The Error of Utilitarianism

Utilitarianism aims to maximize the usefulness for the greatest majority using some utility function. This has a fatal flaw in that it is trying to synthesize human preferences as some objective scale that can be used to compare different actions against it to see which has more utility.

To understand why this is a flaw we must look at the core data types:
Nominal Data - These are just descriptive statements, observations of reality such as 'The sky is blue', 'I like Porsche cars'
Ordinal Data - These are lists of entries in some particular order that demonstrates preference, such as Likert scales (strongly agree, agree, neutral, disagree, strongly disagree), your top 10 favourite movies of all-time etc etc. Notably with ordinal data, we see there is no implied distance from rank to rank i.e. 'strongly agree' isn't 2x or 3.5x 'agree'
Cardinal Data - This is quantitative data using numbers where arithmetic is meaningful
- Interval Data: This is data is measured along a numerical scale that has equal distances between adjacent values. These distances are called “intervals.” There is no true zero on an interval scale Temperature is interval data as it has an arbitrarily chosen 0-point (the temperature water freezes) as well as 35C is 10C more than 25C. However because of this arbitrary 0-point we cannot make meaningful statements such as 35C is 2x/3x hotter than 25C. This also means negative temperature is simply a 'colder temperature' and nothing else can be derived from it.
- Ratio Data: This is interval data with an object 0-point such as Length. We know 0mi = 0" = 0cm as well as make meaningful statements such as 10cm is 2x 5cm. We also can make meaningful statements about negative values unlike interval data such as -$10 is $10 that I owe.

So what does this mean for the hopeful utilitarian? Well, human preferences would be needed to be transformed into ratio level data for us to decide which actions have more 'utility' but this is not possible.
Human preferences are ordinal, your favourite hobbies/foods/movies etc are subjective and no meaningful arithmetic can be performed in such a list similarly for the rest of man. Therefore, no aggregation of these preferences can be made across all of man in order to create ratio level data — it is a non-starter.

Additionally, ratio level data needs a non-arbitrary 0-point but this would entail the concept of 0 utility. What would that be? What is to have 0 satisfaction or an indifference to any satisfaction across all of man? Man acts because of his state of current dissatisfaction, so what would be an action that results in 0 utility, what would that imply? Wouldn't 0 be an improvement from negative utility in some cases? But that nullifies it being an objective 0-point and more like interval level data such as 0 Celsius instead.

Furthermore, if buying a car increases a man's utility in terms of transport from 15 utility to 20, should we then make him buy another so that we can double his utility to 25? Why stop at two cars, we can 100x his utility which is the entire aim right?

Utilitarianism fails since it is attempting to convert ordinal data which has no equal distances between rankings that is completely subjective from man to man, into a ratio level scale where it's 0-point is not just impossible but nonsensical as this does not even exist for an individual.

An equivalence of this would be if we tried taking nominal data and tried converting it to ordinal data. Take these statements, "The sky is blue", "I like Porsche cars", "My favourite team is Liverpool FC". How on earth would anyone make a ranking for such statements? What is even the criteria? We cannot extrapolate any of the necessary information from nominal level statements to construct the ordinal level data with. Similarly, we cannot extrapolate the necessary information from ordinal level data to construct ratio level data.
Utilitarianism is a fool's errand.