Are partwise comparisons reliable?

It is not unusual for decisions in engineering or customer surveys to compare pairs or subsets of alternatives. Surprisingly, this standard, natural approach can cause valued information to be lost: a loss so severe that it can cause demonstrably incorrect decisions. By understanding why these errors occur, we identify an alternative, closely related decision approach that eliminates these problems. Also, we identify the nature of the lost information, and we show how to compute the likelihood that an incorrect outcome will occur.