This paper formally analyzes the distributional structure of random utility models, focusing on the processes that prevent perfect predictions of choice behavior. It contrasts with existing literature that often imposes distributional assumptions implicitly, leading to a lack of awareness of the model's restrictiveness. Historically, random utility models were developed by psychologists to explain observed inconsistencies in individual behavior and later adopted by economists as an econometric representation of maximizing behavior. The Luce and McFadden model is widely used due to its analytical and computational properties, but it has limitations, particularly in handling counter-intuitive behavioral forecasts. The paper introduces two alternative models—Tversky’s elimination-by-aspects model and a model by Quandt and Young generalized by Domenechic and McFadden—that are more intuitive and less restrictive. Despite these advancements, understanding the appropriate domain for IIDRU models remains fragmented, and the paper aims to address this by reformulating the random utility model to focus on the processes that make perfect choice predictions unattainable.This paper formally analyzes the distributional structure of random utility models, focusing on the processes that prevent perfect predictions of choice behavior. It contrasts with existing literature that often imposes distributional assumptions implicitly, leading to a lack of awareness of the model's restrictiveness. Historically, random utility models were developed by psychologists to explain observed inconsistencies in individual behavior and later adopted by economists as an econometric representation of maximizing behavior. The Luce and McFadden model is widely used due to its analytical and computational properties, but it has limitations, particularly in handling counter-intuitive behavioral forecasts. The paper introduces two alternative models—Tversky’s elimination-by-aspects model and a model by Quandt and Young generalized by Domenechic and McFadden—that are more intuitive and less restrictive. Despite these advancements, understanding the appropriate domain for IIDRU models remains fragmented, and the paper aims to address this by reformulating the random utility model to focus on the processes that make perfect choice predictions unattainable.