Fairness and guaranteed output delivery
Intuitively anything the honest minority can do the dishonest majority can do as well. So if the minority can force a correct outcome the majority can force an incorrect outcome. 

Side note:The question is ill-defined, not mentioning a specific problem where these requirements are to be held, is this a computation? who has the input? In some situations we can deal with a dishonest majority such as limiting them to no more than failing the process.