An interesting mathematical fact is that the margin of error depends only on the sample size and not on the population size, provided that the population is significantly larger than the sample size. Thus for instance, the poll in the running example with 1,013 randomly sampled registered voters would yield essentially the same margin of error (4% with a 99% level of confidence) regardless of whether the population of registered voters consisted of 100,000 people or 100,000,000 people.
This may seem counter-intuitive at first; after all, each person in the population has a unique personality and opinion, and in a very large population, only a very small fraction of such people would actually be polled, and it would thus seem that the poll is not capturing enough information. However, because a poll involves only a very specific question, there is only one relevant attribute in the population that needs to be considered, and this means that an individual's opinion is effectively equivalent to those of many other members of the population, some fraction of which will be polled. For instance, in the running example, the only relevant attribute of a population member is whether he or she is a Bush voter, a Kerry voter, or a Nader voter - all other characteristics of a population member are irrelevant. Thus for instance if there are 100,000,000 registered voters, and 48,000,000 of them were Kerry voters, then for the purposes of this statistical analysis all of the 48,000,000 individuals in this group would be completely interchangeable and equivalent. An individual Kerry voter has 47,999,999 other voters with identical opinions (as far as the poll question is concerned), and it is exceedingly likely that a poll of 1,013 voters will contain a properly representative fraction of this group, provided of course that the voters being polled were selected randomly.
To give an analogy, suppose that one is trying to estimate the percentage of salt in an ocean. This can be easily accomplished by taking a glass of seawater and then chemically analyzing the proportion of salt in that sample. The amount of salt and water in this glass is far smaller than the amount of salt and water in the ocean under study. Nevertheless, the sample is likely to give a very accurate measurement of the ocean's salinity, provided of course that the salt is evenly distributed across the ocean (this hypothesis is the analogue of the hypothesis that the poll sample is being randomly chosen). In fact, one could already obtain a crude but reasonable estimate of salinity by testing just a single drop of seawater, though of course the larger sample in the glass would provide a more accurate measurement. This analogy may help explain why it is the sample size, rather than the population size, that determines the margin of error in a poll.