Many things that should be a vector are treated as a magnitude. For example, when someone says “inflation is at 5%” they are multiplying the rate of increases of prices over a year (a vector) against another vector, which is how important is each increase. In my home country of Argentina, this has been a source of discussion many times, with different organizations reporting different inflation rates because of the importance they gave to each product.

  Category   Increase  W1     W2
  ───────────────────────────────
  Food       +8%       .3     .1
  Fuel       +12%      .5     .1
  Energy     +3%       .1     .3
  Housing    +2%       .1     .5
  ───────────────────────────────
  Inflation:         8.9%   3.9%

In addition, deciding who’s right and who’s wrong is not easy, and in many cases even impossible. Different perspectives and lifestyles demand different solutions. My inflation is not your inflation. But we live in a world that loves such simplifications, even though they are wrong.

While inflation (the vector) of a particular product by some particular seller is something that can be accurately measured and objective, there are other categories of measurable things that are impossible to measure accurately nor objectively. Star-ratings of products are the ultimate example of this. The rating of a book or movie are extremely subjective and multidimensional; and the summarization of these ratings as the average of all opinions by all persons creates a number that represents nobody’s actual experience.

A 3.5-star rating could mean everyone found the product mediocre, or it could mean half the people loved it and half hated it. These are radically different situations compressed into the same number.

   "Mediocre      "It depends on
    consensus"     whom you ask"
       │                 │
       ▼                 ▼
       ██          ██          ██
       ██          ██          ██
    ██ ██ ██       ██          ██
    ██ ██ ██       ██          ██
 ──────────────   ───────────────
 1  2  3  4  5     1  2  3  4  5

What would it look like to preserve the dimensionality? Recommendation systems try to do this: instead of telling you “this movie is 4.2 stars”, they try to find people with similar taste vectors and tell you “people like you rated this 4.8”. But even this is a simplification, since it assumes your taste is a stable vector rather than something that shifts with mood, context, or phase of life.

The honest answer is that some things resist measurement entirely. Not because they’re mystical or ineffable, but because the act of collapsing them into a number destroys the information that makes them useful. We pretend we’re being rigorous when we’re actually being reductive.

Perhaps the better question isn’t “what’s its rating?” but “what are the dimensions, and which ones matter to me right now?”