A multi-party system for presidential elections would be chaotic in the US.
Consider the fact that to be elected, one must receive a majority (not just plurality) of electoral votes. The greater the number of "electable" candidates (candidates who could realistically win a state and receive electoral votes) you have, the less likely that any one candidate would receive the necessary 270 electoral votes.
So then it goes to the House of Reps, where a majority vote is needed (and each state only gets one vote).and what happens then if the House has multiple parties and no candidate receives a majority? Or if the party that has a majority in the House has a presidential candidate who comes in third or forth in electoral votes, but is elected president on a strictly partisan basis?
We would probably have to repeal the
12th amendment.
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added:
The only thing I would change with the current system is to lower the requirement for third party candidate(s) to participate in the presidential debated. The current requirement is support of 15% of voters in aggregate polls during the campaign season in order to be included in the debates.
I would lower it to 5%....a number signficant enough to affect the outcome.