Lies, Damned Voting Fraud Lies, and Statistics

Steve Vigdor, Dec. 15, 2020

1. Introduction

Donald Trump’s reaction to the timeline of the 2020 U.S. Presidential election has been entirely predictable, given his pre-election behavior and his personality disorder.  It was clear beforehand that the unprecedented wave of absentee ballots in most states would be cast primarily by Democrat voters concerned about in-person voting during a pandemic, and would be counted late in many states, while Republican voters were likely to dominate in-person and early-counted voting on Election Day, since Trump had long preached the unreliability of mail-in ballots to his supporters. Thus, many people – prominently including Senator Bernie Sanders – accurately predicted that Trump might try to declare his own victory at the end of Election Day, before much of the absentee vote was counted, especially in high-population cities.  It appears to have been Trump’s tactical approach to spread false allegations before the election that absentee balloting would be riddled with fraud, and to urge his supporters to turn out in large numbers in person, precisely in order that he could declare premature victory in an election he knew would not necessarily favor him.

Indeed, as it turned out, Trump appeared to be leading the count in several critical battleground states at halftime, but lost those leads in the second half. Psychologically incapable of accepting an outcome with him as the loser, Trump would inevitably resist that result by claiming massive voter fraud in absentee ballot counting, planting conspiratorial seeds of doubt, and trying to get courts and Republican-led state legislatures to overturn the choice of electors. These moves were all telegraphed before the election.

What was less predictable was the extent to which unsupported claims of “statistical anomalies” in the vote would be parroted by Republican office holders, propagated through and accepted by a large fraction of the Republican voter base.  For example, Senator Rand Paul of Kentucky tweeted the following on November 29: “Interesting…Trump margin of ‘defeat’ in 4 states occurred in 4 data dumps between 1:34—6:31 am [on Nov. 4]. Statistical anomaly? Fraud? Look at the evidence and decide for yourself. (That is if Big Tech allows you to read this.)” Paul’s tweet is a classic example of the “black or white” and “loaded question” logical fallacies we dealt with in our post on Tuning Your Bullshit Detector.  I and many others have looked at the evidence and don’t find it to support either statistical anomalies or fraud.

Trump himself stated, in a 46-minute rambling rant about election fraud that he posted on Facebook on December 2, that “It’s statistically impossible that I lost.” But he has never exhibited the quantitative cognitive ability needed to seriously evaluate statistical probabilities, let alone impossibilities.  However, first place in the mathematical illiteracy sweepstakes is reserved for Texas Attorney General Ken Paxton, who included the following ludicrous claim in his legally dubious motion of Dec. 7, 2020, requesting the U.S. Supreme Court to invalidate election results from the states of Georgia, Michigan, Pennsylvania and Wisconsin, and thereby hand the election to Donald Trump even though he lost both the popular and Electoral College votes:

The probability of former Vice President Biden winning the popular vote in the four Defendant States—Georgia, Michigan, Pennsylvania, and Wisconsin—independently given President Trump’s early lead in those States as of 3 a.m. on November 4, 2020, is less than one in a quadrillion, or 1 in 1,000,000,000,000,000. For former Vice President Biden to win these four States collectively, the odds of that event happening decrease to less than one in a quadrillion to the fourth power (i.e., 1 in 1,000,000,000,000,0004).”

Paxton based this absurd claim on an attached declaration from one Charles J. Cicchetti, Ph.D. Paxton apparently did not bother to actually read the details of what Cicchetti claimed.  He did, in fact, claim less than 1 in a quadrillion statistical probability that two independent facts were true: (a) that the outcomes in Georgia were similar for Joe Biden in 2020 and Hilary Clinton in 2016; (b) that the early and late vote tabulations in Georgia were “randomly drawn from the same population.” Duh! Biden won and Clinton lost in Georgia, so nobody would have claimed that their outcomes were statistically “similar,” whatever Cicchetti thinks the definition of similarity should be. Nor would anybody who has paid the remotest attention to U.S. elections expect that early-counted in-person votes from many counties and late-counted absentee votes primarily from densely populated urban counties in each state would represent random samples drawn from identical distributions of partisan preferences. Furthermore, it is completely unjustified to raise whatever probability Cicchetti calculated for a single state to the fourth power when considering results in the four states, because the deviations from Cicchetti’s nonsensical premise (random draws from the same population) are strongly correlated among the four states.

