The top two vote-getters were the Republicans. The Constitution says that the issue is settled in the House. The kicker - the House was dominated by Federalists. Jefferson smoothed some feathers and was elected, with Burr as his second. The 12th Amendment was passed a few years later as a result of this near-crisis.
Federal systems are common among large nations where several levels of government are needed.
Australia, Canada, and Brazil are federal as well. Federations do not always work, such as in the case of the United Arab Republic. The mere fact that a nation has a constitution, is a federation, or is a republic, does not imply that minorities are fairly treated. Note that a democracy, in the true sense of the word, does not protect the minority - majority rules. It has no power over private individuals or organizations.