What factor plays an important role in determining who runs for office?

Democracy.

Explanation:

Democracy denotes forms of rule, political orders or political systems in which power and government emanate from the people.  This is involved either directly (direct democracy) or through the selection of decision-making representatives (representative democracy) in all decisions that are binding on the general public. In democratic states and political systems, the government emerges from the people through political elections. Since power is exercised by the general public, freedom of opinion and freedom of the press are essential for political decision-making. Other important features of a modern democracy are free and equal elections, the majority or consensus principle, protection of minorities, acceptance of a political opposition, separation of powers, constitutionality, and protection of basic, civil and human rights.

Now, to determine which candidate will run for office, democracy is also used as a means of decision: the internal democracy of each political party, by which registered voters decide who will be the party's candidate in the internal elections prior to the general elections.

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