Yesterday we discussed the final polls of the New Jersey, Virginia, and New York City elections, and I converted these to approximate election forecasts by using some simple analysis based on the normal distribution and assumptions about vote swings and nonsampling errors.

How did that go? We can compare to the reported election outcomes. At this time not all the votes have been counted, but it’s over 90% and I’ll use the numbers in the newspaper right now.

Governor of New Jersey:

Polling average: Sherrill (D) at 53% of the two-party vote
SD of uncertainty (including nonsampling error): +/- 3%
Actual outcome: 56.5%

Governor of Virginia:

Polling average: Spanberger (D) at 55.5% of the two-party vote
SD of uncertainty (including nonsampling error): +/- 3.2%
Actual outcome: 57.6%

Mayor of New York:

Polling average: Mamdani (D) at 46%, Cuomo (I) at 32%, Sliwa (R) at 16%
Crude forecast anticipating a shift of voters after national Republicans’ endorsement of Cuomo: Mamdani 47%, Cuomo 37%, Sliwa 10%
Actual outcome: Mamdani 50.4%, Cuomo 41.6%, Sliwa 7.1%
So, not far from what you’d get if you transfer another 3% of Sliwa’s votes and also reallocate the rest. (In my calculations yesterday I’d forgotten to renormalize the numbers so that the three candidates’ shares would add to 100%.)

Summary

The pre-election polls were close to the actual election outcomes but not perfect. As we’ve discussed many times, polls can often have systematic errors on the order of 3 percentage points, and that’s what happened here. That’s why we account for nonsampling errors in our probabilistic summaries.

P.S. For more, see this long discussion from Elliott Morris of yesterday’s election results, with lots of graphs. There’s a lot to say, even though it’s only a few elections.