A large sample is not a guarantee for a representative sample. The way in which the sample is drawn is at least as important as the sample size. However, there are guidelines that tell you how large your sample at least should be. In general, it is the case that the smaller the population, the larger the part has to be that is included in your sample. For example, if the population consists of 50 people, you need approximately 49 to obtain representative results. A rule-of-thumb is that, for small populations (<500), you select at least 50% for the sample. For large populations (>5000), you select 17-27%. If the population exceeds 250.000, the required sample size hardly increases (between 1060-1840 observations).

In sum: the smaller the population, the larger the required sample ratio.