514:, any leximin function is Pareto-inefficient for a society that must make tradeoffs under uncertainty: There exist situations in which every person in a society would be better-off (ex ante) if they were to take a particular bet, but the leximin rule will reject it (because some person might be made worse off ex post).
451:
Often, there are many different states with the same minimum utility. For example, a state with utility profile (0,100,100) has the same minimum value as a state with utility profile (0,0,0). In this case, the egalitarian rule often uses the
735:
526:, that is: if utility is "moved" from an agent with more utility to an agent with less utility, and as a result, the utility-difference between them becomes smaller, then resulting alternative is preferred.
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represents all possible allocations, and the goal is to find an allocation which maximizes the minimum utility, or the leximin vector. This rule has been studied in several contexts:
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Independence of common utility pace - if all utilities are transformed by a common monotonically-increasing function, then the ordering of the alternatives remains the same.
456:, that is: subject to maximizing the smallest utility, it aims to maximize the next-smallest utility; subject to that, maximize the next-smallest utility, and so on.
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Moreover, the leximin rule is the only social-welfare ordering rule which simultaneously satisfies the following three properties:
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The leximin rule is Pareto-efficient if the outcomes of every decision are known with perfect certainty. However, by
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50:) is a rule saying that, among all possible alternatives, society should pick the alternative which maximizes the
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be a set of possible `states of the world' or `alternatives'. Society wishes to choose a single state from
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For example, suppose there are two individuals - Alice and George, and three possible states: state
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is leximin-optimal, since its utility profile is (2,4) which is leximin-larger than that of
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610:- a different rule that emphasizes the sum of utilities rather than the smallest utility.
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which are `best' for society. The question of what 'best' means is the basic question of
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of all individuals in society. It is a formal mathematical representation of the
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The egalitarian rule strengthened with the leximin order is often called the
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be a finite set, representing a collection of individuals. For each
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62:' principle of maximizing the welfare of the worst-off individual.
857:
Nicosia, Gaia; Pacifici, Andrea; Pferschy, Ulrich (2017-03-16).
818:"Computing leximin-optimal solutions in constraint networks"
916:"Individual Monotonicity and Lexicographic Maxmin Solution"
548:
The egalitarian rule is particularly useful as a rule for
471:
gives a utility of 1 to Alice and 8 to George. Then state
371:, that is, it solves the following optimization problem:
689:"Equity and the Informational Basis of Collective Choice"
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gives a utility of 9 to Alice and 1 to George; and state
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in 1970, and discussed in depth in many later books.
859:"Price of Fairness for allocating a bounded resource"
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The leximin rule for social choice was introduced by
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gives a utility of 2 to Alice and 4 to George; state
437:{\displaystyle \max _{x\in X}\min _{i\in I}u_{i}(x).}
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241:{\displaystyle u_{i}:X\longrightarrow \mathbb {R} }
816:Bouveret, Sylvain; Lemaître, Michel (2009-02-01).
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687:D'Aspremont, Claude; Gevers, Louis (1977).
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621:- max-min fairness in process scheduling.
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158:may represent all possible allocations.
27:Rawlsian decision rule for social choice
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764:Axioms of Cooperative Decision Making
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793:Fair Division and Collective Welfare
655:Collective Choice and Social Welfare
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267:is a mechanism which uses the data
58:philosophy. It also corresponds to
258:derives from each possible state.
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597:Egalitarian (leximin) bargaining.
306:{\displaystyle (u_{i})_{i\in I}}
734:Kolm, Serge-Christophe (2002).
544:Egalitarian resource allocation
522:The leximin rule satisfies the
313:to select some element(s) from
767:. Cambridge University Press.
693:The Review of Economic Studies
512:Harsanyi's utilitarian theorem
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18:Egalitarian social choice rule
1:
835:10.1016/j.artint.2008.10.010
761:Moulin, Herve (1991-07-26).
658:. Harvard University Press.
594:Egalitarian item allocation.
652:Sen, Amartya (2017-02-20).
552:. In this setting, the set
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885:10.1016/j.ejor.2016.08.013
625:Regret (decision theory)
589:Egalitarian cake-cutting
822:Artificial Intelligence
619:Max-min fair scheduling
583:Fair subset sum problem
536:Pigou-Dalton principle;
614:Proportional-fair rule
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524:Pigou–Dalton principle
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360:{\displaystyle x\in X}
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200:{\displaystyle i\in I}
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112:single-winner election
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110:. For example, in a
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978:Fairness criteria
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565:{\displaystyle X}
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962:Categories
876:1508.05253
636:References
501:Properties
479:(9,1) and
66:Definition
60:John Rawls
940:0012-9682
893:0377-2217
844:0004-3702
713:0034-6527
405:∈
389:∈
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231:⟶
192:∈
138:setting,
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602:See also
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483:(1,8).
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840:ISSN
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