**Very quick updates:** **Corona:** Israel is struggling with the pandemic with some successes, some failures, and much debate. **Peace:** We have peace agreements now with several Arab countries, most recently with Sudan. This is quite stunning.** Internal politics:** As divided as ever, after three neck-to-neck general elections, with not-fully functioning unity government, and with many protests calling for the resignation of our PM who face trial for bribery in a couple of months.

And for our main topic:

## Maine’s Influence

Four years ago we had a long post demonstrating some notions regarding voting with Nate Silver’s famous site FiveThirtyEight. This time with the flow of corona related statistics I am less addicted to Silver’s site, but I noticed an interesting new feature. You can explore the ways Trump or Biden could win the election: You decide the outcome in some states and see the forecast for the entire elections based on that.

Earlier today Nate Silver’s site gave Biden 88% probability to win and Trump 12% probability to win.

Now, if you force a Trump’s victory in the State of Maine with only two electoral votes, Trump’s chances for winning the entire elections goes up to 40%

**Test your intuition:** what is the reason for Maine’s huge influence on the elections’ outcomes?

**Silver’s prediction earlier today: Biden: 88, Trump: 12**

**The prediction when you give Maine to Trump. Biden:59, Trump:40.**

Due to conditional probability. They are only averaging over simulations where Trump won in Maine in this case. To contrast this, if you pick Biden to win say North Dakota (where trump has 99% chance of winning) this increases Biden’s chance of winning the elections to over 99%.

conditional probability. As Shachar said.

It a very reasonable explanation, but them it means the simulations are built such that different states are not independent, and it meanly makes me curious how the dependencies are modeled. Are there some national variables of some latest movements affecting all states in the same way?

538 definitely assumes dependencies of all sorts.

the reason why everyone assumed contain is 98% to win in 2016 was ignoring one way polling type error affecting multiple states in a dependent manner.

but 538 might use a stronger way.

if he says “assume Maine goes to Trump given current polling, then do the whole lot of inferences”, this might actually be why it moves so violently…..

PS. fivethirtyeight.com has lots of details on how they are modeling and how their gaming the model Gil used work. I am sure you can burn a few hours going through the thing 🙂

Indeed, as most commentators observed the issue is the various notions of influence when the votes of voters (and in this case, of voters in different states) are not statistically independent. This is a very interesting issue that I studied in a paper with Olle Haggstrom and Elchanan Mossel “A Law of Large Numbers for Weighted Majority.” Some related issues are also discussed in my paper: Noise Sensitivity and Chaos in Social Choice Theory.

Here’s something even stranger. If you give MN, MI, WI to Biden and PA to Trump Biden has a 53% chance of winning. If you then give ME to Trump, Biden’s chances go up to 71%.

The reason for this in this scenario, a Trump win in Maine is evidence that Biden lost Pennsylvania because of a regional weakness in the Northeast, and not a national weakness. Thus making Maine red conditional on these other things improves Biden’s chances in Georgia and Florida.