> "Intuitively, with some survey measure of 0 to 10, maximum polarization would be 50% of respondents responding 0 and 50% of respondents responding 10. Minimum polarization would be 100% of respondents giving the same answer (regardless of what that answer is)."
A world where 50% of people live at the North Pole, 50% at the South Pole and nobody at the equator, is polarized. So is a world where 90% of people live at the North Pole, 10% at the South Pole and nobody at the equator. Seems like "polarization" is about how many people live somewhere in between, rather than whether the groups at the poles are balanced or not.
Or even, that there exist places between the poles where people could be, even if they aren't. A world where 100% are at the North Pole, the South Pole exists but nobody is there, and between them is only water, is still polarized. The only place you can be, or go, is the two extreme positions. If the survey says "do you LOVE Politician X or HATE them?" and I can't be indifferent to them or mildly in favour or slightly against, it's a polarizing survey, isn't it?
> A world where 50% of people live at the North Pole, 50% at the South Pole and nobody at the equator, is polarized. So is a world where 90% of people live at the North Pole, 10% at the South Pole and nobody at the equator.
First, in order to make sense, it should be "would like to live" not "live", with some context that a new city needs to be built, or something. Polarization is about opinions and attitudes.
Secondly, a world where 90% of people would like everyone to live at the North Pole and 10% would like everyone to live at the South Pole is less polarized. Society is able to make a compromise that is acceptable to more people.
If 8 billion people think soap tastes terrible, 1 person thinks soap tastes delicious, and nobody thinks soap tastes meh, we've reached consensus as a society. There will always be some issues where there is a strong consensus at one extreme or another, but that doesn't hamper society's ability to agree on decisions.
Indeed, and the discourse around American political polarization is centered around the Pew poll which poses binary choices like the one between "homosexuality should be accepted by society" or "homosexuality should be discouraged by society", not questions that have scales of agreement from 0-10.
A world where 50% of people live at the North Pole, 50% at the South Pole and nobody at the equator, is polarized. So is a world where 90% of people live at the North Pole, 10% at the South Pole and nobody at the equator. Seems like "polarization" is about how many people live somewhere in between, rather than whether the groups at the poles are balanced or not.
Or even, that there exist places between the poles where people could be, even if they aren't. A world where 100% are at the North Pole, the South Pole exists but nobody is there, and between them is only water, is still polarized. The only place you can be, or go, is the two extreme positions. If the survey says "do you LOVE Politician X or HATE them?" and I can't be indifferent to them or mildly in favour or slightly against, it's a polarizing survey, isn't it?