In mathematics, leximin order is a total preorder on finite-dimensional vectors.
The leximin order is particularly important in social choice theory and fair division.
The following algorithm can be used to compute whether x is leximin-larger than y: The leximax order is similar to the leximin order except that the first comparison is between the largest elements; the second comparison is between the second-largest elements; and so on.
In a typical social choice problem, society has to choose among several alternatives (for example: several ways to allocate a set of resources).
It is often called the egalitarian rule; see that page for more information on its computation and applications.
[9] It is also studied in the context of fuzzy constraint solving problems.
[10][11] The leximin order can be used as a rule for solving network flow problems.