Cuil Theory could be used to measure the distance between a persons words or beliefs and his actions when it comes to ethics. Thus, my ex-girlfriend who constantly nagged me about saving the world from poverty and hunger would happily eat an expensive steak every once in a while. Another example would be people who are against American dependence on foreign oil, but happily drive their terrorist-supporting SUVs.
Going back to the original inspiration for this, imagine searching for 'end world hunger' on the cuil search engine and getting back 'eat a juicy steak now!' as one of the top results.
Thus there is a certain amount of ethical/moral incoherence. Obviously, there is a certain amount in each person, and cuil theory would be a good way to measure that. The same kind of thinking can be applied to political candidates and their statements. Cuil Theory can measure the level of abstraction between a candidates platform and their actions/attempted actions.
This would be more than a simple check of how many campaign promises they've fulfilled four years after. This would instead be a check of whether the candidate is who he says he is. Cuil Theory would be a useful tool to measure levels and amounts of flip-flopping, pandering and outright lying. A campaign where the candidate moves from centrist-maverick to right-wing panderer would have a few cuils. A campaign where the candidate clings to his fringe beliefs regardless of how unpopular or how crazy they make him look would be closer to 0.
Going back to the ethical coherence measurement, I think it would also be great if cuils were used as a measurement of each action to each ethical viewpoint. For example, if someone were devoted to the three ideals of
A: Ending World Hunger
B: Becoming a Doctor
C: Banging lots of Hot Chicks,
he could measure each action he took in terms of cuils to see how far they help in reaching those goals. So, his expensive, sit-down dinner with a hot chick is 2 cuils away from A, 1 cuil away from B and 0 to 0.5 cuils away from C (the dinner doesn't make the hot chick materialize in his bed, but it does increase his chances of getting laid).
Cuil Theory can help measure one's progress towards achieving one's goals.