I'm not convinced that "median distribution" is correctly represented here by the selection of the "median" value in the table for first, second, and third rank votes. Yes, out of three "values" for a work, it's the middle one. But if a work "really was the best", you'd expect it to get all first-rank votes. The one way you could try to distinguish that is that no other work would get first-ranked votes, whereas in this case it's mixed. But then, maybe that was simply the bias of their fans?
The value that matters, when representing the distribution of votes for a particular candidate, is the median of the individual votes for that candidate. Which in all three cases, would be one selecting it for first place. Now, you could say it should be the median across the distributions of "people who voted in the category", but that falls down because these works also got the highest number of ballots with a vote for them in their respective categories, as shown by "total votes". I tried taking the "median" ballot by dividing the number of first preference votes by two and then counting down from the highest-ranked ballots for each candidate, but because most works didn't get votes on half the ballots, the only non-Garrison candidate that appeared at all was Freefall - and its median vote was third preference, while Carry On's was second. Foxes in Love did not appear at all, because its voter base was not as wide; less than half of the ballots for that category ranked it.
Garrison's works got 44.7%, 49.8% and 47.8% of first-ranked votes - they were close to being the majority winners. They were probably not condorcet winners - victors of head-to-heads between them and all other candidates - which is one thing this voting system (a form of Borda count) is intended to represent. But nor were the others. The competition was divided and support for Garrison's work too strong, so it won - it probably would have won under most voting systems.
I'm not convinced that "median distribution" is correctly represented here by the selection of the "median" value in the table for first, second, and third rank votes. Yes, out of three "values" for a work, it's the middle one. But if a work "really was the best", you'd expect it to get all first-rank votes. The one way you could try to distinguish that is that no other work would get first-ranked votes, whereas in this case it's mixed. But then, maybe that was simply the bias of their fans?
The value that matters, when representing the distribution of votes for a particular candidate, is the median of the individual votes for that candidate. Which in all three cases, would be one selecting it for first place. Now, you could say it should be the median across the distributions of "people who voted in the category", but that falls down because these works also got the highest number of ballots with a vote for them in their respective categories, as shown by "total votes". I tried taking the "median" ballot by dividing the number of first preference votes by two and then counting down from the highest-ranked ballots for each candidate, but because most works didn't get votes on half the ballots, the only non-Garrison candidate that appeared at all was Freefall - and its median vote was third preference, while Carry On's was second. Foxes in Love did not appear at all, because its voter base was not as wide; less than half of the ballots for that category ranked it.
Garrison's works got 44.7%, 49.8% and 47.8% of first-ranked votes - they were close to being the majority winners. They were probably not condorcet winners - victors of head-to-heads between them and all other candidates - which is one thing this voting system (a form of Borda count) is intended to represent. But nor were the others. The competition was divided and support for Garrison's work too strong, so it won - it probably would have won under most voting systems.