Final answer:
Public support for political machines was largely due to the economic benefits they provided to urban working-class populations, who saw timely relief from the challenges of urban life through jobs, housing, and infrastructure in exchange for political loyalty.
Step-by-step explanation:
The public allowed political machines to operate for several reasons. The primary reason was the economic benefits provided by political machines. These organizations, such as Tammany Hall in New York City, managed to provide timely solutions for citizens' immediate problems in exchange for political support. Political machines extended tangible advantages like jobs, housing, and infrastructure improvements, which had significant appeal to urban, working-class populations who were coping with the challenges of urban life. The aldermen within these political machines offered a more expedient method for addressing day-to-day issues, bypassing the slow bureaucratic processes associated with city hall.
Additionally, during the Gilded Age and Progressive Era, widespread corruption was rampant in elections, where political machines like Tammany Hall, led by individuals such as William 'Boss' Tweed, provided small bribes to impoverished voters, were allied with businesses, and provided social services in return for votes, securing their political strongholds.