Where'd you get the 24.7% figure though? Because if you got it from the product of all of the chances of Republicans winning (assuming you did since that gives 24.7%), that figure is still only valid when assuming they're independent events. Even when accounting for the interlinkages, a model can't give you figures that can be multiplied together to get the chance of their intersection if the events aren't independent.
They're independent in the sense that the outcome of one is not reliant on the other,and instead all of them are reliant on the same factor, that being voter choice. Kinda like the Christian Trinity.
Trump winning the White House does not give a better chance of the GOP taking the house. There is no causal link there—the only thing it could theoretically do is affect public sentiment, but it can't because we don't know who won until everyone has already voted. But it indicates that voters are leaning Rep over Dem, and that does mean a higher likelihood of the GOP getting control of the house.
Right, but then that means that if one of the outcomes happens, it affects the probability for the others. You can't justify the 24.7% figure if the probabilities that went into it are dependent. That claim is only valid when the probabilities are independent.
Say that everyone who votes for a party in the executive branch votes the same way in the legislative branch, and we say that the population is split evenly between Dems and Reps, and all elections are decided by popular vote. That would mean there's a coinflip chance for either party to win the House and the Presidency. However, it does not imply that there's a 25% chance of both happening for the same party. If a party wins the House, they would necessarily win the Presidency and vice versa. That's what happens when events aren't independent. Naturally, when you take the assumptions away the argument is not as strong, but you can still see what I'm getting at: Republicans are up in every race, they have a very high chance of performing about the same across the board because people tend to vote for a party, not random candidates, therefore you're underestimating how likely they are to sweep.
I see what you're getting at and it aligns with other things that I've heard--namely, that a swing state blowout to either side is more likely than 4-3 or 5-2. However, I still don't think it's accurate to says that these probabilities are dependent on each other. Like I said, they're not dependent on each other, they're dependent on the same thing.
Republicans are up in every race, they have a very high chance of performing about the same across the board because people tend to vote for a party, not random candidates, therefore you're underestimating how likely they are to sweep.
Aren't these factors already baked in to the individual races, though? Like, surely part of tuning the model is looking at polling performance in other races and adjusting based on how that will affect the race in question.
Like I said, they're not dependent on each other, they're dependent on the same thing.
I hate to sound like but Bayes' theorem is really all you need here: in statistics those 2 things have the same effect on the probabilities. I agree with you that there isn't a causal relationship between the outcomes in each race and the causal relationship is to the voter preferences upstream in the chain of causality, but P(Rs winning House|Rs win presidency) > P(Rs winning presidency) regardless of what causes what.
They're clearly not independent, it's much more than a 24.7% chance (can't say by how much)
I would assume that the model takes their interlinkages into account. That's part of what makes it a model rather than just a polling aggregate
Where'd you get the 24.7% figure though? Because if you got it from the product of all of the chances of Republicans winning (assuming you did since that gives 24.7%), that figure is still only valid when assuming they're independent events. Even when accounting for the interlinkages, a model can't give you figures that can be multiplied together to get the chance of their intersection if the events aren't independent.
That is how I got that figure, yeah
They're independent in the sense that the outcome of one is not reliant on the other,and instead all of them are reliant on the same factor, that being voter choice. Kinda like the Christian Trinity.
Trump winning the White House does not give a better chance of the GOP taking the house. There is no causal link there—the only thing it could theoretically do is affect public sentiment, but it can't because we don't know who won until everyone has already voted. But it indicates that voters are leaning Rep over Dem, and that does mean a higher likelihood of the GOP getting control of the house.
Right, but then that means that if one of the outcomes happens, it affects the probability for the others. You can't justify the 24.7% figure if the probabilities that went into it are dependent. That claim is only valid when the probabilities are independent.
Say that everyone who votes for a party in the executive branch votes the same way in the legislative branch, and we say that the population is split evenly between Dems and Reps, and all elections are decided by popular vote. That would mean there's a coinflip chance for either party to win the House and the Presidency. However, it does not imply that there's a 25% chance of both happening for the same party. If a party wins the House, they would necessarily win the Presidency and vice versa. That's what happens when events aren't independent. Naturally, when you take the assumptions away the argument is not as strong, but you can still see what I'm getting at: Republicans are up in every race, they have a very high chance of performing about the same across the board because people tend to vote for a party, not random candidates, therefore you're underestimating how likely they are to sweep.
I see what you're getting at and it aligns with other things that I've heard--namely, that a swing state blowout to either side is more likely than 4-3 or 5-2. However, I still don't think it's accurate to says that these probabilities are dependent on each other. Like I said, they're not dependent on each other, they're dependent on the same thing.
Aren't these factors already baked in to the individual races, though? Like, surely part of tuning the model is looking at polling performance in other races and adjusting based on how that will affect the race in question.
I hate to sound like
but Bayes' theorem is really all you need here: in statistics those 2 things have the same effect on the probabilities. I agree with you that there isn't a causal relationship between the outcomes in each race and the causal relationship is to the voter preferences upstream in the chain of causality, but P(Rs winning House|Rs win presidency) > P(Rs winning presidency) regardless of what causes what.
I have little to no stats knowledge so I'll defer to you even if I don't get it