Final answer:
The best diagram explaining the relationship between political machine staffers and voters during the late 19th century is where machine staffers help voters navigate city bureaucracy, facilitating public services in return for votes.
Step-by-step explanation:
During the late 19th century, political machine staffers played a pivotal role in the relationship between urban voters and the political system.
The correct answer to the question of which diagram best explains the relationship between political machine staffers and voters in cities is option 'b'. Machine staffers helped voters navigate city bureaucracy, offering solutions for citizens' immediate problems in return for votes.
An example is how Tammany Hall, under 'Boss' Tweed, would expedite public works like sidewalk construction and provide assistance in exchange for votes. This sometimes included practices such as graft and financial kickbacks, showcasing a corrupt yet efficient exchange that benefited both the political machines and the electorate who relied on them.