Ordinal numbers are ranked. In contrast, cardinal numbers are equidistant. So you can do mathematical operations on cardinal numbers, but not ordinal, because 15th place isn’t 5 times better (or worse) than 3rd place.
The ordinal critique of effective altruism is centred on interpersonal comparisons. The ordinal critique makes the claim that a dollar, or an intervention that increases the subjective well-being of a donation recipient cannot be said to give more utility in your pocket because utility is ordinal, not cardinal.
But isn’t it obvious to say that a starving person in the developing world gets more utility from a hotdog than a bodybuilder in the developed world? Perhaps, but that can be an ordinal comparison. The question of how many bodybuilders fed by hotdogs is equivalent utility to a starving person getting a hot dog, that’s a mathematical operation, cardinal, and by an ordinal theory of value, nonsensical. You can substitute persons with charities here.
The case against the ordinal argument
In 1947, Game theorists Von Neumann and Morgenstern’s published on Expected Utility Theory, arguing that individual’s ordinal rankings of options under certain axioms mimiced a cardinal utility function anyway.
The steelmanning of the ordinal critique
The ‘’Allais paradox’’ reveals that people often behave in ways inconsistent with von Neumann and Morgenstern axioms, so cardinal numbers can’t be assigned to ordinal preferences.
Temperature on thermometers can be viewed as cardinal because molecules are doing their thing and there’s an absolute zero to which we can calibrate our scale. Can we say the same for any or a particular measure of utility utilised by the effective altruism movement? How bad is torture? How bad is death? How good is the value of a human life compared with an animal, or a friend, or an effective altruism, or a person with a disability?