A Comparative Analysis of the Cobb-Douglas Habitability Score (CDHS) with the Earth Similarity Index (ESI)

TL;DR

This paper analytically compares the Cobb-Douglas Habitability Score (CDHS) with the Earth Similarity Index (ESI), highlighting their differences, mathematical properties, and the lack of causal relationship, suggesting independent use.

Contribution

It provides a mathematical and visual comparison of CDHS and ESI, establishing their independence and differing properties for habitability assessment.

Findings

CD-HPF satisfies scalability and stability conditions

No causal relationship exists between ESI and CD-HPF

Both indices should be used independently

Abstract

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.