The preferential treatment of relatives, friends, and peers is, and has always been, a problem in the appointment of individuals to positions of power, such as executive managerial positions, judgeships, professorships, or leadership roles in public administration and regulatory agencies. Are there viable institutional alternatives to today’s reliance on recusals and consensus-based selection? In this paper, we examine a historical regime in 18th-century Basel, Switzerland, that combined meritocratic preselection with randomized choice through a qualified lottery to reduce favoritism in political appointments. In Basel, variants of qualified lotteries were implemented for over 100 years with the intent of combating nepotism and corruption. Using data on 22,017 male citizens and the families they married into, we analyze how three forms of social dependency relations—being born into, marrying into, or being embedded among the “right” families—shaped appointments to entry-level political office. We find that as the citizenry expanded, social dependencies became increasingly predictive of appointment outcomes. Yet under the qualified lottery regime, these dependencies lost their salience. Thus, our findings indicate that qualified lotteries can neutralize conflicts of interest not only in theory but also in practice. Qualified lotteries offer compelling alternatives to consensus-driven candidate selection because they can be designed to enhance fairness, reduce search costs, and mitigate conflicts of interest. Our study contributes to the broader discourse on institutional governance and on practices that mitigate conflicts of interest in the appointment of individuals to positions of power.