Question

Describe the matrices and formulae used to determine centralization or distribution of data. In the absence of subjective reasoning, would the matrices and formulae lead to a rational decision? Why or why not?

Answer 1

In order to determine the centralization or distribution of data, here are few matrices or formulae we can use:

• Leading eigenvector: Suppose choosing an eigenvector x in order to define a centrality measure, then the condition becomes x ∈ R_n⁺ and for non-negative matrix, the leading eigenvector is non-negative that are irreducible as well as primitive matrices.
• So, for non-negative matrices the equation remains A >= 0 element wise

For irreducible matrices: A >= 0,

(A kij)ij > 0, for some kij ≥ 1 m ∀ permutation matrix P : P^T AP not equals to [ X Y 0 Z]

For regular matrices: A >= 0; A^k > 0 for k >= 1

Most of the subjective decisions regarding the metrices are rational, but sometimes in the absence of subjective reasoning, the solution can be rational too. Rational reasoning is more about making choices between the alternative. The decision can be made in terms of favor logic, analysis and insight. So, here the formula could lead to a solution, though it does not have an subjective decision.