Mexico's political structure differs from that of the United States primarily in how the executive branch is organized and functions, as well as its electoral system.
Let's break down the given options:
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"There exists three branches of government." - This statement is true for both Mexico and the United States; both countries have an executive, legislative, and judicial branch.
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"The vice president does not serve under the president." - This is true for Mexico, as the country does not have a vice president like the U.S. does. Instead, Mexico has a cabinet system and the president is the sole executive leader.
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"There exists a multi-party electoral system." - While the U.S. generally operates under a two-party system (Democrats and Republicans), Mexico has a multi-party system with several significant political parties, which can lead to coalition governments.
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"The president heads the government." - This is true for both countries; in Mexico, as in the U.S., the president is the head of state and government.
Given these points, the most distinct difference between the political structures of the two countries is the presence of a vice president in the United States versus the absence of one in Mexico. Therefore, the correct answer would be:
"The vice president does not serve under the president."
This statement highlights a key structural difference in the executive branch of the two countries.