# Lexicographic preferences

**Lexicographic preferences**(lexicographical order based on the order of amount of each good) describe comparative preferences where an economic agent infinitely prefers one good (X) to another (Y). Thus if offered several bundles of goods, the agent will choose the bundle that offers the most X, no matter how much Y there is. Only when there is a tie of Xs between bundles will the agent start comparing Ys.For example, if for a given bundle (X;Y;Z) an agent orders her preferences according to the rule X

**>**Y**>**Z, then the bundles {(5;3;3), (5;1;6), (3,5,3)} would be ordered, from most to least preferred:# 5;3;3

# 5;1;6

# 3;5;3*Even though the first option contains fewer total goods than the second option, it is preferred because it has more Y.

*Even though the third option has the same total goods as the first option, the first option is still preferred.

*Even though the third option has far more Y than the second option, the second option is still preferred because it has slightly more X.**Implications**If all agents have the same lexicographic preferences, then

general equilibrium cannot exist because agents won't sell to each other (as long asprice of the less preferred is more than zero). But if the price of the less wanted is zero, then all agents want an infinite amount of the good. Equilibrium cannot be attained.Lexicographic preferences can still exist with general equilibrium. For example,

*Different people have different bundles of lexicographic preferences.

*Some people have lexicographic preferences, not all.

*Lexicographic preferences extend only to a certain quantity of the good.Lexicographic preferences are the classical example of rational preferences that are not representable by a ml|Utility|Utility_functions|utility function, if amounts can be any non-negative real value. If there were such a function "U" then, e.g. for 2 goods, the intervals ["U"("x",0),"U"("x",1)] would have a non-zero width and be disjoint for all "x", which is not possible for an uncountable set of x-values. If there are a finite number of goods and amounts can only be rational numbers, utility functions do exist.

The relation is not continuous because for a decreasing

convergent sequence $x\_n\; ightarrow\; 0$ we have $(x\_n,0)>(0,1)$, while the limit (0,0) is smaller than (0,1).

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Lexicographical order**— In mathematics, the lexicographic or lexicographical order, (also known as lexical order, dictionary order, alphabetical order or lexicographic(al) product), is a generalization of the way the alphabetical order of words is based on the… … Wikipedia**Utility**— This article is about the economic concept. For other uses, see Utility (disambiguation). Part of a series on Utilitarianism … Wikipedia**Preference**— (also called taste or penchant ) is a concept, used in the social sciences, particularly economics. It assumes a real or imagined choice between alternatives and the possibility of rank ordering of these alternatives, based on happiness,… … Wikipedia**Strict weak ordering**— The 13 possible strict weak orderings on a set of three elements {a, b, c}. The only partially ordered sets are coloured, while totally ordered ones are in black. Two orderings are shown as connected by an edge if they differ by a single… … Wikipedia**Jose Encarnacion, Jr.**— José Encarnación, Jr. [1928 1998] was professor of economics at the University of the Philippines, where he served as dean of the School of Economics from 1974 until his retirement in 1994. Encarnación was educated at the University of the… … Wikipedia**Cooperative game**— This article is about a part of game theory. For video gaming, see Cooperative gameplay. For the similar feature in some board games, see cooperative board game In game theory, a cooperative game is a game where groups of players ( coalitions )… … Wikipedia**Linguistic prescription**— Linguistics … Wikipedia**Multi-criteria decision analysis**— Multiple criteria decision making or multiple criteria decision analysis is a sub discipline of operations research that explicitly considers multiple criteria in decision making environments. Whether in our daily lives or in professional… … Wikipedia**List of PSPACE-complete problems**— Here are some of the more commonly known problems that are PSPACE complete when expressed as decision problems. This list is in no way comprehensive. Games and puzzles Generalized versions of: Amazons· Atomix· Geography· Gomoku· Hex· Reversi·… … Wikipedia