Conservation of information in relative search performance

While conservation of information popularized by the No Free Lunch (NFL) theorem establishes that all search algorithms have the same performance on the average, this appears not to be true when performance is compared in a relative manner. Some algorithms look to perform better than others. However, this advantage is lost when averaging is over a group of related algorithms. Every advantage against one algorithm is balanced by a disadvantage against a related algorithm. From this perspective, conservation of information still applies. As a consequence, comparative transitivity does not hold. If search procedure Z beats Y which, in turn, beats X, we cannot conclude that Z beats X. Indeed, the opposite might be true.