The core challenge in decision-making lies in comparing apples to oranges—specifically, when utilities representing different outcomes (like money versus happiness) can't be directly compared due to mismatched scales. Traditional methods often force these utilities into a single scale, risking oversimplification or flawed conclusions. This idea proposes reframing the problem: instead of trying to reconcile incompatible scales, uncertainty about scaling differences could be transformed into uncertainty about the underlying probabilities of outcomes. This shift could enable cleaner comparisons while preserving the nuances of each utility's original context.

The Rescaling Revolution

Here's how the transformation might work visually: imagine two thermometers—one measuring temperature in Celsius, the other in Fahrenheit—but you're unsure about the exact conversion formula between them. Rather than guessing a fixed conversion rate, you could treat your uncertainty as part of the temperature reading itself. Mathematically, this involves reparametrizing utility functions so their scaled differences become part of a probability distribution over possible outcomes. For example:

• A policymaker comparing GDP growth (linear scale) with survey-based life satisfaction (logarithmic scale) could model scaling differences as uncertainty about how economic gains translate to happiness
• A reinforcement learning system balancing short-term rewards with long-term safety could treat their relative importance as a probabilistic weighting rather than a fixed parameter

From Theory to Practice

Implementation could begin with open-source tools demonstrating the transformation on benchmark problems—say, a Python library that takes heterogeneous utility functions and outputs comparable expected values with confidence intervals reflecting scaling uncertainty. Early adopters might include:

1. Tech companies optimizing trade-offs between user engagement and privacy costs
2. Development economists weighing infrastructure investments against education outcomes
3. Healthcare systems prioritizing treatment options with both clinical and quality-of-life metrics

The Road Ahead

This approach essentially adds a new mathematical lens to existing decision frameworks—it doesn't replace multi-objective optimization or Bayesian methods but rather extends them to handle real-world scaling ambiguity. The key insight is that scaling differences and probability distributions are two sides of the same coin: by treating one as the other, we might make better decisions when perfect comparability isn't possible.