What we should do is consider reasons this disadvantage might unequally disadvantaged, or consider example data from the real world, that might show up in ranked choice ballot data, for instance.
Again, I’m arguing that this is highly unlikely. And it should be detectable mathematically, and to some degree, tested against real world data.
So again, your example (the only one that was complete), was this:
There are two separate issues that make it unrealistic. Only one of them could be detected if the ballots were reduced to being ranked rather than scored.
You could detect that lots of people ranked things A>B>C, and lots ranked C>B>A, while very few rated B on top (technically zero rated B on top in your example, but let’s generalize that into “very few”). So we should be able to see if this scenario ever happens with ranked choice, by looking at real world ballot data. I would guess that it would be very rare, even though it is easy enough to imagine a scenario where it would be expected, for instance a room full of people who either like cold temperatures or who like warm temperatures, with no one liking a middle temperature most.
The other thing that made your example unrealistic was that those who put B in the middle (everyone in your example) scored B in the highest middle position, with exactly zero scored B with 1, 2, or 3. We can’t tell this if the ballots were ranked choice, of course.
Note that this second situation is much harder to imagine a real world situation where that could happen. It’s one thing to imagine that all the people like either cold or warm best, but it is distinctly weird that middle temperatures are seen “almost as good” as their first preference (to every single person), while not a single person liked middle temperatures most. Why would that be? It makes no sense to me.
A realistic simulation wouldn’t use purely random ballots, of course, that would be meaningless. But it also shouldn’t use ones where they are completely contrived as in your example.
I have done simulations where I have created ballots with random input, but with structure to them. For instance, give every candidate a position in 2-dimensions (an x and a y, between 0 and 100), as well as a “universal appeal” value, also between 0 and 100. Then give every voter a random position in those same 2 dimensions. To make a ballot, consider the distance from the voter of each candidate, as well as that candidate’s universal appeal.
You can add extra sophistication by applying clustering algorithms to the locations of the voters. You can increase the number of dimensions beyond 2, and so on. You can also add varying degrees of random fuzz when determining each voter’s score for each candidate. You can put voters on a normal distribution rather than purely random. Etc.
While there is randomness, it isn’t purely random, and the set of ballots will have some structure to them.