mathematics, leximin order is a total preorder on finite-dimensional vectors. A more accurate, but less common term is leximin preorder. The leximin order is particularly...

strengthened with the leximin order is often called the leximin rule, to distinguish it from the simpler max-min rule. The leximin rule for social choice...

Lexicographic order topology on the unit square Lexicographic ordering in tensor abstract index notation Lexicographically minimal string rotation Leximin order Long...

value; and so on. It is also called leximin cake-cutting, since the optimization is done using the leximin order on the vectors of utilities. The concept...

Lexicographic max-min optimization (also called lexmaxmin or leximin or leximax or lexicographic max-ordering optimization) is a kind of multi-objective optimization...

as possible, and so on (by the leximin order). Therefore, an egalitarian item allocation is sometimes called a leximin item allocation. The special case...

the nucleolus satisfies the second-smallest excess; and so on, in the leximin order. The nucleolus was introduced by David Schmeidler. In a cooperative...

in R 2 N {\displaystyle \mathbb {R} ^{2^{N}}} ) is smallest in the leximin order. The nucleolus was introduced in (Schmeidler 1969). (Maschler, Peleg...

dominant resource given to a user (then the second-minimum etc., in a leximin order). The dominant resource may be different for different users. For example...

a smaller cost for him, the vector of costs becomes smaller in the leximin order. If the weights are player-independent (equivalently: the CG is unweighted...

positive integer numbers, weak majorization is called Dominance order. Leximin order Talagrand, Michel (1996-07-01). "Majorizing measures: the generic...

This corredponds similarly to the egalitarian rule, refined by the leximin order. Konieczny, Lang and Marquis present the DA2 framework, which generalizes...

ordinally-egalitarian allocation is one that maximizes the vector t in the leximin order. PS is the unique rule that returns an ordinally-egalitarian allocation...

transfer rate. River-sharing with different entitlements, based on the leximin order. River-sharing when the river is not linear. Scott Barret (1994). "Conflict...

Yager, Ronald R. (1997-10-01). "On the analytic representation of the Leximin ordering and its application to flexible constraint propagation". European Journal...

members: The limit when η → − ∞ {\displaystyle \eta \to -\infty } is the leximin ordering. For η = 0 {\displaystyle \eta =0} we get the Nash bargaining solution—maximizing...

maximizes the smallest utility (based on the egalitarian rule and the leximin order). It is group strategyproof, and attains a 1/2-factor approximation...

minimize the next-largest unfairness etc., using the leximin order. This yields a method called the leximin apportionment method. It was first developed by...

(1984). "Rindërtimi i mbishkrimit të Arbërit dhe mundësitë e reja për leximin e tij / La reconstruction de l'inscription de l'Arbër et les nouvelles...

(1984). "Rindërtimi i mbishkrimit të Arbërit dhe mundësitë e reja për leximin e tij / La reconstruction de l'inscription de l'Arbër et les nouvelles...

or when there are n agents with identical valuations. In this case, the leximin-optimal allocation is EFx and Pareto-optimal. However, it requires exponentially...

maximizing the smallest utility, egalitarian optimality is often refined to leximin-optimality: from the subset of allocations maximizing the smallest utility...

second-maximum load, etc. (using lexicographic max-min optimization). Leximin-Phragmen: Maximizing the minimum load, and subject to that the second-minimum...

polynomial-time reductions for the solutions of maximum Nash welfare and leximin, between the models of private goods, public goods, and public decision...

(1984). "Rindërtimi i mbishkrimit të Arbërit dhe mundësitë e reja për leximin e tij / La reconstruction de l'inscription de l'Arbër et les nouvelles...

group-FS) but is easier to compute.: Thm.3 in 2002 draft  The egalitarian (leximin) rule maximizes the smallest utility, then the next-smallest, etc. It is...

classrooms to schools using a non-trivial implementation of the randomized leximin mechanism. Unfortunately it was not deployed in practice, but it was tested...

that the egalitarian rule is Lorenz dominant (a property stronger than leximin-optimality), unique in utilities, and group-strategyproof. Garg, Hoefer...

satisfied by three welfare-maximization rules: utilitarian, egalitarian (leximin) and Nash-product; they also study their computational complexity. They...

PE; therefore this is the PEEEA. Note that the resulting allocation is leximin-optimal - it maximizes the utility of the poorest agents, and subject to...