In other words, Cicchetti’s analysis involves numbers, but is utterly irrelevant.  Nonetheless, Paxton managed to get 17 other Republican state Attorneys General and 126 Republican members of Congress to sign on to support this embarrassing statistical claptrap, in the few days before the Supreme Court summarily dismissed the petition. And now, calls for secession or violence are beginning to emerge from politicians and partisans apparently willing to die in support of the delusions of a desperate sore loser. 

In this post, we will examine the timeline trends of vote counting and reporting in several states, including the Trump-contested results from Wisconsin, Michigan, Pennsylvania and Georgia, four of the five states that Biden flipped from the 2016 election outcome. We will offer the logical explanations for the “data dumps” that so worry Rand Paul, Ken Paxton and other mathematically deficient conspiracy theorists.  We will examine the share of Biden votes and of Trump votes that came via absentee ballots in the four “defendant” states, across many counties spanning a wide spectrum in partisan lean. We will compare voter turnout in those counties in 2020 to that in 2016 and Biden’s 2020 margins with Clinton’s in 2016. In all of this publicly available data from the 2020 Presidential election, we find no evidence whatsoever of statistical anomalies or fraud in the “big, bad” cities Trump says stole the election from him.

While these particular statistical impossibility claims are at the heart of Trump’s ongoing, and increasingly desperate, insistence that he won the election, we will not deal here with the many other false voting fraud conspiracies spread since Nov. 4. These have already been debunked in many places (e.g., here, here and here) and judged by numerous courts to be unsupported by credible evidence.  In one typical opinion, U.S. District Judge Matthew Brann on Nov. 21 dismissed a case seeking to invalidate Pennsylvania election results, with the following withering criticism: “One might expect that when seeking such a startling outcome, a plaintiff would come formidably armed with compelling legal arguments and factual proof of rampant corruption. Instead, this Court has been presented with strained legal arguments without merit and speculative accusations un-pled in the operative complaint and unsupported by evidence.”

2. Spikes in vote count reporting

The most prevalent claims of voting fraud concern what have been labeled as “anomalous middle-of-the-night Biden vote spikes” in the early hours of Nov. 4, using loaded words intended to suggest something nefarious was going on. Some of these claims relied on a Nov. 5 tweet from Nick Adams, who describes himself as a best-selling author endorsed by Donald Trump.  The tweet claims: “Between 3:40-4:30AM, they ‘found’ 140,000 mail in ballots for Biden in Wisconsin. Between 3:30-5:00AM, they ‘found’ 200,000 mail in ballots for Biden in Michigan. Between 2:00-4:00AM, they ‘found’ 1,000,000 mail in ballots in Pennsylvania. All for Biden. None for Trump.” The claim that there were “none for Trump” is completely bogus, but was added to fuel the conspiracy.

Rand Paul referred to a more detailed analysis, but one unleavened by common sense, posted on Nov. 24 by someone or some group referring to themselves as “vote integrity.” By considering 8,954 individual vote updates from many states, their analysis leads to the following claim: “Our analysis finds that a few key vote updates in competitive states were unusually large in size and had an unusually high Biden-to-Trump ratio. We demonstrate the results differ enough from expected results to be cause for concern.” What is the nature of the concern? The author’s expectation is that there should not be single large vote updates that strongly favor one candidate over another, even if they emerge from counties that have a very strong partisan lean.  It would apparently be fine if that strong partisan lean were reported in a sequence of smaller batch updates, but if the votes are lumped into a large batch for reporting purposes, then it becomes suspicious.  This is nonsense, as I describe below.

Here are the four suspicious vote updates reported by “vote integrity” and referred to by Rand Paul:

  • An update in Michigan listed as of 6:31AM Eastern Time on November 4th, 2020, which shows 141,258 votes for Joe Biden and 5,968 votes for Donald Trump
  • An update in Wisconsin listed as 3:42AM Central Time on November 4th, 2020, which shows 143,379 votes for Joe Biden and 25,163 votes for Donald Trump
  • A vote update in Georgia listed at 1:34AM Eastern Time on November 4th, 2020, which shows 136,155 votes for Joe Biden and 29,115 votes for Donald Trump
  • An update in Michigan listed as of 3:50AM Eastern Time on November 4th, 2020, which shows 54,497 votes for Joe Biden and 4,718 votes for Donald Trump

So, what did actually go on overnight in Michigan, Wisconsin, Georgia and Pennsylvania on Nov. 4?

