Final answer:
An elected board is designed to be responsive to its members, making the statement true. Dillon's Rule does not offer local governments freedom and flexibility, making this assertion false. The claim about term limits and the increase of women in state legislatures cannot be verified without specific data, so it's neither clearly true nor false.
Step-by-step explanation:
An advantage of an elected board is that it helps ensure that the organization will be responsive to member needs. This is true because board members who are elected are accountable to the members who elected them, motivating them to act in the members' best interests. Elected boards are a feature of democratic governance in organizations ranging from non-profits to public corporations. In the case of a corporation, the board of directors is meant to govern in the interests of the shareholders, the true owners of the company. However, in some instances, top executives exert significant influence over the selection of board candidates, which can potentially lead to a conflict of interest if those executives prioritize managerial interests over shareholder interests.
In contrast, Dillon's Rule states that local governments have only those powers expressly granted to them by the state government. The assertion that Dillon's Rule gives local governments freedom and flexibility to make their own decisions is false. Local autonomy is actually more constrained under Dillon's Rule than under its counterpart, home rule.
Regarding term limits in state legislatures, whether they have produced a statistically significant increase in the number of women serving is a topic of empirical study. Some studies suggest that term limits may have had a positive effect on the diversity of legislatures, but it's important to examine the statistical data to make a definitive claim. As for the claim presented in the question, without specific evidence or data, the statement cannot be deemed categorically true or false.
With respect to the members of the Board of Governors of the Federal Reserve having longer terms in office, this is designed to shield them from the short-term political pressures that elected officials like the President may face. The aim is for them to make decisions based on economic considerations and the long-term interests of the national economy.