Mechanism design is a field in economic theory and game theory that focuses on creating systems or institutions (mechanisms) that lead to desired outcomes or behaviors among self-interested agents. It is often described as "reverse game theory," as it starts with the desired outcomes and then works backward to devise rules or mechanisms that will result in those outcomes when individuals act in their own interests.
A median graph is a specific type of graph in graph theory that has a distinctive property related to distances between its vertices. In particular, a median graph is defined as a graph in which, for any three vertices \( u, v, w \), the distance between any two of these vertices is less than or equal to the sum of the distances from the third vertex to the two others.
In social choice theory, neutrality refers to a principle that is used to evaluate and compare different voting systems or decision-making methods. Specifically, a social choice rule is said to exhibit neutrality if it treats all options (or candidates) equally, meaning that the procedure does not favor any particular alternative over another when determining the outcome of the collective decision. Formally, a social choice rule is neutral if, whenever the set of options is permuted (i.e.
Optimal apportionment is a mathematical concept often used in the context of allocating resources, representatives, or seats in a legislative body among different groups or regions in a way that is considered fair and efficient. The goal of optimal apportionment is to achieve a distribution that reflects the relative sizes or populations of the groups involved while adhering to certain fairness criteria.
The Proportional-Fair (PF) rule is an allocation strategy commonly used in the context of resource allocation in wireless networks and other network systems, particularly in scenarios involving multiple users sharing a limited resource, such as bandwidth or power. The goal of the PF rule is to balance efficiency and fairness in resource allocation while maximizing the overall system utility.
A **quasitransitive relation** is a type of binary relation that generalizes the concept of transitivity. A binary relation \( R \) on a set \( A \) is called quasitransitive if it satisfies the following property: For all \( x, y, z \in A \): - If \( x R y \) and \( x R z \), then \( y R z \) or \( z R y \) holds.
Ranked voting, also known as ranked-choice voting (RCV), is an electoral system in which voters rank candidates in order of preference rather than selecting just one candidate. This system allows voters to express their preferences more fully and can lead to more representative outcomes. Here’s how ranked voting typically works: 1. **Ranking Candidates**: Voters rank the candidates on the ballot according to their preferences.
The term "unrestricted domain" can refer to different concepts depending on the context in which it is used. Here are a few interpretations: 1. **Mathematics**: In the context of mathematics, particularly in functions and calculus, an "unrestricted domain" refers to a set of inputs for which a function is defined without any limitations.