I’ve switched over to responding to your comments/suggestions one-by-one.
On your point 1, regarding loss functions: I agree that a strictly utilitarian/consequentialist PoV would care about which side won, not about vote totals. I think there are three reasons to nevertheless build a loss function around vote totals.
1. Mathematically more well-behaved. For instance, the whole “MSE decomposition” idea I bring in later would be much much messier with a binary-outcome-based loss function.
2. I believe that in practice, if there’s a question where the target support would be, say, 70%, but the legislature supports it at 90%, you can probably use it to construct some other at-least-somewhat-reasonable question where the target support would be 40% but the legislature supports it at 60%. That is, in practice, errors in vote totals go hand-in-hand with errors in outcomes, even if this is not a logical necessity (at least, not without additional assumptions about convex lotteries and stuff).
3. Some of the votes/decisions of the legislature may be made in a non-majority-rules fashion. For instance, you could have some situations where each legislator gets to allocate a share of some resource. In such cases, the vote-total-based loss function is clearly correct even from a consequentialist standpoint. (This might be seen as a special case of 2, but it’s different enough to list separately.)
I think that saying 1 and 2 in the main article would be too much of a digression, but I will think further about whether there’s a way to include point 3.
I’ve switched over to responding to your comments/suggestions one-by-one.
On your point 1, regarding loss functions: I agree that a strictly utilitarian/consequentialist PoV would care about which side won, not about vote totals. I think there are three reasons to nevertheless build a loss function around vote totals.
1. Mathematically more well-behaved. For instance, the whole “MSE decomposition” idea I bring in later would be much much messier with a binary-outcome-based loss function.
2. I believe that in practice, if there’s a question where the target support would be, say, 70%, but the legislature supports it at 90%, you can probably use it to construct some other at-least-somewhat-reasonable question where the target support would be 40% but the legislature supports it at 60%. That is, in practice, errors in vote totals go hand-in-hand with errors in outcomes, even if this is not a logical necessity (at least, not without additional assumptions about convex lotteries and stuff).
3. Some of the votes/decisions of the legislature may be made in a non-majority-rules fashion. For instance, you could have some situations where each legislator gets to allocate a share of some resource. In such cases, the vote-total-based loss function is clearly correct even from a consequentialist standpoint. (This might be seen as a special case of 2, but it’s different enough to list separately.)
I think that saying 1 and 2 in the main article would be too much of a digression, but I will think further about whether there’s a way to include point 3.