What expansion factor should be used in binned probability proportional tosize sampling?

In probability proportional to size sampling, including prism cruising and other forms of point and line sampling, calculation of an exact expansion f actor requires that size be recorded exactly. When sizes are binned or reco rded by class, this information is lost. While several alternatives for cal culating the expansion factor have been proposed, theoretical attention has been lacking. A decision-theoretic perspective helps distinguish between t he alternatives and offers some support to the use of the arithmetic mean s ize in calculating the expansion factor, a choice which had previously come under some criticism. However, consistency arguments strongly favor estima tors based on squared error loss or minimax principles. Some new alternativ es are suggested when prior information about the diameter distribution in a stratum is available.