“LIMBO: Modeling the Varieties of Indecision”
Threshold and threshold-like processes are commonly postulated in the biological, social, and behavioral sciences, and they are frequently modeled using logistic or other sigmoidal functions. Such models have many merits for describing discrete choices between alternatives or acts. The threshold of a sigmoid function is its inflection point, implying that even the slightest perturbation will tip the actor toward one option or another. Yet phenomenologically, we are all familiar with situations of indecision in which we are "stuck in the middle", "on the fence," or "up in the air". I will describe a more complex model (provisionally called “LIMBO”) which contains the basic sigmoid and several other simple models (“monotonic propensity functions”) as special cases. The model can be motivated by several different theoretical accounts, including a weighted averaging process and a mixture model. The model delineates several different ways of being “indecisive,” and helps to distinguish among states of uncertainty, ambiguity, ambivalence, confusion, and protest. I will illustrate the model with analyses of jury decisions (standards of proof, jury nullification, hung juries, the Scotch "Not Proven" verdict) and I briefly compare and contrast this approach with item-response theory, signal detection theory, drift diffusion modeling, Bayesian modeling, and Dempster-Shafer belief functions.