This book stems from a desire to understand the underlying assumptions and structure of the choice probability models most often used in transportation planning. The book investigates how far a new way of defining cost minimizing behavior can take us. All commonly used choice probability distributions of the logit type log linear probability functions follow from cost minimizing behavior defined in the new way; some new nested models also appear. The new approach provides a deeper understanding of what is at work in the models. The new way of defining cost minimizing behavior is as follows: cost minimizing behavior pertains if the likelihood (probability) of any independent sample of observations is a decreasing function of the average cost of the sample. Extreme value distributed random variables are not used in the derivation of models. A measure of freedom of choice related to the Shannon measure of how much 'choice' is involved is used to obtain a welfare measure which is equal to composite cost.