On the number of orderings of n items

Abstract:

Suppose that consumers have to classify n items or baskets of goods according to their individual preferences or utility and such that ties are allowed. In this paper we study the number of possible classifications or outcomes f(n). We obtain different representations for f(n) and use singularity analysis to determine the asymptotic behaviour of f(n). We also give a probabilistic interpretation of f(n) and use a renewal argument to study f(n) as n → ∞. Assuming that each of the f(n) outcomes has equal probability to occur, we study the random variable Nn where Nn equals the number of most preferred items, i.e. the number of items on the top of the list.

Año de publicación:

2007

Keywords:

• Renewal theory
• Preferences
• Singularity analysis
• Combinatorics

Fuente:

scopus