Short answers, pulled from the story.
Peter Corning identified equality, equity, and reciprocity as the three distinct categories of substantive fairness. These categories must be combined to achieve a truly fair society.
Economists use tools like the Gini index to measure equity levels within economies. This metric quantifies distributional gaps between rich and poor populations.
Horizontal equity means treating people alike if they are in similar economic situations while vertical equity treats people differently according to differences in their income or ability to pay. Vertical equity typically advocates that better-off individuals contribute more to public coffers through progressive taxation.
Hammond's equity principle suggests progressive transfers enhance overall welfare without altering relative positions. Sen's weak equity axiom prioritizes needs of most disadvantaged when allocating total income.
Defining equity presents inherent challenges due to its subjective nature depending on societal values. Economists find it difficult to formulate acceptable definitions requiring interpersonal comparisons of utility which remain complex and controversial.