Which personality do you feel is most ideal for a president to possess? Remember, the president at times must compromise with congressional leaders, not to mention the other limits to presidential power (i.e., advice and consent, impeachment and conviction). Therefore, which personality is most ideal, in spite of the limitations to the office of the presidency? Please place President Barack Obama and Donald Trump in a respective category. Be sure to explain your reasoning, and mention specific aspects that support your answer (do a Google search if you must). This question is intended to be fun but also requires you to be specific within your categorization.

Jung defined eight psychological types that relate to the makeup of an individual person's personality. Four of these are variations of extroverts and four are variations of introverts.
First, for reasons that should be self-evident, a president should have extroverted characteristics. Second, in their important volume Policy Design for Democracy, Schneider and Ingram describe the fundamental goal of politicians as being to maintain their own power, and their continual search to achieve this goal is what makes democracy work.
Barack Obama was an Extrovert-Intuition–type personality. The extroverted component of his personality type was evidenced by the fact that he successfully mounted a national presidential campaign. His intuition characteristic, defined as the ability to sense the drives and motivations of other people, was evidenced by his ability to successfully mount and achieve policies that appealed to the greatest number of people to sustain him in office, even if they did not always make logical sense to everyone. For instance, the ACA was criticized by the Republican opposition, but it was also criticized by health reform advocates who identified it as a major restructuring of the health care system that would achieve only incremental progress or mark a wholesale sell-out to private insurance. Ralph Nader called it the "biggest insurance scam in history." However, Obama's insistence on pushing it through represented not a logical process of policy analysis but an intuitive identification of what was most probably achievable within the boundaries of what would keep him in office.
Donald Trump is also an Extrovert-Intuition–type personality. Again, the extroverted component of his personality type was evidenced by the fact that he successfully mounted a national presidential campaign. His intuition characteristic is demonstrated by his ability to apply and release pressure on institutions—such as NATO and NAFTA—at times and in ways designed to maximize his political support among constituencies that matter most to his own political viability. This is done without an overarching policy framework but, rather, with an innate and fundamental sense and reading of what the most important segments of the population desire.
In other words, Obama and Trump share a common personality type. And this is probably true of all presidents. The perception of difference between them is only a realization of differences in their personal mannerisms and the choices they have made as to how to brand and present themselves to achieve their political objectives. These differences are superficial only and not indicative of a difference in their underlying personalities.
Therefore, by point of fact that the United States has survived more than two centuries under a succession of presidents who were most probably all of the Extrovert-Intuition personality type, this is probably the most ideal personality type for a president.
https://philosophy.lander.edu/ethics/jung.html