First of all, why were these states counting ballots in the middle of the night? The four states in question all allow no-excuse absentee voting, and that policy was in effect in each state already prior to the COVID-19 pandemic.  This does not make them unusual – 2/3 of U.S. states allow either no-excuse absentee voting or universal mail-in balloting.  However, Georgia, Michigan, Pennsylvania and Wisconsin are among the states that do not allow counting of absentee ballots before Election Day. This is in sharp contrast, for example, to Florida, which allows absentee vote counting to start 22 days before Election Day.  Furthermore, Pennsylvania and Wisconsin do not even allow processing of absentee ballots – i.e., checking of signatures, removal of ballots from mailing envelopes – prior to Election Day.  It was thus always understood that these four states would be counting absentee ballots after the poll workers completed their work processing voters and tabulating in-person votes on Election Day. In an attempt to get as far along as they could on counting the absentee ballots, their poll workers worked well into the middle of the night on Nov. 4.  The “spikes” referred to were large-batch releases of initial absentee ballot results.  There was nothing nefarious about the timing, and the counting was observed throughout by both Republican and Democrat observers, as well as by closed-circuit TV cameras.

Second, vote “spikes” are not at all anomalies.  They are common in elections, where states and counties often release vote counts in large batches. Given the extreme polarization of the American electorate at the present time, those large batches often contain large margins for one candidate or another, depending on the counties doing the reporting: large advances for Republican candidates when it’s deep red counties, and large advances for Democrat candidates when it’s deep blue counties doing the reporting. 

For example, consider the Pennsylvania vote count results shown in Fig. 1, taken from the New York Times election tracking (the same source of vote counts used in the “Voting Integrity” post about anomalies). At the 20% vote share mark, there was a spike in which Trump gained about 500,000 votes over Biden, dwarfing the magnitude of any other spike we will consider below. Another spike, this time gaining about 100,000 votes for Trump, occurs near the 55% vote share point in the tracking results shown in Fig. 2 for North Carolina, a state where later vote counting allowed Trump to overtake Biden. Should we consider those Trump spikes to be anomalous and worthy of elimination from the vote count? If not, why should the vote spikes that favored Biden be dismissed?

Figure 1. Biden (blue) vs. Trump (red) vote share (top frame) and vote margin (bottom frame) in Pennsylvania election result reporting, plotted as a percentage of total votes counted at the time of each batch release. The figure is from the New York Times.
Figure 2. Like Fig. 1, but now for North Carolina.

Now, it is true that the latest spikes in vote count tended to favor Biden, as was the case for the approximately 100,000 vote gain for Biden in Pennsylvania at the 75% vote share point in Fig. 1 (though that spike just counterbalanced a 100,000-vote gain for Trump at about the 60% point).  That is the case simply because the largest volume of absentee votes to process and count occurred in densely populated urban and near suburban counties, which have a strong partisan lean toward Democrats. The small late spike for Biden in Pennsylvania is hardly the dominant feature of the trend in Fig. 1; rather, it’s the steady growth of Biden votes among the absentee ballots, a subject we’ll return to below. The trend in the other three states in question is shown in Figs. 3-5.

Figure 3. Like Fig. 1, but now for Georgia.

In Georgia, Michigan and Wisconsin there were indeed Biden-dominated spikes in the overnight counting, occurring in each case near 80-85% of the vote share reported in Figs. 3-5.  In each case, there were no further batches of votes reported for some time – this was the end of the overnight reporting, and batch reporting was delayed as the poll worker crews changed shifts. The spikes followed by flat vote counts simply had the effect of “discretizing” the trend that was apparent just before and long after the spikes occurred: namely, the absentee ballots in each state were strongly favoring Biden over Trump, a trend that was entirely anticipated. So, let’s review the details in each state.

Figure 4. Biden (blue) vs. Trump (red) vote share in Michigan election result reporting, plotted as a function of the percentage of total votes counted at the time of each batch release. The figure is from the New York Times.
Figure 5. Like Fig. 4, but now for Wisconsin.

