Evans Analysis This white paper discusses whether the United States Electoral College appropriately represents the will of the nation, as well as analyzes if the elected president is the true reflection of the people’s expression through their votes. A sampling plan entails the approach used to acquire a representative sample before collecting data. The United States Electoral College uses a sampling plan that entails selecting a sample from electors who vote for the presidential candidate on behalf of the population. The statistical inference of this process is according to the majority win rule. This process is subject to the different statistical problems involved in sampling. Since United States Electoral College is a sample, the process of elections based on this system faces statistical problems, which require pertinent solutions.
Background/Problems Concept of Sampling and Estimation The type of sampling method used to choose electors implies that there is low bias in sample selection indicating proper representation of the population’s will. The sampling method used to determine the electors is judgment sampling, which is a subjective sampling method that entails selection of electors through expert judgment (Evans 4). A common problem in this method is the occurrence of bias. Federal officials are barred from selection as an elector, which implies reduced bias.
The US Electoral College fails to truly represent the will of the people as the process of selecting representatives to votes is subject to statistical errors. Statistical errors in sampling include sampling and non-sampling errors. The occurrence of sampling error is due to the inherent characteristic of the sample as part of the entire population and; thus, not an exact representation of the population (Evans 7). In the United States, the electors who represent the entire American population in selecting a new president cannot comprehensively reflect the wishes of an entire state which allows for a sampling error. Non-sampling errors can result from the lack of pledges by some of the electors as well as insufficient data reliability.
Larger states are better represented due to larger sample sizes in terms of the allocated number of electors. The sampling error decreases with an increasing sample size (Evans 12). American states differ in terms of population density and thus it is essential to account for such variations by selecting sample sizes that reflect the size of the population. The US Electoral College’s sampling plan takes into account the size of the population in determining the number of electors to represent such a state; reducing the sampling error. The District of Columbia, for instance, has three electors as it is categorized a small state while larger states have more representatives according to their population demands.
Normally distributed states in the United States are better represented in comparison to their more skewed distributed counterparts. The central limit theorem based the assumption of a normally distributed population suggests that regardless of the sample size, the sampling distribution is also normal (Evans 14). This implies that for the states where the population is normally distributed then the electors accurately represent such as distribution regardless of the size of the population. However, for states with skewed population distributions this theory will not apply unless the second assumption – a large enough sample size, is adhered to. With a large enough sample size, the mean is roughly normally distributed despite the population distribution (Evans 14).
Concept of Statistical Inference The statistical inference in an election is expressed in terms of the winning candidate who becomes president. To assess the relationship between the elected president and the voting population, it is necessary to analyze the resulting information statistically. Using hypothesis testing deductive information can be obtained regarding opposing candidates. Hypothesis testing does not indicate which candidate will win but rather who is likely to win based on evidence that leads to the acceptance or rejection of the suggested null hypothesis (Evans, 39). For example the null hypothesis (Ho) can be that the most popular candidate always wins and the alternative (H1) can be the most popular candidate does not always win based on the general assumption that popularity is an important contributory factor in the elections.
Ho: The elected president is the most popular H1: The elected president is not the most popular The evidence provided by the sample data, which is the voting information from the election process, determines whether to accept or reject the null hypothesis. However, it is essential to take into consideration the presence of Type I and Type II errors which might arise in the process of hypothesis testing (Evans 41). The conclusion is based on a comparison between the computed value and the critical value in the selected level of significance. It might be possible to determine whether the selected president is a true expression of the population’s will by computing different tests such as the student t-test, p-value test, F-test, and Chi-test in order to accept or reject a proposed null hypothesis.
Solution Making prior estimations on the probability of different candidates winning based on the confidence level improves the level of confidence that the elected president truly reflects the expression of the people. It is necessary to take into account the margin of error in these estimations (Evans 20). Another solution would be to consider augmenting the sample size – the number of electors per state in order to reduce risk and increase accuracy in the inference of the election process. Using the prediction interval, it is more accurate. For instance, in determining the number of voters who will result in a smaller sampling error with/without information (Evans 32).
Conclusion The United States Electoral College is a representation of the entire population of American voters and is thus a sample subject to the problems of sampling. This introduces the element of lack of proper representation of the will of the population of voters due to problems such as sampling errors and non-sampling errors, inadequate sample sizes, and skewed population distribution which influence the sampling process. To deduct accurate inference it is essential to take into account the different problems of sampling and to resolve them. Solutions include increasing the sample sizes which is the number of representatives who elect a president.