Connecticut is unique; I don’t know how many states do it but here in Connecticut if you vote for a third party candidate who is also the Republican or Democratic tickets the candidate receives the total number of votes.
John Doe is running on the Democratic Party line and receives 1000 votes.
Joe Doe (his brother) is running on the Republican Party line and receives 2500 votes
But if John Doe is also on the Green Party line and receives 1600 votes
Then John Doe wins with 2600 votes compared to his brother’s 2500 votes.
Why is this important?
First you are not “wasting” your vote by voting for a third party candidate and second you can send a message that you like the third party platform better than the major party’s platform.