There is a lack of consensus in measuring observer performance in search tasks. To pursue a consensus, we set our goal as to obtain metrics that are practical, meaningful and objective. We consider a metric practical if it can be implemented to measure human and computer observers' performance. To be meaningful, we propose to <i>discover</i> metrics that reflect the intrinsic properties of search observers. Thus, the meaningfulness of the metrics is ensured by the discovered properties being intrinsic. We set our success criteria as that the discovered properties can make verifiable predications. Thus the objectivity of the metrics is ensured by their prediction ability. The goal of this work is to present a theory and a conjecture toward two intrinsic properties of search observers: rationality in classification as measured by the location-known-exactly ROC curve and location uncertainty as measured by the effective set size. These two properties are used to develop search models in both single-response and free-response search tasks. To confirm whether these properties are "intrinsic", in a companion paper, we investigate their ability in predicting search performance of both human and scanning channelized Hotelling observers.