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Lexicographic preferences or lexicographic orderings describe comparative preferences where an economic agent prefers any amount of one good -LRB- X -RRB- to any amount of another -LRB- Y -RRB- .. economic agent. agent ( economics ). Specifically , 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 between bundles with regard to the number of units of X will the agent start comparing the number of units of Y across bundles .. Lexicographic preferences extend utility theory analogously to the way that nonstandard infinitesimals extend the real numbers .. With lexicographic preferences , the utility of certain goods is infinitesimal in comparison to others .. infinitesimal. infinitesimal. For example , if for a given bundle -LRB- X ; Y ; Z -RRB- an agent orders his preferences according to the rule X >> Y >> Z , then the bundles -LCB- -LRB- 5 ; 3 ; 3 -RRB- , -LRB- 5 ; 1 ; 6 -RRB- , -LRB- 3,5,3 -RRB- -RCB- 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. Note that the number of X 's is the same , and so the agent is comparing Y 's .. Even though the third option has the same total goods as the first option , the first option is still preferred because it has more X.. Even though the third option has far more Y than the second option , the second option is still preferred because it has more X.. A distinctive feature of such lexicographic preferences is that a multivariate real domain of an agent 's preferences does not map into a real-valued range .. domain. domain ( mathematics ). range. range ( mathematics ). That is , there is no real-valued representation of a utility function .. utility function. utility function. In terms of real valued utility , one would say that the utility of Y and Z is infinitesimal compared with X , and the utility of Z is infinitesimal compared to Y .. infinitesimal. infinitesimal. The model of real numbers is always logically ambiguous ; one is allowed to adjoin infinitesimal quantities to make a nonstandard model .. infinitesimal. infinitesimal. nonstandard model. nonstandard analysis. Standard models of the real numbers exclude infinitesimals , so lexicographic preferences are not precisely described by standard reals .. But by assigning a utility to X which is much much larger than the utility of Y , which in turn is much much larger than the utility of Z , the infinitesimal order relation can be approximated arbitrarily closely , which means this is a problem of idealized limits only .. infinitesimal. infinitesimal