Quantitative measures require units of measurement.

When the same taster is judging two dishes at the same time, the emotional state is the same, the taste buds are the same, the mental state is the same. The effect is the same as if you had a tasting robot programmed to output a number when you drop food into its sampling port. Most of the subjectivity is removed. But different people/tastebots have different calibration settings, so you can't compare results between tasters, or even between different times for the same taster. It's only objective if you taste steps to remove the subjectivity: blindfolds on, equal-sized portions, neutral-flavor palate-cleanser between tastes, quiet room, etc.; but if you are careful, you can then have reasonable confidence that if A > B in that subjective state, it is likely that A > B in most other subjective states, too. (Any state that caused B > A would then be considered "interesting".)

A subjective, qualitative measurement would be something like Scoville heat units. Each taster has a different sensitivity to piquant chemicals, and different rates of sensory adaptation, so multiple judges are used, and results are imprecise.

An ordinal ranking is not quantitative. You can't tell the following apart:

  qualitative ordinal ranking
  A > B > C > D > E > F > G > H
  
  |<-theoretic quantitative measurement->|
  ----A---B--C-------D-EF---G------H------
  ------AB----C----D----E----F-----G--H---
  A------------------------------BCD--EFGH
  -------------A-B-C-D-E-F-G-H------------