Multiple choice voting. (I.e. you give 1 point to all candidates you like, the ones with most amount of points wins. Very simple to understand system with no spoiler effect.) It will fix the issue within one set of elections and I don't even think it would require any changes to the constitution.
>>collle+(OP)
The constitution is completely silent on voting methodology. States are free to choose whatever they wish so long as it is representative, with the exception of federal Senators (and maybe representatives), I believe.