Ranking and Rating
Let’s say you’re buying a car, and you want to shortlist a few good models to choose from.
You can rank multiple options in order of preference: MG Windsor > Tata Curvv EV > Creta1.
Alternatively, you can give each car a numeric rating like 100/100 for the Windsor2, 95 for the Curvv and 70 for the Creta. This communicates more information: The Windsor and the Curvv are both excellent, and it’s a significant downgrade to the Creta. Another common example is star ratings for for restaurants on Google Maps, where one could be 4.5 stars, another could be 4.1 stars, and a third could be 2.3 stars3. In this case, go to one of the first two restaurants. Don’t stress about which one — as long as you avoid the third restaurant, you’re good.
If you’re given ratings, you can convert them to a ranking by sorting them in decreasing order of the rating, and then deleting the numbers. But you can’t go the other direction. A rating always gives more information than a ranking4.
Is more information better? In some situations, yes — too little information may not be credible. But in other situations, information overload overwhelms people, and they lose sight of the important aspect, which ranking captures. Too much information can also invite nit-picking. For example, someone could argue with you that “The Creta isn’t 70; it’s 80.” Since the distance to 95 is much more than the distance between 95 and 100, it doesn’t matter. So, if you’re giving ratings and people are nit-picking, switch to a ranking.
You can rank with or without taking the price into consideration. That’s an independent dimension.
In this example, the best car receives a rating of 100/100. This makes it a relative rating. In other words, you’re rating cars in comparison with the leader.
Alternatively, you could go for an absolute rating, where you compare cars against the hypothetical perfect car for you. Since that doesn’t exist, no car gets 100/100. If I were to follow this approach, I might rank Windsor 80/100, Curvv EV 75/100, and Creta 50/100.
Neither ranking nor rating imply substitutability. Instead of watching a movie rated 9 stars out of 10, you can’t watch two movies rated 4.5 stars each.
These concepts are referred to in the literature as cardinal and ordinal utility.