Final answer:
The prediction based on historical trends from the U.S. Bureau of Labor Statistics suggests a decline in union membership in relation to the labor force size, especially due to the transition from manufacturing to the service sector where unions have traditionally been weaker.
Step-by-step explanation:
Based on historical data, it appears that the number of union members in the United States has shown a tendency to decline over a prolonged period, particularly as the economy transitions from manufacturing to services. This is reflected in patterns shown by data from the U.S. Bureau of Labor Statistics (BLS), which illustrates a consistent decline in manufacturing jobs, from 19 million in the late 1970s to 17 million in 2013, while jobs in the service sector increased.
The portion of unionized labor being stronger historically in manufacturing than in services suggests that the growth in the labor force has not significantly benefitted unions, given their lower success in organizing the service sector. Big unions like AFSCME, Service Employees International Union, and the National Education Association largely comprise government workers, but beyond that specific demographic, unionization in the service sector has seen limited success according to the BLS data.
The relationship between union membership and the size of the labor force is complex and influenced by numerous economic and industry trends, but if current trends continue, the prediction would lean towards a continued decline in the proportion of union members within the United States labor force.