Now you’re making a different argument—you have to show that making your decide_winner function take more arguments is going to improve the quality of the output, and it’s far from clear it will. You could put more information into the system by asking every voter to list their favourite colour, but unless you can show that this would actually improve the output, it’s irrelivant.
Having more information can allow us to have more accurate beliefs, but it’s not the case that putting more marks on a ballot paper will lead to a better result, especially when you’re pushing against Arrow.
No, because the information here changes the result of the election. That’s the whole point...
Now you’re making a different argument—you have to show that making your decide_winner function take more arguments is going to improve the quality of the output, and it’s far from clear it will. You could put more information into the system by asking every voter to list their favourite colour, but unless you can show that this would actually improve the output, it’s irrelivant.
Having more information can allow us to have more accurate beliefs, but it’s not the case that putting more marks on a ballot paper will lead to a better result, especially when you’re pushing against Arrow.