The tune in-and-out model: A random walk and its application to a presidential election survey

The stochastic model for the evolution of preferences proposed by Falmagne, Regenwetter, and Grofman [1997. Journal of Mathematical Psychology, 41, 129-143] and tested by Regenwetter, Falmagne, and Grofman [1999. Psychological Review, 106, 362-384], as well as the alternative Thurstonian model of Böckenholt [Falmagne, J.-C., Regenwetter, M., & Grofman, B. (1997). A stochastic model for the evolution of preferences. In A. A. J. Marley (Ed.), Choice, decision and measurement: Essays in honor of R. Duncan Luce (pp. 113-131). Mahwah, NJ: Lawrence Erlbaum.], gave a good statistical account of attitudinal panel data from the 1992 US presidential election. We show, however, that both models have the defect of underestimating the number of respondents who did not change their order of preference for the candidates across different polls. We present a generalization of Falmagne et al.'s model based on the idea that some individuals may become momentarily impervious to all matters related to the campaign and 'tune out.' This behavior could be triggered by some personal reason or by some external event related to the campaign. Like the original model, the resulting model is a random walk, but on an augmented set of states. A respondent in a 'live' state behaves as in the previous model, except when receiving a 'tune-out' token, which effectively freezes the respondent's preference state until it is reversed by a 'tune-in' token. We describe and successfully test the new model on the same 1992 National Election Study panel data as those used by Böckenholt (2002) and Regenwetter et al. (1999).