We propose a family of measures of difference between ordinal prefer- 

ence relations. The difference between two preferences is the probability 

that they would disagree about the optimal choice from a random avail- 

able set. It is in this sense that these measures are choice-based. Measures 

differ according to the distribution of the random available sets. We use 

these measures to propose new social choice rules that achieve maximal 

expected assent among the members of the population. We also propose 

two further applications of these measures. The first is to welfare mea- 

surement when choice is irrational. The second is to the measurement of 

polarization in a population.