Final answer:
The greatest challenge for a maximizer aiming to make decisions logically is dealing with an abundance of information and conflicting interests when making choices that affect the happiness of many, especially given that real-life decision-making often does not align with ideal theoretical models.
Step-by-step explanation:
The greatest challenge to a maximizer who wants to make decisions logically arises in situations where there is an overwhelming amount of information, conflicting interests, and the decision requires considering the happiness or utility of numerous people. A maximizer, using a utilitarian approach, aims to choose actions producing the greatest happiness or satisfying the greatest number of interests for the greatest number of people. This aligns with utilitarian principles which consider the net utility of a decision's outcomes. However, as highlighted by the first objection, real-life decision-making often involves incomplete information and a less systematic approach, contrasting the theoretical requirements for utility maximization.
Given this, the most challenging scenario for a maximizer is when they are forced to make decisions in complex situations without the ability to fully analyze every consequence or without having certainty about how their choices will affect everyone's happiness. This challenge is compounded by the fact that people and societal structures often do not operate strictly according to economic models or principles of justice such as those proposed by Rawls, who emphasized maximizing liberty while minimizing inequalities.