Final answer:
The maximum number of elimination rounds in a ranked choice voting election with 5 candidates is 4. In each round, the candidate with the least votes is eliminated until one achieves a majority.
Step-by-step explanation:
In a ranked choice voting election with 5 candidates, the maximum possible number of elimination rounds is 4. This is because in each round, the candidate with the least number of first-choice votes is eliminated, and their votes are redistributed according to the next preference indicated by the voters. The process continues till a candidate has more than 50% of the votes.
In the context of the Instant Run-Off Voting (IRV) system, if no candidate receives a majority (more than 50%) from the first-choice votes, the elimination rounds begin. The candidate with the least votes is eliminated, and their votes are redistributed to the remaining candidates based on the voters' next preferred choice. This process is repeated until a candidate achieves the necessary majority to win.
Case in point, with 5 candidates in a ranked choice election, after the first round, if no majority is achieved, the candidate in the last place is eliminated. Now 4 candidates remain for the second round. If there's still no majority winner, another candidate is eliminated, leaving 3 candidates for the third round. The process would continue until the second to last round, where 2 candidates compete, and one is bound to have a majority since it's impossible to continue beyond this point without having a winner.