Explain what options the constitutional convention considered and the reason why

The Virginia Plan was the unofficial agenda of the Convention, written mostly by James Madison. It was aimed at favoring the interests of the largest states, and among other proposals were: A powerful bicameral Congress with a House of Representatives and a Senate. An executive power (president) elected by the legislature. A judicial power, with periods of service for life, with vague powers. Federal Congress could veto state laws

An alternative proposal, the New Jersey Plan, granted states equal prerogatives regardless of their size and was defended by the smaller states.  

Therefore, in the Virginia Plan the sole holder of sovereignty would be the central government, so the states would be mere administrative divisions. On the contrary, in the New Jersey Plan the depositaries of the sovereignty of the republic would have to be the states, in equal conditions among all of them. The first proposal was intolerable for those who, like the author of the Declaration of Independence Thomas Jefferson (who was not present at the Convention), believed that a strong central government posed both a betrayal of the enlightened ideals of the Revolution and a threat to the people and the states.

Another difference that seemed irreconcilable between these plans was that the Virginia defended that the states should be represented in the federal Legislative in terms of their population. As this clearly harmed the smaller or depopulated states, the New Jersey Plan demanded identical representation for each state. The solution adopted in the Connecticut Compromise settled the discussion salomónicamente: the legislative power of the new republic would be bicameral, being applied in one of those chambers the proposal of Virginia and in the other the one of New Jersey. Thus, in the House of Representatives its members would be elected according to the proposal of Virginia, according to its population, so to more inhabitants, more representatives. But in the other chamber, in the Senate, the New Jersey proposal would apply and senators would be elected in equal numbers for each state, regardless of their size and population. Both principles apply to this day.

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