I read someone saying that ~half of the universes in a neighborhood of ours went to Trump. But… this doesn’t seem right. Assuming Biden wins in the world we live in, consider the possible perturbations to the mental states of each voter. (Big assumption! We aren’t thinking about all possible modifications to the world state. Whatever that means.)
Assume all 2020 voters would be equally affected by a perturbation (which you can just think of as a decision-flip for simplicity, perhaps). Since we’re talking about a neighborhood (“worlds pretty close to ours”), each world-modification is limited to N decision flips (where N isn’t too big).
There are combinatorially more ways for a race to be close (in popular vote) than for it to not be close. But we’re talking perturbations, and so since we’re assuming Biden wins in this timeline, he’s still winning in most other timelines close to ours
I don’t know whether the electoral college really changes this logic. If we only consider a single state (PA), then it probably doesn’t?
I’m also going to imagine that most decision-flips didn’t have too many downstream effects, but this depends on when the intervention takes place: if it’s a week beforehand, maybe people announce changes-of-heart to their families? A lot to think about there. I’ll just pretend like they’re isolated because I don’t feel like thinking about it that long, and it’s insanely hard to play out all those effects.
Since these decision-flips are independent, you don’t get any logical correlations: the fact that I randomly changed my vote, doesn’t change how I expect people like me to vote. This is big.
Under my extremely simplified model, the last bullet is what makes me feel like most universes in our neighborhood were probably also Biden victories.
I think this depends on the distance considered. In worlds very very close to ours, the vast majority will have the same outcome as ours. As you increase the neighborhood size (I imagine this as considering worlds which diverged from ours more distantly in the past), Trump becomes more likely relative to Biden [edit: more likely than he is relative to Biden in more nearby worlds]. As you continue to expand, other outcomes start to have significant likelihood as well.
General intuition that “butterfly effect” is basically true, meaning that if a change occurs in a chaotic system, then the size of the downstream effects will tend to increase over time.
Edit: I don’t have a good sense of how far back you would have to go to see meaningful change in outcome, just that the farther you go the more likely change becomes.
Sure, but why would those changes tend to favor Trump as you get outside of a small neighborhood? Like, why would Biden / (Biden or Trump win) < .5? I agree it would at least approach .5 as the neighborhood grows. I think.
I think we’re in agreement here. I didn’t mean to imply that Trump would become more likely than Biden in absolute terms, just that the ratio Trump/Biden would increase.
I read someone saying that ~half of the universes in a neighborhood of ours went to Trump. But… this doesn’t seem right. Assuming Biden wins in the world we live in, consider the possible perturbations to the mental states of each voter. (Big assumption! We aren’t thinking about all possible modifications to the world state. Whatever that means.)
Assume all 2020 voters would be equally affected by a perturbation (which you can just think of as a decision-flip for simplicity, perhaps). Since we’re talking about a neighborhood (“worlds pretty close to ours”), each world-modification is limited to N decision flips (where N isn’t too big).
There are combinatorially more ways for a race to be close (in popular vote) than for it to not be close. But we’re talking perturbations, and so since we’re assuming Biden wins in this timeline, he’s still winning in most other timelines close to ours
I don’t know whether the electoral college really changes this logic. If we only consider a single state (PA), then it probably doesn’t?
I’m also going to imagine that most decision-flips didn’t have too many downstream effects, but this depends on when the intervention takes place: if it’s a week beforehand, maybe people announce changes-of-heart to their families? A lot to think about there. I’ll just pretend like they’re isolated because I don’t feel like thinking about it that long, and it’s insanely hard to play out all those effects.
Since these decision-flips are independent, you don’t get any logical correlations: the fact that I randomly changed my vote, doesn’t change how I expect people like me to vote. This is big.
Under my extremely simplified model, the last bullet is what makes me feel like most universes in our neighborhood were probably also Biden victories.
I think this depends on the distance considered. In worlds very very close to ours, the vast majority will have the same outcome as ours. As you increase the neighborhood size (I imagine this as considering worlds which diverged from ours more distantly in the past), Trump becomes more likely relative to Biden [edit: more likely than he is relative to Biden in more nearby worlds]. As you continue to expand, other outcomes start to have significant likelihood as well.
Why do you think that? How do you know that?
General intuition that “butterfly effect” is basically true, meaning that if a change occurs in a chaotic system, then the size of the downstream effects will tend to increase over time.
Edit: I don’t have a good sense of how far back you would have to go to see meaningful change in outcome, just that the farther you go the more likely change becomes.
Sure, but why would those changes tend to favor Trump as you get outside of a small neighborhood? Like, why would Biden / (Biden or Trump win) < .5? I agree it would at least approach .5 as the neighborhood grows. I think.
I think we’re in agreement here. I didn’t mean to imply that Trump would become more likely than Biden in absolute terms, just that the ratio Trump/Biden would increase.