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In order for a party's nominee to have the possibility of becoming president by majority vote of the electoral college (as opposed to by decision of the United States House of Representatives after an electoral majority has failed to be reached), they must be on the ballot in states whose collective electoral vote total is at least half of the Electoral-College votes. In addition to the two main parties listed above, three additional parties met this criterion in the 2008 Presidential Election.
These parties have offered candidates in recent elections, but did not in 2004, and they did not have ballot status in enough states in 2008 to win the presidency by majority of the electoral college. Some do not have presidential candidates, and only field candidates for Congressional and/or state-level offices.
Some of these parties have nominated candidates in the past, but have not done so recently for various reasons. Others have not yet nominated any candidates.
Few, if any, of these parties have nominated presidential candidates. The years are when they were founded.