Advancing Knowledge to Advance Society: Specific Functions and Probability Distributions

Thomas M. Menino Convention & Exhibition Center 

To advance the growth of social science knowledge, the key is to mathematize the mechanisms and link them to probability distributions. This paper describes the four stages in mathematizing mechanisms and the link of fourth-stage specific functions to probability distributions, providing illustrations of both theoretical and empirical work, drawn largely from the study of status, justice, power, identity, and happiness. As shown, when an idea appears as an input-outcome relation, denoted X→Y, where X is a personal quantitative characteristic (e.g., income, beauty, skill) and Y a personal outcome (e.g., self-esteem, status, happiness), its mathematization leads to two sets of testable implications, via the specific function and via the probability distributions of X and Y, plus substantial additional empirical analysis. Testable predictions reach farflung topical domains – theft, gifts, classrooms, marital cohesion, conversation, salary secrecy, religious vocations, migration, polarization, intergroup relations, proportions integrationist and segregationist, whistleblowers, differential mourning for fathers and mothers, and whether parents buy more toys at birthdays or Christmas.

deductive theory

testable predictions, including novel predictions

inequality in personal characteristics (e.g., income) and inequality in personal sociobehavioral outcomes (e.g., happiness)

specific functions

probability distributions 

Social Statistics Section