  In many situations, the decision maker observes items in sequence and needs
to determine whether or not to retain a particular item immediately after it is
observed. Any decision rule creates a set of items that are selected. We
consider situations where the available information is the rank of a present
observation relative to its predecessors. Certain ``natural'' selection rules
are investigated. Theoretical results are presented pertaining to the evolution
of the number of items selected, measures of their quality and the time it
would take to amass a group of a given size.
