1.0000	0.9643
Gemma 2 (9B Instruct)	0.9960	0.5236	1.0000	1.0000	0.9238
Llama 3.1 (8B Instruct)	0.9021	0.9250	1.0000	1.0000	0.9851
Llama 3.1 (70B Instruct)	0.7580	0.0648	1.0000	1.0000	0.9562
Llama 3.1 (8B Fine-Tuned)	0.9977	0.9966	1.0000	1.0000	0.9994

03 · Results

Fine-tuning Preferences

Prefers grid bundle Prefers base bundle Empirical indifference curve (Δz = 0) Base bundle (σ=30, μ=10)

PART 04

Conclusion

Contributions, limitations, and implications for agentic AI deployment.

04 · Conclusion

Contributions & implications

Formal equivalence between LLM softmax and the RUM. This places language model choice inside structural discrete choice methods, enabling recovery of cardinal utility indices directly from a model's single token logit outputs over choices.
Experiments support the existence of a utility function. The results on our five axiom measures indicate the existence of a utility function over risky portfolios.
Specific preferences can be induced via fine-tuning. Existing alignment pipelines allow for us to engineer the preferences of LLMs in a targetable way.

The Upshot

To deploy agentic AI, the models must be economically coherent and internally consistent. We show preferences governing their behaviour can be measured and targeted.

END · 04

Thank you.
Fin.

Joy BuchananBrock School of Business
Samford University

Joshua FosterIvey Business School
Western University

LLMs Live in Plato's Cave, We Project the Shadows

05 · Extra

LLMs Are Ideal Experimental Subjects

Environmental control for ceteris paribus variation.
AIs are cheap and fast.

AI never gets tired of answering your questions.
Every simulation is "real" to the AI.

Do LLMs Have Utility Functions?

Introduction

Do LLMs need a utility function?

How LLMs Work

How LLMs Generate Text

A Typical Choice Experiment Prompt

The Core Insight

The LLM's choice mechanism is McFadden (1974)'s conditional logit.

Llama 3.1 8B Indifference Curve

Utility Axioms

Utility Axioms

Utility Axioms

Utility Axioms

Utility Axioms

Utility Axioms

Experimental Design

Portfolio choice laboratory

Binary menus over risky assets with known payoff moments.

Results

Rationality diagnostics

Do LLMs satisfy the axioms of choice over risky portfolios?

Fine-tuning Preferences

Conclusion

Contributions & implications

Thank you.Fin.

LLMs Live in Plato's Cave, We Project the Shadows

LLMs Are Ideal Experimental Subjects

Thank you.
Fin.