The vote spike in Wisconsin (Fig. 5) highlighted by “vote integrity” corresponded to approximately 170,000 absentee ballots reported out of Milwaukee.  About 85% of these ballots were cast for Biden. Is that fraction anomalous? Not at all, as Biden won about 70% of the Milwaukee County vote overall and Biden’s absentee margins were systematically larger in all counties, whether deep red, purple, or deep blue, as we’ll show below.  Furthermore, polling before the election in Wisconsin indicated that roughly 81% of the absentee ballot requests statewide were from people expecting to vote for Biden, while only 14% were from people expecting to vote for Trump.  And Milwaukee tends to vote far more for Democrats than Wisconsin as a whole.

The Georgia spike (Fig. 3) was comparable in magnitude to Wisconsin’s and Biden won about 82% of those votes.  Again, this is not at all surprising, as these votes came from the Atlanta region (Fulton and DeKalb Counties), where Biden won 65-70% of the Election Day votes and averaged over 80% of the absentee votes.

In Pennsylvania (Fig. 1) there was not much of a notable spike, but rather a steady increase in votes for both Biden and Trump between midnight and 3 am, especially.  But as results came in from Philadelphia and Allegheny (Pittsburgh area) Counties, Biden began to eat steadily into Trump’s lead, and eventually overtook him in the following days.  Again, this was all easily predictable, as Biden won 79% of the Allegheny County absentee votes and 92% of the Philadelphia County absentee votes.

The most complicated case is that in Michigan, where some legitimate vote batch releases from the Detroit area (Wayne County) were further confused by clerical errors in vote reporting from Republican-leaning counties.  For example, the Nick Adams claim that “Between 3:30-5:00AM, they ‘found’ 200,000 mail-in ballots for Biden in Michigan” includes the impact of a soon-recognized typo in results reporting from Shiawassee County, where the Biden vote count of 15,371 was temporarily misreported by inadvertently adding a zero at the end (153,710). This error appeared to give Biden an extra 138,000 votes, with no corresponding addition to the Trump total.  But the error was soon recognized and corrected, and in no way affects Biden’s actual lead of some 154,000 votes over Trump in Michigan.  That correction, however, did not stop Trump supporters from continuing to claim the momentary error as evidence of fraud.

As can be seen in the Michigan vote trend shown in Fig. 4, there was only one real spike overnight in Michigan, corresponding to nearly 150,000 votes reported out of Wayne County shortly after 6 am (corresponding to 80% vote share in the figure).  Those votes came from Detroit city, where Biden won 95% overall of the vote split between Biden and Trump.  In the 6:31 am vote spike, Biden won 96% of the vote, not at all out of line with the overall result from Detroit.

In summary, the overnight spikes labeled as fraud candidates by Trump supporters simply result from large absentee vote batches counted late, in states that did not permit absentee ballot counting prior to Election Day, and reported out of urban counties, where the absentee voting overwhelmingly favored the Biden/Harris ticket.

3. Were the absentee margins in big cities anomalous?

But don’t these incredible Biden margins in absentee vote share in “big, corrupt” cities themselves reflect voting fraud? Trump supporters have maintained that these excess Biden votes were either fraudulently “found,” rather than actually cast, or illicitly switched from Trump to Biden. If either claim were true, adding 100,000 or more fraudulent votes, we would expect to see anomalies in the big city results, vis-à-vis those from Republican-leaning counties in the same states, in one or more of the following metrics: voter turnout; Biden improvements over Clinton’s results in 2016; the share of Biden and/or Trump votes cast by absentee ballots. As we will see, there is zero evidence of any such anomalies.

In Figs. 6-8, we compare Biden and Trump vote shares in various counties on Election Day with those in the absentee ballots.  For Pennsylvania, Michigan and Georgia, we survey a handful of counties varying from deep red to purple to deep blue. The results are based on the official final vote tallies reported by the states themselves, noting that the Pennsylvania results do not include absentee ballots that arrived after 8 pm on Election Day, as the state was instructed by Supreme Court Justice Samuel Alito to separate these ballots out.  We are unable to include Wisconsin in these plots, because no Wisconsin counties report in-person and absentee voting results separately.  In Michigan, only some counties report them separately, which explains why we omit a statewide result in Michigan, including only counties that do separate Election Day from absentee ballots.

