  The Buridan's ass paradox is characterized by perpetual indecision between
two states, which are never attained. When this problem is formulated as a
dynamical system, indecision is modeled by a discrete-state Markov process
determined by the system's unknown parameters. Interest lies in estimating
these parameters from a limited number of observations. We compare estimation
methods and examine how well each can be generalized to multi-dimensional
extensions of this system. By quantifying statistics such as mean, variance,
frequency, and cumulative power, we construct both method of moments type
estimators and likelihood-based estimators. We show, however, why these
techniques become intractable in higher dimensions, and thus develop a
geometric approach to reveal the parameters underlying the Markov process. We
also examine the robustness of this method to the presence of noise.
