A crowding index for finite populations.

Area of Science:

• Social Science
• Mathematical Modeling
• Human Factors Engineering

Background:

• Traditional population density metrics in social sciences overlook spatial orientation, leading to inaccuracies in assessing physical crowding.
• Assessing crowding is crucial in confined environments like U.S. Navy nuclear submarines.

Purpose of the Study:

• To propose and validate a novel formula for measuring physical crowding that accounts for spatial orientation.
• To correct the deficiencies of conventional population density formulations.
• To evaluate the proposed index based on parsimony, mathematical soundness, and empirical verifiability.

Main Methods:

• Developed a new population density index as a generalization of the Euclidean distance formula.
• Utilized Monte Carlo simulations to support mathematical conjectures about the index.
• Applied the formula in Concepts of Operations Experiments within U.S. Navy nuclear submarine workspaces.

Main Results:

• The proposed formula accurately measures relative population density as a function of spatial orientation and geometric area size.
• Mathematical properties of the index were supported by simulation data.
• Empirical data from U.S. Navy submarine experiments demonstrated the formula's applicability.

Conclusions:

• The novel population density formula offers a more accurate measure of physical crowding than conventional methods.
• The index is mathematically sound, parsimonious, and empirically verifiable.
• This approach provides a valuable tool for analyzing and managing crowding in confined environments.