Minimum Sample Sizes are calculated differently for Count Data (e.g. votes in an election) and Measurement Data (e.g. weight, temperature, etc.) Count Data are non-negative integers like 0, 1, 2, etc. Proportion is a statistic commonly used with Count Data. Here are some examples:
The following things increase the minimum Sample Size:
Alpha, α, the Significance Level, is selected by the tester. It is the largest Probability of an Alpha (False Positive) Error which they are willing to accept and still conclude that any difference, change, or effect is Statistically Significant. Most commonly α = 5% is selected. If are willing to accept only a low Probability of Alpha Error, then we need a larger Sample Size (n).
If we want a smaller Margin of Error, then n has to be larger.
And if the Proportion is closer to 50%, then we need a larger Sample Size, n.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.