Wednesday, December 16, 2020

Hurricane Rates Fitted to the Poisson Distribution, as Evidence of Climate Change

This 2020 Atlantic hurricane season set the all-time record (back to 1851) for named storms (30), and had the 2nd most number of hurricanes (13) and major hurricanes (6, 7-way tie for 2nd) (both of these records held by 2005).

One year does not make a trend - so the larger question is whether hurricanes/named storms are a Poisson process, and can we can use the Poisson distribution to determine whether recent years are exhibiting an increased trend. This has been shown mathematically, and the criteria certainly seems to fit tropical systems, just like it does with shark attacks:

The Poisson distribution arises in connection with Poisson processes. It applies to various phenomena of discrete properties (that is, those that may happen 0, 1, 2, 3, ... times during a given period of time or in a given area) whenever the probability of the phenomenon happening is constant in time or space.

The key part here is "probability of the phenomenon happening is constant in time" - is the probability of a hurricane/named storm increasing over time? 

In each chart, I'll present two comparisons - one over the entire HURDAT history of tropical cyclones in the Atlantic (1851 to now), and another just in the satellite era, which is 1967 to now. While NOAA undergoes extensive reanalysis projects to fill in past years prior to satellites, it is still very possible that more storms are named today due to increases in data and technology, including satellites:

To account for this, I'll do both 1851-Now and 1967-Now (satellite era), across:
  • Named storms
  • Hurricanes
  • Major Hurricanes (Category 3 or Higher)
  • Accumulated Cyclone Energy - ACE (more on this later)

Friday, December 11, 2020

The Rate of Voter Fraud is Too Low To Have Swung the 2020 Election

Before the 2020 election, I concluded that the rate of voter fraud was so low that it was extremely unlikely to affect the outcome - and the only scenario in which it could, would be if the election was unfathomably close - 2000 Bush/Gore close.

And that didn't happen. But the election was close in the electoral college, with 3 states once again deciding the presidency: Georgia (+0.3%), Arizona (+0.3%), and Wisconsin (+0.6%) account for 37 electoral votes, which would have resulted in a 269-269 tie, which would have almost certainly gone Trump's way (in effect, tie goes to the Republican, based on the current geographical distribution of votes). In fact, the margin in those 3 states was actually closer than in 2016 - making this election the second-closest (electorally), behind only 2000.

And with turnout at its highest since 1900, applying the estimated rates of voter fraud to the larger turnout and narrower margin... still doesn't swing the election. Updated close electoral college margins:

  • 2020
    • Deciding states: Wisconsin, Arizona, Georgia
    • Margin in deciding states (3): 43,809 votes
    • Fraud estimate (Max): 31,679 votes
    • Fraud estimates (Meta-Estimate): 1,415 votes
  • 2016
    • Deciding states: Pennsylvania, Wisconsin, Michigan
    • Margin in deciding states (3): 77,744 votes
    • Fraud estimate (Max): 27,357 votes
    • Fraud estimate (Meta-Estimate): 1,222 votes
  • 1976
    • Deciding states: Wisconsin, Ohio
    • Margin in deciding  states (1): 44,578 votes
    • Fraud estimate (Max): 16,321 votes
    • Fraud estimate (Meta-Estimate): 729 votes
  • 2000
    • Deciding states: Florida
    • Margin in deciding state (1): 537 votes
    • Fraud estimate (Max): 21,119 votes
    • Fraud estimate (Meta-Estimate) 943 votes
Updated table, with sources:

Rate1 in...Equivalent in 2020% of Pop Vote Margin% of Electoral MarginSource #

Source #SourceInstitution TypeElection(s)# StatesDate
1Working PaperUnaffiliated201250Oct 2017
2Iowa Secretary of StateRepublican Administration20121May 2014
3White House (Trump)Republican Administration201620Aug 2018
4Washington PostNewspaper2016, 20183June 2020
5Brennan Center at NYUUniversity2000 to 200650Nov 2007
6Arizona StateUniversity2000 to 201050Aug 2012
7Brennan Center at NYUUniversity201642May 2017
8ReutersInternational News1998 to 20181July 2020
9Heritage FoundationConservative Think Tank2000 to 201850Oct 2020
10MITUniversity2000 to 201850April 2020
11US Court of Appeals for the Fifth CircuitFederal Court2000 to 20101July 2016
12Loyola Law SchoolUniversity2000 to 201250Aug 2014
13Washington PostNewspaper201650Dec 2016
14Kansas Secretary of StateRepublican Administration2010 to 20141Jun 2015
15US Department of Justice (W Bush)Republican Administration2000 to 200650Apr 2007
Estimate (Meta-Analysis)UnaffiliatedAllAllOct 2020

It then naturally follows that Biden's popular vote margin is nowhere close to the above fraud estimates:

ElectionPopular Vote MOV% of Margin (Max)% of Margin (Estimate)

But turnout was historic, as noted earlier - is that evidence of fraud with so many more voters than four years ago? The number of votes jumped 15.8% compared to 2016! Which... is not even the highest increase in the past 20 years: from 2000 to 2004 there were 15.87% more votes cast.

The 2018 midterms had a historic rise too, gaining 44.7% compared to 2014. So how many more voters voted in the presidential election, relative to the most recent midterms? That turnout metric was up 38.9% compared to 2018! Which... is the lowest midterm-to-presidential increase since 2000. The next closest is 2012 (presidential) vs 2010 (midterms), which grew 48.8%.

In chart form, the record-breaking turnout doesn't even appear that out of line with recent trends:

No matter which trend is challenged, the conclusion holds: the rate of voter fraud did not change the outcome of the election.