A person stands at a crossroads, symbolizing decision-making under uncertainty.

Decoding Decision-Making: Can Multi-Utility Models Explain Our Inconsistent Choices?

Avery Sinclair in Business & Economy December 2025 • 4 min read.

"Explore how expected multi-utility representations are reshaping our understanding of preferences and rationality in economics."

Classical economic theory relies on the idea that people make decisions based on a clear, consistent set of preferences. This means we supposedly weigh our options and pick the one that maximizes our happiness or 'utility.' The cornerstone of this idea is Debreu's utility representation theorem, which essentially states that if your preferences are complete and transitive, we can create a utility function that perfectly represents them. In simpler terms, if you always know what you prefer and your preferences are consistent, we can map those preferences onto a numerical scale.

However, real-world decision-making often throws a wrench into this neat framework. People aren't always sure about their preferences, and those preferences can shift depending on the context. Think about buying a car – you might value fuel efficiency, safety, and style, but those priorities might change based on your budget or current needs. This is where the concept of 'incompleteness' comes in, challenging the traditional view of rationality.

The exploration of preferences over lotteries emerges as a response to the limitations of classical utility theory. These preferences acknowledge that individuals often make decisions amidst uncertainty and potential outcomes, diverging from the assumption of complete rationality. This approach seeks to provide a more nuanced understanding of how individuals evaluate choices, considering the inherent complexities and subjectivity that influence decision-making processes.

What are Expected Multi-Utility Representations?

A person stands at a crossroads, symbolizing decision-making under uncertainty.

Instead of assuming a single, fixed utility function, expected multi-utility representations consider a set of possible utility functions. The decision-maker's preferences are then based on whether one option is preferred across all of those utility functions. Imagine you're choosing between two investments. With a single utility function, you'd pick the one that gives you the highest expected return. But with multi-utility, you might only choose an investment if it's considered better across a range of different economic scenarios, reflecting different risk tolerances or beliefs about the future.

This approach acknowledges that we might lack confidence in our ability to perfectly evaluate different outcomes. It could be because we're unsure about future tastes, risk attitudes, or even the probabilities of different events. Each utility function in the set represents a different possible perspective, and our decisions reflect a kind of 'unanimity' across those perspectives.

Aumann [5] and Bewley [7]: These seminal works questioned the assumption of completeness in decision-making.
Dubra, Maccheroni, and Ok [14]: They provided conditions for multi-utility representations but left open the question for uncountable outcome sets.
Hara, Ok, and Riella [24]: They explored coalitional representations, offering a different perspective on preferences.

For simple lotteries (those with a finite number of possible outcomes), the authors found that a multi-utility representation is possible if and only if the set of outcomes is finite or countably infinite. This provides a key insight: the complexity of the outcome space directly impacts whether we can neatly represent preferences with a set of utility functions. When we move to uncountable outcome sets, things get much trickier, and the simple characterization breaks down.

The Takeaway: Embracing the Complexity of Choice

Expected multi-utility representations offer a more nuanced and realistic way to model decision-making under uncertainty. They acknowledge the inherent limitations of human rationality and the fact that our preferences are often incomplete and context-dependent. While this approach might add complexity, it brings us closer to understanding the messy, fascinating world of human choice.

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Everything You Need To Know

What is the main problem with the traditional economic model of decision-making?

Classical economic theory assumes people make decisions based on a clear, consistent set of preferences, choosing the option that maximizes their 'utility.' This approach relies on the idea of complete and transitive preferences, which can be represented by a single utility function, as established by Debreu's utility representation theorem. However, real-world choices often contradict this model because preferences can be incomplete and change depending on the context. People may be uncertain about their preferences, leading to inconsistent choices that a single utility function cannot explain.

How do expected multi-utility representations improve the understanding of decision-making?

Expected multi-utility representations enhance our understanding of decision-making by moving beyond the assumption of a single, fixed utility function. Instead, they consider a set of possible utility functions. A decision-maker's preferences are then based on whether one option is preferred across *all* of those utility functions. This approach acknowledges that individuals may lack confidence in their ability to perfectly evaluate different outcomes, recognizing the inherent limitations of human rationality and the context-dependent nature of preferences.

What is 'incompleteness' in the context of decision-making, and why does it matter?

Incompleteness refers to the situation where individuals are not always certain about their preferences or unable to compare all available options. This challenges the traditional view of rationality, which assumes complete and transitive preferences. Incompleteness is significant because it reflects real-world decision-making scenarios where preferences are fluid and subject to contextual factors, making it impossible to represent them with a single utility function. This necessitates the use of multi-utility models to better capture the complexities of human choice.

Can multi-utility representations be applied to all types of outcomes, and what are the limitations?

Multi-utility representations can be applied to a variety of outcomes, but their applicability depends on the complexity of the outcome space. For simple lotteries (those with a finite number of possible outcomes), a multi-utility representation is possible if and only if the set of outcomes is finite or countably infinite. However, when dealing with uncountable outcome sets, the simple characterization breaks down, and the models become more complex. This highlights a key limitation: the challenge of representing preferences when the potential outcomes are vast and diverse.

How does the exploration of preferences over lotteries relate to multi-utility models?

The exploration of preferences over lotteries responds to the limitations of classical utility theory. These preferences acknowledge that individuals often make decisions amidst uncertainty and potential outcomes, diverging from the assumption of complete rationality. Multi-utility models provide a more nuanced understanding of how individuals evaluate choices, considering the inherent complexities and subjectivity that influence decision-making processes. By considering multiple utility functions, these models better capture how individuals make choices when faced with uncertainty and potential outcomes.