Theory Choice and the Intransitivity of 'Is a Better Theory Than'

There is a very plausible transitivity principle for theory choice. It says that if all criteria of theory evaluation are considered, and theory A is a better theory than theory B, and theory B is a better theory than theory C, then A is a better theory than C. I argue against this principle. It turns out that whenever there are two or more relevant and independent criteria of theory evaluation, and that whenever at least of one the criteria is 'nonlinear' in a certain sense, there may be violations of transitivity that do not violate any standards of rationality (of theory choice). This shows, again, that theory choice cannot be seen as merely the application of given rules of rational theory choice.