Okay, then, we all agree before the vote to break ties based on some arbitrary binary digit of pi, which we don’t look at until after the vote is done.
Or, equivalently, we can agree to break ties based on the outcome of the rand() function seeded with the time in milliseconds at the time of agreement.
Neither of those fulfills the relevant functional definition of determinism. The same inputs either do or do not lead to the same outputs; if they do, then it is deterministic and subject to Arrow, and if they do not, they they are functionally random.
Neither of those fulfills the relevant functional definition of determinism.
Exactly. Both do or both don’t. As (I assume) you were implying with your earlier question, ties in this system are broken either arbitrarily (limited dictator situation) or functionally randomly. Which of these categories ‘alphabetical’ and ‘PI picking’ could vary by assumption but one of the two is implied.
The same inputs either do or do not lead to the same outputs; if they do, then it is deterministic and subject to Arrow, and if they do not, they they are functionally random.
The suggested methods for tiebreaking are therefore not helpful, because the voters have to know the voting function beforehand, without even epistemic randomness. I was just noting that this system is extremely sensitive to tactical voting on the margin.
The suggested methods for tiebreaking are therefore not helpful, because the voters have to know the voting function beforehand, without even epistemic randomness. I was just noting that this system is extremely sensitive to tactical voting on the margin.
So was I. (I was expanding grandparent somewhat along these lines as you were replying.)
How do you break numerical ties without randomness?
You can just choose the first one in alphabetical order, or some equivalent.
I volunteer to choose the language and wording of the preferences.
Okay, then, we all agree before the vote to break ties based on some arbitrary binary digit of pi, which we don’t look at until after the vote is done.
Or, equivalently, we can agree to break ties based on the outcome of the rand() function seeded with the time in milliseconds at the time of agreement.
Neither of those fulfills the relevant functional definition of determinism. The same inputs either do or do not lead to the same outputs; if they do, then it is deterministic and subject to Arrow, and if they do not, they they are functionally random.
Exactly. Both do or both don’t. As (I assume) you were implying with your earlier question, ties in this system are broken either arbitrarily (limited dictator situation) or functionally randomly. Which of these categories ‘alphabetical’ and ‘PI picking’ could vary by assumption but one of the two is implied.
Yes.
The suggested methods for tiebreaking are therefore not helpful, because the voters have to know the voting function beforehand, without even epistemic randomness. I was just noting that this system is extremely sensitive to tactical voting on the margin.
So was I. (I was expanding grandparent somewhat along these lines as you were replying.)