From Figs. 6-8, we can draw the following conclusions:

  • Biden performed far better and Trump far worse in absentee ballots than in Election Day ballots in all counties and statewide in each state.  Some of the most striking performance differences were in deep red counties. Biden even won the absentee vote in counties where he garnered only about 20% of the Election Day vote, such as Westmoreland and Washington Counties in Pennsylvania.  He won the overall vote in suburban counties like Montgomery (PA), Oakland (MI) and Cobb (GA), and pulled out victories in each of these states, by winning the absentee votes by a larger margin than he lost the Election Day vote.
  • The fraction of Biden votes that came in via absentee ballots (see bottom frames in Figs. 6-8) in the urban counties, such as Philadelphia, Allegheny, Wayne, Fulton and DeKalb, is quite consistent with the corresponding fraction in the reddest counties, such as Westmoreland, Livingston and Cherokee. No anomalies are seen in the urban counties.  Biden’s share of the total absentee vote (as well as of the total Election Day vote) was higher in urban counties simply because those counties have a higher proportion of Democrat voters, and Democrat voters were far more likely to use absentee ballots.
  • The stark differences in absentee vote shares between Biden and Trump are consistent with the partisan lean in absentee ballot requests.  For example, in Pennsylvania, 63% of absentee ballots were requested by registered Democrat voters and 25% by registered Republican voters, a discrepancy reflected clearly in the bottom frame of Fig. 6.
  • The difference was not as stark in Michigan or in Georgia.  The absentee vote percentage is significantly lower for both candidates in Georgia because all the counties there report early in-person voting, Election Day voting and absentee voting separately, and the early in-person voting options were strong and attractive to many voters.
Figure 6. Biden (upper) and Trump (middle) shares of the Election Day and absentee votes in various Pennsylvania counties. The bottom frame shows the fraction of overall Biden and Trump votes in each county that was recorded on absentee ballots.
Figure 7. Same as Fig. 6, but now for Michigan counties.
Figure 8. Same as Fig. 6, but now for Georgia counties.

A conspiracy theorist might respond to the data in Figs. 6-8 by claiming: “OK, then maybe the Biden votes in urban counties, both on Election Day and via absentee ballot, were just multiply counted, or similar percentages of both counts were fraudulently converted from Trump to Biden votes.” After all, some Trump supporters have claimed that turnout percentages in Democrat counties sometimes exceeded 100%. If that were the case, we would expect to see anomalies in 2020 vis-à-vis 2016 turnout percentages in the urban counties specifically, as well as anomalous improvements in Biden’s vote share vis-à-vis Hilary Clinton’s in 2016.  The turnout and Democrat margins are compared for 2020 and 2016, across counties over a wide spectrum of partisan lean in all four “defendant” states in Figs. 9 and 10.

Figure 9. Comparison of voter turnout rates in the 2016 (blue) and 2020 (orange) Presidential elections, across various counties in the four “defendant” states, and for the U.S. as a whole.

The results in Fig. 9 show that voter turnout systematically increased by several percent from 2016 to 2020 in all counties in Pennsylvania, Michigan and Wisconsin, as well as nationally, while they decreased by several percent throughout Georgia. The turnout percentages in each county and state were calculated by dividing the total number of votes cast by the number of registered voters by the time of the election.  While turnout reached 90% in some Wisconsin counties, it did not exceed 100% anywhere; disinformation claims that it did were based on using outdated voter registration tallies. The nationwide voter turnout was calculated relative to the estimated voter-eligible population, rather than to the number of registered voters summed over all states.

The most important takeaway from Fig. 9 is that turnout changes in the urban counties questioned by Trump supporters are in no way anomalous.  In fact, they tend to have somewhat lower turnout performance than the deep red counties, so there is no evidence that Biden votes were magically found or manufactured in big cities.  The same basic conclusion is drawn from Fig. 10, showing Biden 2020 vote percent margins vs. Clinton’s 2016 margins. There is nothing anomalous in the urban county results, with the possible exception that Biden did slightly worse in Philadelphia than Clinton had, despite improving on Clinton’s performance in the clear majority of both red and blue counties. Indeed, Biden’s most notable improvements were in deep red and purple suburban (e.g., Cobb) counties in Georgia. So, if your favorite conspiracy theory has votes being switched from Trump to Biden, you have to allow that it was done with the consent of Republican election supervisors, rather than in Democrat-controlled big cities.

