Final answer:
Local political bosses in the 19th century who controlled political machines were in a position to influence voters within their precincts, ensuring control over districts through various means, including patronage and pressure from employers.
Step-by-step explanation:
The entities that were in a position to influence their customers and their votes were the local political leaders or bosses affiliated with political machines during the 19th century. These individuals wielded substantial power within their communities and could indeed deliver their precincts, thereby controlling the wards or districts. This system of political influence was underpinned by a combination of resources, community relationships, and sometimes corrupt practices like bribery or patronage, which included offering jobs or government contracts to supporters.
During elections, political machines and their leaders had the resources to conduct extensive outreach to constituents. For instance, constituent casework and favoritism played a critical role in maintaining voter loyalty. Employers and landlords, often allied with the political machines, could pressure voters to support certain candidates, leveraging their economic influence to sway votes.