What are the two main arguments for keeping the electoral college with one argument being that it gives small states a bigger voice in choosing the president?

The opposing argument is that the basic principle of democracy is that the majority rules; why would we want to create a complicated system by which a minority of the votes cast can elect a President contrary to the wishes of the majority? It's undemocratic.

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The founding fathers were not interested in putting together a democracy. They created a republic. They envisioned a government with various interacting layers, and a system of checks and balances. The intention was that no one branch of government would have too much control. In part, the electoral college was a "check" against the basic ignorance of the people at large, a charge that seems less harsh historically given the slow pace at which information travelled in the early days of the US.