The following claim has appeared and been widely retweeted on Twitter:

REVEALED: 'Simple Math' Shows Biden Claims 13 MILLION More Votes Than There Were Eligible Voters Who Voted in 2020 Election @JoeHoft via @gatewaypundit

The source for that tweet is The Gateway Pundit and it makes the following argument based on a shorter claim by Bill Binney. They compare the number of registered voters and the reported votes for each candidate:

Using the numbers as of today, which are materially similar to Binney’s, we find a huge issue. If we have 213.8 million registered voters in the US and 66.2% of all voters voted in the 2020 election, that equals 141.5 voters who voted in the 2020 election (Binney shows 140 million which is materially the same).

If President Trump won 74 million votes, then that leaves only 67.5 million votes remaining for Biden. This means 13 million duplicate or made up ballots were created and counted for Biden!

Putting side the serious logical errors in the argument as it is laid out here (eg only Biden received dodgy votes), are the basic numbers correct? Are there inconsistencies in the reported votes and turnout numbers that suggest fraud (by democrats or anyone else)?

The numbers claimed as fact are:

• 213.8 million registered voters in the US
• 66.2% of all voters voted in the 2020 election
• 141.5 voters who voted in the 2020 election
• Trump won 74 million votes

Then the logic is: It's then implied that some report Biden's votes as 67.5M + 13M = 80.5M. Then, the contention is that 80.5 + 74 > 141.5, ergo, 13M false votes.

• And the obvious one is: 239.2 million Americans were eligible to vote. cnbc.com/2020/11/04/… – DJClayworth Dec 20 '20 at 18:12
• @DJClayworth It is unclear whether the definition of turnout used in the source is registered or eligible voter population. I was hoping that someone with better knowledge could verify this which would thoroughly debunk the claim. – matt_black Dec 20 '20 at 18:23
• If that claim was true it would say that Trump and the Republican legal teams are extremely incompetent as that seems like pretty good evidence to bring up in a legal challenge or investigation of the election instead of announcing it on twitter, – Joe W Dec 20 '20 at 18:43
• The Gateway Pundit article posts a chart by the WP (not sure about the copyright issues on that) with the heading "How 2020 compares to other high-turnout presidential elections As a share of the voting-eligible population" (bolding added) – Acccumulation Dec 20 '20 at 22:44
• @Acccumulation Then add to the answer that the claim deliberately deceives in switching its definitions. I assumed (perhaps too charitably) that they were confused. If they knew what they were doing, that is actively deceitful. – matt_black Dec 20 '20 at 22:45

There is a basic error in the claim's calculation of the number of votes cast.

Turnout can be calculated in a number of ways, but the one preferred (and the 66% figure quoted) is the percentage of people voting compared with the Voting Eligible Population, not with the number of registered voters. The Voting Eligible Population is the number of people who are legally permitted to vote - i.e. citizens, over 18 and not excluded for some other reason. You do not have to be registered to be part of the Voting Eligible population. You can find turnout calculated as a proportion of registered voters in other places, but it is rarely used. Many states allow voter registration on the day of the election, so proportion of registered voters is rarely useful, and can technically go over 100%.

Also the number of votes cast determines the turnout, not the other way around. We know the turnout is 66.7% because somebody took the number of votes (which is counted) and divided it by the eligible voters. We don't find the number of votes cast by taking the eligible voters and multiplying by the turnout.

An example of the calculation is here.. Here is another.. Both of these use eligible voters as the baseline and give 66.7% as the voter turnout. This calculation explicitly gives 239.2 million as the number of eligible voters, and 66.8% as the turnout. Here is another link explicitly stating that the 66.2% is the proportion of Eligible Voters who voted.

The 66.7% turnout is the proportion of eligible voters, not registered voters.

This means The Gateway Pundit's calculation of votes cast is wrong. The correct figure can easily be found from actual published results. The "missing votes" are simply a product of The Gateway Pundit's profound ignorance or deliberate misinformation.

To parallel the figures given in the question:

• 213.8 million registered voters in the US
• 239.2 million eligible voters in the US
• 66.7% of all eligible voters voted in the 2020 election (the usual turnout calculation)
• 74.6% of all registered voters voted in the 2020 election1
• 159.6 million voters voted in the 2020 election (i.e. 66.7% of 239.2m, or 74.6% of 213.8m)
• Trump won 74.2 million votes
• Biden won 81.2 million votes2

1Technically some voters will have registered on the day, throwing this calculation off by a small and irrelevant amount

2With the remainder going to third party candidates, spoilt ballots, or a few people who voted in the general election but did not vote for President.

• Your third paragraph is the most important one in my opinion. This is what made the original claim entirely ludicrous. Votes cast are the known amount and the turnout percentage is calculated based on this. Trying to use the calculated value to "prove" the input is wrong only works for very specific circumstances like "turnout was 110% of eligible voters". – Eric Nolan Dec 22 '20 at 11:28