Two Groups, Two Demands

A lending model is audited on $2{,}000$ past applicants whose outcomes are now known: $1{,}000$ from group P and $1{,}000$ from group Q. In group P, $600$ of the applicants went on to repay their loan. In group Q, $300$ did.

The model's decisions on them were:

	group P	group Q
repaid, approved	$540$	$270$
repaid, refused	$60$	$30$
did not repay, approved	$40$	$70$
did not repay, refused	$360$	$630$

The auditors use the chapter's three fairness definitions, made precise as follows:

Equal accuracy: the share of decisions that were correct is the same in both groups.
Equal error types: the share of repayers who are approved is the same in both groups, and the share of non-repayers who are approved is the same in both groups.
Equal outcomes: the share of all applicants who are approved is the same in both groups.

A regulator now requires a replacement model that satisfies both equal error types and equal outcomes, measured on these same $2{,}000$ applicants.

Which statement is correct?

Two Groups, Two Demands

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