Bicameralism in the U.S.
In the United States, each state is given the same number of seats in the legislature's upper house. This takes no account of population differences between states — it is designed to ensure that smaller states are not overshadowed by more populous ones. (In the United States, the deal that ensured this arrangement is known as the Great or Connecticut Compromise.) In the lower houses of each country, these provisions do not apply, and seats are allocated based purely on population. The bicameral system, therefore, is a method of combining the principle of democratic equality with the principle of federalism — all citizens are equal in the lower houses, while all states are equal in the upper houses.
The Founding Fathers of the United States eschewed any notion of separate representation for aristocracy, but they accepted the prevailing disposition towards bicameralism. However, as part of the Great Compromise between large states and small states, they invented a new rationale for bicameralism in which the upper house would have states represented equally and the lower house would have them represented by population.