Answer:
The method that might have been used to result in Garcia winning is the Instant RunOff method.
In this method, voters rank the candidates in order of preference. If no candidate has a majority of first-choice votes, the candidate with the fewest votes is eliminated, and their votes are redistributed to the remaining candidates according to the second-choice preferences of the voters who supported the eliminated candidate. This process is repeated until one candidate has a majority of the votes.
In the preference ballot provided, Garcia received the most first-choice votes with a total of 26, but did not receive a majority of the votes. Therefore, the Instant RunOff method could have been used to determine the winner by redistributing the votes of the eliminated candidates (Müller and Ivanov) to the remaining candidates. Based on the preferences of the voters who chose Müller and Ivanov as their first choice, it is possible that the redistributed votes would have favored Garcia, leading to a majority win for Garcia.
The Instant RunOff method might not be fair to the other nominees because it can result in a candidate winning with a majority of second-choice or even lower preferences, rather than being the first choice of the majority of voters. This means that the candidate who is ultimately chosen may not have broad support, and may not be the candidate that the most voters actually prefer. Additionally, the method can be influenced by strategic voting, where voters rank their choices based on who they think is most likely to win, rather than their actual preferences. This can result in outcomes that do not accurately reflect the preferences of the voters.