The Quick Count and Election Observation

CHAPTER FIVE: STATISTICAL PRINCIPLES AND QUICK COUNTS
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FIGURE 5-1:
DESIRED SAMPLE SIZES FOR THE US,
CANADA AND SWITZERLAND
UNITED STATES CANADA SWITZERLAND
Population: 263,814,032 28,434,545 7,084,984
Margin of error: +/-2% +/-2% +/-2%
Desired sample size: 1200 2400 4300
The safest strategy is
to make the conservative
assumption that
the voting population is
heterogeneous.
As Figure 5-1 demonstrates, heterogeneity is not determined by the ethnic
characteristics of these populations. Heterogeneity is determined by the likelihood
that one candidate will win a majority of the electoral support. In a two
party system, as in the United States, the electoral race is often easier to follow
and much easier to predict – voters usually have only two choices. But in
Switzerland, the larger number of parties makes electoral competition more
complicated. Swiss political parties are clearly supported by different language
and religious groups. Even a country such as Canada, with five official parties,
is less heterogeneous than Switzerland.
A related principle is also illustrated in Figure 5-1. The required sample size is
determined by the expected level of homogeneity in voting results, not by the
total population size of a country. These three countries with very different total
populations require different sample sizes to maintain a margin of error of plus
or minus two percent (+/-2%). Indeed, it turns out that the country with the
larger population requires the smallest sample. In fact, the variations in the
required sample size are attributable to variations in the homogeneity of the
three different populations.
The more confidence
required that the sample
distribution will
reflect the population
distribution, the larger
the sample has to be.
In practice, reliable information about the heterogeneity, or homogeneity, of
voting populations in many countries is hard to find. The safest strategy under
these circumstances, one that requires no guess-work, is to make the conservative
assumption that the voting population is heterogeneous. As will become
clear, that assumption has a profound impact on how a quick count’s sample
size is calculated.
Confidence Levels: Specifying the Relationship between Sample
and Population
One additional piece of information has an important impact on how statisticians
estimate population on the basis of a sample—the confidence level. Confidence
levels concern how the sample data can be compared to the population. The
more confidence required that the sample distribution will reflect the population
distribution, the larger the sample has to be. This is because, in larger samples,
exceptional individual results will have less effect on the distribution.