Thu Nov 15, 2012, 02:12 PM
cthulu2016 (10,960 posts)
A mathematical irony
Nate Silver gave odds on all the states. Obama won every state where his odds were more than 50% and lost the rest.
Nate Silver went 50 for 50. (51 for 51 with DC) Here's the irony... that result suggests that his odds were way off. 85% states probably should have should have been 97% states. Using Nate Silver's odds, what were the odds of Obama winning all the swing states (other than NC)? About 18%. Using Nate Silver's odds, what was the chance of going 51 for 51? I don't have the time to calculate them, but it is a small number. For there to be no upsets, Nate's state odds in probably disfavored Obama significantly. (All of Romeny's states were 99%, 100%, so it is expected that Obama didn't win a Romney state.) I am sure Nate will ponder this. It's a fun puzzle.

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4 replies  Author  Time  Post 
A mathematical irony (Original post) 
cthulu2016  Nov 2012  OP 
immoderate  Nov 2012  #1  
mathematic  Nov 2012  #2  
gravity  Nov 2012  #3  
unblock  Nov 2012  #4 
Response to cthulu2016 (Original post)
Thu Nov 15, 2012, 02:26 PM
immoderate (18,412 posts)
1. The odds of hitting any one particular combination were a lot lower.
Nate's odds predicted the most likely outcome.
imm 
Response to cthulu2016 (Original post)
Thu Nov 15, 2012, 03:06 PM
mathematic (573 posts)
2. I think you're doing the math wrong
It seems like you're assuming these odds are independent and thus you can find the probability of winning any particular set of states by multiplying the probabilities of winning the individual states together.
If you look at Silver's "Scenario Analysis" bar chart, you'll see that the chance for going 51 for 51 (well, 332 electoral votes to be precise) was just over 20%. By eyeballing it, you'll see that 50/51 adds up for at least 30% more. To explain a little more with some intuition, let's say I assign a probability to Obama winning OH. I later find out that Obama has won VA. Based on this information, I'd increase the probability I have of Obama winning OH. I do this because a lot of the unknown, random, or otherwise unaccounted for possibilities that would favor a Romney win in OH are reduced or eliminated by knowing that Obama won VA. In particular, Silver's methodology specifically includes national biases that break one way or the other. 
Response to cthulu2016 (Original post)
Thu Nov 15, 2012, 03:15 PM
gravity (4,157 posts)
3. I think Silver was being conservative with estimates
He tested for assumptions that polls could have been wrong or systematically biased one way or the other.
The polls however were surprisingly more accurate than expected. 
Response to cthulu2016 (Original post)
Thu Nov 15, 2012, 03:30 PM
unblock (26,747 posts)
4. if you asked nate prior to the election the odds of him getting ALL 51 calls right, he would have
agreed that the odds were long.
after all, several of the states were virtual coin tosses. getting 3 coin tosses correct gets you down to 1/8th chance, 12.5% (as other have pointed out, though, these are not entirely independent variables). if he had a state at 60% obama and obama actually won, he was admitting he had a 40% chance of being "wrong" just on that one state. nothing surprising here. it's a bit like having a baby naturally EXACTLY on your due date. there's only about a 5% chance of this, even though there's plenty of statistics that show this is the best guess. 