Figure 10. Comparison of the percentage vote margins by which Hilary Clinton in 2016 (blue) and Joe Biden in 2020 (orange) won or lost the Presidential election vote count in various counties in the four “defendant” states, and in the U.S. as a whole.

4. Summary and outlook

Our analysis of the voting results from four of the states that Biden flipped from Trump’s 2016 victory leads to the following conclusions:

  • There is no aspect of the surviving (i.e., not due to quickly corrected clerical errors) Nov. 4 overnight vote “spikes” that suggests either statistical anomalies or fraud.  They simply reflect the long-anticipated late counting of absentee ballots, with an overwhelming Democrat partisan lean, in largely blue urban and suburban counties, in states that forbid absentee counting before Election Day.
  • Comparison of 2016 and 2020 election results, for both voter turnout and Democrat vote margins, show no anomalies in the results from the large cities with heavy black population that Trump has insisted committed fraud to rob him of the election.
  • The claims that Trump really won the election are based on his insistence that voting is only fair if it stops while he’s ahead.  He has clearly lost both the popular and electoral college vote by significant margins.  His supporters are submitting to deep-seated confirmation bias in choosing to believe fraud reports that have no supporting evidence and so-called “anomalies” that have mundane explanations.
  • Trump may have hurt himself by casting so many aspersions on mail-in voting. Relatively few Trump voters used absentee ballots, and some of his potential voters must have kept away from in-person voting out of fear of contracting COVID-19 by standing in long lines for many hours.
  • All of these results were predicted beforehand, including Trump’s voting fraud claims. Georgia, Pennsylvania, Michigan and Wisconsin were not “stolen” from him; he lost each of these states by vote margins exceeding 10,000, margins much larger than any that have ever been altered in voting recounts.  None of these states were called for Trump on Election Night by any respectable vote-calling outlet – including the far from unbiased Fox News – precisely because of the clearly anticipated Biden surge in late-counted absentee votes.
  • Trump’s legal representatives have systematically failed in court after court to present any credible evidence of voting fraud or irregularities on a scale that might alter more than tens of events, nothing like the tens of thousands of votes by which he lost each of these four states. His inept and frivolous lawsuits amount to no more than a clumsy attempted clown-coup.

While some Republican state legislators continue to try to overturn the election results, even after the Electoral College has formally designated Joe Biden as President-Elect, many more are now redirecting their focus to “improving” their voter suppression tactics for future elections.  With two Senate run-off elections still to come in early January 2021, Georgia is leading this charge. While no credible evidence has been presented in any state for actual fraud in absentee ballots, the overwhelming partisan lean in the absentee ballots cast in the 2020 election has led Republican legislators to push specifically for new restrictions on voting by mail.  For example, Georgia lawmakers want to ban the sort of mass mailing of absentee ballot request forms that occurred prior to the 2020 election, and to add stringent photo ID requirements on absentee ballots, to replace the current system of voter signature matching with signatures in the state’s elections database. Those moves are coupled with changes to enhance pruning of voter registration rolls and to restrict the number of early voting locations in communities with large black populations.

It is increasingly clear that the evidence-free claims of voter fraud promoted by Trump and his supporters, and the new changes now being contemplated in Republican-led legislatures, are fundamentally racist in intent. Trump claims that the 2020 election was “stolen” in the cities of Philadelphia, Detroit, Milwaukee and Atlanta – all with large black populations – despite the evidence we have shown in this post that Biden’s huge wins in absentee ballots also occurred in many Republican-leaning counties with predominantly white populations. His legal point-man Rudy Giuliani has recently revived an outdated racist dog-whistle in claiming that Atlanta poll workers were “passing around USB ports [sic] like they were vials of heroin or cocaine.”

The message that many Republicans have drawn from this election is that more black voters should be disenfranchised. The message the election actually delivered is that absentee balloting facilitated record turnout in the midst of a deadly pandemic, with no evidence of appreciable voting fraud. States such as Oregon, Washington, Utah and Colorado have already demonstrated in multiple elections that universal mail-in balloting is safe and efficient. The primary voting process reform that would help to prevent Trump-like attempts at after-the-fact voter disenfranchisement in future elections is an allowance in more states to begin counting absentee ballots prior to Election Day, to avoid exploitable counting delays.


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