This paper provides a formal analysis of the distributional structure of random utility models, emphasizing the processes that make perfect prediction of choice behavior unattainable. Unlike existing literature that directly imposes distributional assumptions, this paper explores the underlying mechanisms that induce distributional properties. This approach reveals the restrictiveness of models and helps researchers understand the limitations of their assumptions. Random utility models, originally developed by psychologists to explain inconsistencies in individual behavior, have since been adopted by economists as an econometric representation of maximizing behavior. Utilities are treated as random variables to reflect the observer's lack of information, not the decision maker's lack of rationality. Both econometric and psychometric literatures have focused on the specification $ U_{at} = V_{at} + \epsilon_{at} $, where $ V_{at} $ are constants and $ \epsilon_{at} $ are independent and identically distributed random variables. The Luce and McFadden models are among the most analytically and computationally efficient. However, these models have been criticized for yielding counter-intuitive forecasts. Alternative models, such as Tversky's elimination-by-aspects model and a model by Quandt and Young, have been developed to be more intuitive but still include IIDRU models as special cases. Despite these developments, the understanding of random utility models remains fragmentary. The paper argues that further progress requires a reformulation of the model, focusing on the processes that make perfect predictions unattainable, rather than ad hoc corrections. Part I of the paper presents this reformulation, while Part II examines the distributional properties of random utility models.This paper provides a formal analysis of the distributional structure of random utility models, emphasizing the processes that make perfect prediction of choice behavior unattainable. Unlike existing literature that directly imposes distributional assumptions, this paper explores the underlying mechanisms that induce distributional properties. This approach reveals the restrictiveness of models and helps researchers understand the limitations of their assumptions. Random utility models, originally developed by psychologists to explain inconsistencies in individual behavior, have since been adopted by economists as an econometric representation of maximizing behavior. Utilities are treated as random variables to reflect the observer's lack of information, not the decision maker's lack of rationality. Both econometric and psychometric literatures have focused on the specification $ U_{at} = V_{at} + \epsilon_{at} $, where $ V_{at} $ are constants and $ \epsilon_{at} $ are independent and identically distributed random variables. The Luce and McFadden models are among the most analytically and computationally efficient. However, these models have been criticized for yielding counter-intuitive forecasts. Alternative models, such as Tversky's elimination-by-aspects model and a model by Quandt and Young, have been developed to be more intuitive but still include IIDRU models as special cases. Despite these developments, the understanding of random utility models remains fragmentary. The paper argues that further progress requires a reformulation of the model, focusing on the processes that make perfect predictions unattainable, rather than ad hoc corrections. Part I of the paper presents this reformulation, while Part II examines the distributional properties of random utility models.