Class SocialMobilityMatrix

java.lang.Object

org.episteme.social.sociology.SocialMobilityMatrix

public final class SocialMobilityMatrix
extends Object

Models social mobility between classes using Markov chain transition matrices. Provides tools to project future class distributions and analyze mobility metrics.

Since:

1.0

Version:

1.1

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static final record	SocialMobilityMatrix.MobilityClass	Represents a socioeconomic class.

Method Summary

Modifier and Type	Method	Description
static Real[]	findEquilibrium(Real[][] matrix)	Finds the equilibrium class distribution (Steady State) of the matrix.
static Real	mobilityIndex(Real[][] matrix)	Calculates the mobility index (Prais Index) of a transition matrix.
static Real[]	projectClassDistribution(Real[] initialDistribution, Real[][] transitionMatrix, int generations)	Projects the class distribution after a specified number of generations.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

projectClassDistribution

public static Real[] projectClassDistribution(Real[] initialDistribution,
 Real[][] transitionMatrix,
 int generations)

Projects the class distribution after a specified number of generations. Formula: P_future = P_current * M^n

Parameters:

initialDistribution - Array representing initial population percentages in each class

transitionMatrix - Square matrix where M[i][j] is probability of moving from class i to class j

generations - Number of time steps to project

Returns:

Array representing the future class distribution

Throws:

IllegalArgumentException - if matrix dimensions do not match distribution

mobilityIndex

public static Real mobilityIndex(Real[][] matrix)

Calculates the mobility index (Prais Index) of a transition matrix.

Index M = (n - trace(P)) / (n - 1)

Where trace(P) is the sum of diagonal elements (stayers). 0 implies perfect immobility (identity matrix). 1 implies perfect mobility (random chance, essentially).

Parameters:

matrix - the transition matrix

Returns:

the mobility index

findEquilibrium

public static Real[] findEquilibrium(Real[][] matrix)

Finds the equilibrium class distribution (Steady State) of the matrix. Iterates until convergence (simplified numerical approach).

Parameters:

matrix - the transition matrix

Returns:

the equilibrium distribution array