Fairness criteria

Fairness criteria refer to a set of standards or principles used to evaluate and ensure equitable treatment and outcomes in various contexts, particularly in areas such as machine learning, data science, public policy, and social justice. The goal of applying fairness criteria is to mitigate bias, promote equity, and ensure that decisions and predictions are just and do not discriminate against any particular group based on characteristics such as race, gender, age, socioeconomic status, or other attributes.

Apportionment is the process of distributing a fixed resource, such as seats in a legislature or representatives, to different groups based on specific criteria. The criteria for apportionment methods can vary, but some key principles generally guide these methods: 1. **Fairness**: The apportionment method should be fair, ensuring that each group receives a number of representatives that reflect its size relative to other groups. The goal is to represent populations accurately.

Coherence, in the context of fairness, generally refers to the consistency and logical alignment of judgments, policies, or actions regarding fairness across different situations or individuals. In areas such as ethics, law, and machine learning, coherence involves ensuring that similar situations yield similar judgments or that rules applied in one context are also applicable in another, without bias or contradiction.

Egalitarian equivalence refers to a concept in economics and social theory that seeks to establish a fair distribution of resources, opportunities, or outcomes among individuals or groups, with particular emphasis on equality. The term is often associated with theories of equity and fairness, highlighting the importance of treating individuals equally or ensuring that any disparities in treatment are justified and reasonable.

Egalitarianism is a philosophical and political principle that advocates for equality among all people, particularly in terms of social, political, and economic rights and opportunities. The central idea is that all individuals should be treated as equals and have equal access to resources and opportunities, regardless of factors such as race, gender, socioeconomic status, or other characteristics.

Envy-freeness is a concept from the field of fair division and resource allocation, primarily used in economics and game theory. It refers to a condition in which each participant in a division of goods (e.g., resources, assets, or cake) prefers their own share over the shares allocated to others. In simpler terms, a division is envy-free if no individual envies another individual's portion.

Equitability generally refers to the quality of being fair and impartial. In various contexts, it emphasizes the importance of justice, fairness, and equal treatment, often within social, economic, and legal frameworks. The concept can be applied in different fields, including economics, education, and social justice.

In economics, equity refers to the concept of fairness or justice in the distribution of resources, opportunities, and benefits within a society. It often contrasts with equality, which emphasizes uniform distribution regardless of individual circumstances. Equity recognizes that different individuals or groups may require different levels of support or resources to achieve fair outcomes due to their varying needs, backgrounds, and barriers.

Group envy-freeness is a concept that arises in the context of fair division, particularly in resource allocation among multiple agents or participants. It is an extension of the individual envy-freeness concept. **Individual Envy-freeness:** An allocation is said to be envy-free for an individual if no participant prefers another participant's share over their own. Simply put, each person believes they have received at least as good a share as anyone else in the group.

Leximin order is a method of ordering or comparing multi-dimensional vectors based on a lexicographic criterion, which considers individual elements of the vectors in a specific sequence. Specifically, the term "leximin" combines elements of two concepts: "lexicographic order" and "minimum." In the context of multi-dimensional vectors, the leximin order prioritizes the worst (minimum) element of each vector.

Population monotonicity is a concept in social choice theory and mechanism design that pertains to the allocation of resources or goods among a group of individuals as the population of individuals changes. Specifically, an allocation method is said to be population monotonic if the allocation to any existing individuals does not decrease when the population increases, assuming that the preferences and resources available remain constant.

Proportional division is a method of dividing something, such as resources, assets, or benefits, among different parties in a way that reflects their respective shares or entitlements. This concept is often applied in various contexts, including finance, law, business, and even social or political settings.

Resource monotonicity is a concept primarily used in the field of computational economics and mechanism design, particularly in the context of allocating resources efficiently among agents with varying preferences or types. The basic idea behind resource monotonicity is that if the total amount of resources available to be allocated increases, then the allocation to each agent should not decrease. In other words, if the total resources are augmented, the allocation strategy should ensure that no individual agent receives less than they would have with fewer resources.