Problem Description

You are provided with aggregated ranked ballots. Each entry in the input dictionary represents a group of voters who submitted an identical preference order for candidates. The key is an ordered tuple of candidate names, indicating a voter's preference from highest to lowest, and the corresponding value is the count of voters who submitted that exact ranking.

You need to implement two distinct methods:

1. popular_vote(ballots) -> candidate

This method should identify and return the candidate who received the largest number of first-place votes across all ballots.

2. ranked_choice_winner(ballots) -> candidate

This method implements the ranked-choice voting system, following these rules:

• In each round, count only the highest-ranked non-eliminated candidate on each ballot.
• If any candidate achieves more than 50% of the active first-place votes, that candidate is declared the winner and returned.
• Otherwise, the candidate with the fewest first-place votes in that round is eliminated. The process then repeats with the remaining candidates.
• The process continues until a candidate secures a majority of active votes or only one candidate remains, who is then declared the winner.

Assumptions

• Every ballot ranks the same set of candidates.
• There will be no ties when determining which candidate to eliminate in a round.

Example Input

ballots = {
    ("A", "B", "C"): 4,
    ("B", "C", "A"): 3,
    ("C", "B", "A"): 2
}

Example Output for Input

• The popular-vote winner is A, as A initially has the most first-place votes.
• The ranked-choice winner is B:
  • Round 1: Initial counts are A=4, B=3, C=2. Candidate C has the fewest votes and is eliminated.
  • Round 2: C's ballots (2 votes) transfer to their next preference, B. The new counts are A=4, B=3+2=5. B now has 5 votes out of 9 total active votes (55.5%), which is more than 50%. Therefore, B is the ranked-choice winner.