Why are the number on a ball in a lotto draw categorical nominal instead of categorical ordinal?
Don’t the numbers have a natural ascending order and would thus be ordinal? Or am I making an incorrect assumption about numbers having a natural order?
You could color-code the balls without fundamentally changing the game. Instead of 6-12-11, we get red-blue-pink.
You could go with letters without fundamentally changing the game. Instead of 6-12-11, we get Y-Q-X.
You could use animal drawings without fundamentally changing the game. Instead of 6-12-11, we get dog-fish-horse.
The 6-ball isn’t worth half as much as the 12-ball. It doesn’t even represent a lesser value. The number is just on the ball as a link to lottery tickets.
It could be different if the number represented some kind of quantity, like rolling dice and advancing a game piece that many spots, but there’s nothing quantitative going on. The numbers on lottery balls just serve as links back to the tickets.
You probably can accept this for something like towns having zip codes or people having phone numbers. It’s the same idea.