Equalized Odds & Opportunity

Equal Opportunity and Equalized Odds are two ways to measure if an AI system is fair. Equal Opportunity demands that for people who are actually qualified (e.g., would repay a loan), the AI gives them a positive outcome (approves the loan) at the same rate, regardless of their group. Equalized Odds is stricter: it requires this and demands that for people who are not qualified, the AI gives them a negative outcome at the same rate across groups.

Think of a spam filter: Equal Opportunity means it correctly marks real emails as 'not spam' at the same rate for all senders. Equalized Odds adds that it must also correctly mark actual spam as 'spam' at the same rate.

Ask this: When evaluating an automated system, are its mistakes distributed evenly across different groups?

When an algorithm makes predictions, it can make two kinds of mistakes: false positives (incorrectly saying 'yes') and false negatives (incorrectly saying 'no'). Equal Opportunity and Equalized Odds are fairness criteria that focus on whether these error rates are equal across different demographic groups.

Equal Opportunity

This metric focuses on fairness for those who deserve a positive outcome. It states that the probability of correctly getting a positive prediction should be the same for all groups. This is the same as saying the false negative rate must be equal. It's about not disadvantaging qualified individuals.

For example, if an AI screens for a scholarship, Equal Opportunity requires that among all students who are truly qualified, the same percentage from each demographic group gets recommended. It doesn't want qualified candidates from one group to be overlooked more often than those from another.

Equalized Odds

This is a stronger condition that builds on Equal Opportunity. It requires that both the false negative rate and the false positive rate be equal across groups. In addition to giving qualified people a fair shot, it also ensures that unqualified people are treated similarly.

Consider an AI used in pre-trial risk assessments to recommend bail. A false negative is releasing someone who reoffends. A false positive is detaining someone who would not have. Equalized Odds would demand that for both people who would and would not reoffend, the algorithm's error rates are the same regardless of race. This prevents one group from being disproportionately exposed to either type of mistake.

Equalized Odds and Opportunity are statistical 'group fairness' definitions that constrain an algorithm's error rates to be equal between groups based on protected characteristics like race or gender [1, 2].

• These metrics were developed to provide a more nuanced approach than simpler criteria like demographic parity, which only considers the overall rate of positive predictions and can be satisfied by models that harm qualified individuals from a protected group [1, 4]. [1] (2016)
• By conditioning on the ground truth outcome, these definitions force a model to perform consistently across groups for both individuals who are qualified for a positive outcome (true positives) and those who are not (true negatives) [1, 5]. [2] (2019)

These metrics have significant limitations. First, they require access to a 'ground truth' label (e.g., who actually would repay a loan), which is often unavailable or reflects the very historical biases the model is intended to correct [2]. Second, satisfying these group-level statistical criteria does not guarantee fairness for any given individual. Finally, it is often impossible to satisfy multiple fairness criteria simultaneously, and enforcing these constraints can reduce the overall accuracy of the model, creating a direct 'fairness-accuracy' tradeoff that must be carefully navigated [3].