Kelvin Lancaster’s consumer behavior theory, in utility theory, and in modern statistical methods. Psychological roots Early psychology work involved the typical experiment: Here are two objects with weights, w1 and w2, which is heavier? The finding from such an experiment would be that the greater the difference in weight, the greater the probability of choosing correctly. Graphs similar to the one on the right result. Louis Leon Thurstone proposed (in the 1920s) that perceived weight, w = v + e, where v is the true weight and e is random with E(e) = 0. The assumption that e is normally and identically distributed (NID) yields the binary probit model. Econometric formulation Economists deal with utility rather than physical weights, and say that observed utility = mean utility + random term. The characteristics of the object, x, must be considered, so we have u(x) = v(x) + e(x). If we follow Thurston's assumption, we again have a probit model. An alternative is to assume that the error terms are independently and identically distributed with a Weibull, Gumbel Type I, or double exponential distribution. (They are much the same, and differ slightly in their tails (thicker) from the normal distribution). This yields the multinomial logit model (MNL). Daniel McFadden argued that the Weibull had desirable properties compared to other distributions that might be used. Among other things, the error terms are normally and identically distributed. The logit model is simply a log ratio of the probability of choosing a mode to the probability of not choosing a mode. Observe the mathematical similarity between the logit model and the S-curves we estimated earlier, although here share increases with utility rather than time. With a choice model we are explaining the share of travelers using a mode (or the probability that an individual traveler uses a mode multiplied by the number of travelers). The comparison with S-curves is suggestive that modes (or technologies) get adopted as their utility increases, which happens over time for several reasons. First, because the utility itself is a function of network effects, the more users, the more valuable the service, higher the utility associated with joining the network. Second because utility increases as user costs drop, which happens when fixed costs can be spread over more users (another network effect). Third technological advances, which occur over time and as the number of users increases, drive down relative cost. An