  We present an analytical comparison of the Cobb-Douglas Habitability
Production Function (CD-HPF) and the Earth Similarity Index (ESI). The key
differences between the ESI and CD-HPF are highlighted and based on
mathematical analysis, we show that the CD-HPF satisfies the conditions for
model scalability and stability but the ESI does not. Using visualizations, we
also demonstrate that there do not exist any causal relationships between the
ESI and CD-HPF. The conclusion from the work done is that the CD-HPF and ESI do
not share any sensible relationship and that both should be used independently.
