At the kind of population sizes we’re working with, the size of the population has no impact on the accuracy of the estimates from a sample.

The only thing that impacts accuracy is the size of the sample itself.
- I.e., a 1,000 sample gives us a 3.1% margin of error no matter what country we are surveying in.

Increasing the sample size will improve accuracy but only marginally at sample sizes above 1,000.
Increasing the sample size by 50% to 1,500, for example, only reduces the margin of error to 2.5%.

Here’s a useful chart that demonstrates this:

What geography are you interested in?