From a mathematical point of view, is the elimination mechanism of I am a singer fair?

Arrow's impossibility theorem refers to several reasonable conditions set by Arrow, and there is no voting mechanism to ensure that any possible personal ranking can meet these conditions. Pay attention to the word "arbitrary", which is very strict. It does not mean that all voting results of all voting mechanisms are necessarily unfair, and the voting results of voting mechanisms may also be in line with real public opinion and fair. When judging whether it is fair or not, we need to distinguish between the unfairness inherent in the voting mechanism and the unfairness of the voting results brought by the voting mechanism. If the voting mechanism is not designed to favor any candidate, it is fair to the candidates. If the voting mechanism does not give any voter higher power than others, it is fair to voters. Manipulation or cheating is not the unfairness of the mechanism itself. If the mechanism cannot guarantee that the voting results can reflect the true evaluation of voters under any circumstances, it is that the unreasonable design of the mechanism may lead to unfair voting results, but it is not necessarily unfair. The rationality of the voting mechanism is measured by whether the voting results truly reflect public opinion, but everyone's vote only reflects the ranking and cannot accurately reflect the real information, which is also the fundamental reason why Arrow's impossibility theorem says that no voting mechanism can be absolutely reasonable. Only according to different applications can we design and improve a relatively more reasonable voting mechanism. The voting mechanism of "I am a singer" is: 7 singers, each voting audience can only cast 3 votes, and each singer can only cast one vote at most. The six singers with the most votes were selected, and the one with the lowest votes was eliminated. That is, each voting audience divides seven singers into two groups, one group is strictly superior to the other, and there is no difference between each group of singers. This mechanism is not based on the strict ranking of each singer, and there will be no circular voting in Arrow paradox. That is to say, under this mechanism, the voting results are always comparable among the participating singers, and the ranking is transitive, that is, if a (number of votes) is ≥ B and B ≥ C, there must be a ≥ c. The voting mechanism of I am a singer is fair to both the singer and the voting audience, but it is certainly not absolutely reasonable, which ensures the fairness of the results, but may lead to unfairness of the voting results. For example, the voter of 10 selects three of the four players (A, B, C and D) and eliminates 1 player. Each player can only cast two votes, and each player can only cast 1 vote at most. The real ranking of each player in the voters' minds is as follows: According to the voting rules, each voter votes for the top 2 players in his heart. But in fact, D is ranked first with 2 people, second with 3 people, third with 0 people and fourth with 5 people, while C is ranked first with 3 people, second with 1 people, third with 4 people and fourth with 2 people. Obviously, the overall evaluation of C is better than that of D. Similarly, the overall evaluation of runner-up A is better than that of champion B. The contestants of "I am a singer" all have great singing skills, with little difference in level. Deciding the outcome by voting is bound to be more accidental, which will make fans feel unfair, and the competition system can only try its best to control controllable factors. I think the existing voting mechanism still has many advantages. For example, the restricted double voting method is adopted instead of the one-person-one-vote system. Otherwise, the only vote of the voting audience is likely to vote for their original favorite singer, completely losing the objectivity of scoring according to live performances.