Modeling the Act of Measurement in the Social Sciences∗

Motivated by time-series experimental designs, we develop a model of the act of measurement in the social sciences. Meaningful measurements are represented by operators that obey a non-commutative algebra. Thus, the order in which information is extracted matters. In addition, responses to questions about an attribute depend on whether information about another attribute has previously been extracted. Measurement “forces” the subject to obtain one value of the attribute, the one measured by the observer. An uncertainty principle imposes a fundamental limit on the ability to extract detailed information about two distinct attributes within a short period of time. ∗I am grateful for suggestions by two anonymous referees. I thank, without implicating in any way, Professors Frank Tabakin and Jim Feigenbaum for suggesting some of the physics references. I also thank Professors Duffy and Oachs for suggesting some of the psychology references. All errors are mine.