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AI systems are often used to make or contribute to important decisions in a growing range of applications, including criminal justice, hiring, and medicine. Since these decisions impact human lives, it is important that the AI systems act in ways which align with human values. Techniques for preference modeling and social choice help researchers learn and aggregate peoples' preferences, which are used to guide AI behavior; thus, it is imperative that these learned preferences are accurate. These techniques often assume that people are willing to express strict preferences over alternatives; which is not true in practice. People are often indecisive, and especially so when their decision has moral implications. The philosophy and psychology literature shows that indecision is a measurable and nuanced behavior -- and that there are several different reasons people are indecisive. This complicates the task of both learning and aggregating preferences, since most of the relevant literature makes restrictive assumptions on the meaning of indecision. We begin to close this gap by formalizing several mathematical \emph{indecision} models based on theories from philosophy, psychology, and economics; these models can be used to describe (indecisive) agent decisions, both when they are allowed to express indecision and when they are not. We test these models using data collected from an online survey where participants choose how to (hypothetically) allocate organs to patients waiting for a transplant.