Who really won, Biden or Trump?


“I see no evidence of vote fraud”


Why aren’t Donald Trump, Joe Biden, and the unhappy Americans one encounters online these days all clamouring for science to be used to find out objectively which candidate would emerge as the real winner of the presidential election if only valid votes could be counted?  (It wouldn’t be necessary to weed out all the invalid votes and start the counting all over again in every state, just to answer this simple question.)

There is a simple algorithm for calculating the winner (if any) of the US presidential election by electoral college vote.  This algorithm requires as its input the vote counts by candidate for all the states.  The algorithm outputs a name, for example, either Trump or Biden this year.  (The number of electors each state returns is static data that is hard-coded into the algorithm.)

It would be interesting to know which candidate that algorithm would say won the US presidential election if the vote counts fed into it were counts of all the valid votes and none of the invalid votes – especially not any votes that were invalid because they were fraudulent, such as the output of so-called “vote factories”.  (For brevity, I will refer to this candidate as the “real winner” of the presidential election.)

Both Biden and Trump are claiming to be the real winner.  Neither is able to prove his claim yet.  Instead, they are both claiming to love more than the other the land and the people that their posturing is threatening to cut in two, due to universal ignorance as to which candidate is the real winner of the election and the heavy emotional investment of so many into wishful-thinking guesses about that, one way or the other.

The American people should not be left to guess who really won the election. The media shouldn’t be threatening that baby Sam will have to be split down the middle in order to find out which harlot proves she loves him like a real mum, by conceding defeat to the  other.  There is no constitutional mechanism anyway for the granting of custody to the whore who is the first willing to surrender to the other out of love for the child who is in peril of bisection.  “What Solomon would do” won’t cut it.  Instead, America can find out the truth and settle the quarrel once and for all using science, if America wants that.



Mathematical v Legal Proof

Trump’s lawyers seem to not have cottoned on yet that the same word that is used in the description of the civil standard of proof, “the balance of probabilities“, echoes the name of a branch of mathematics – Probability.  Proving things is as much the bread and butter of the mathematician as it is in the legal professions, albeit with greater rigour.  What America can enjoy, if it acquires an appetite for truth, is the glorious spectacle of one Professor of Probability and Statistics after another testifying before the Supreme Justices in their expert evidence exactly what they have all, independently but unanimously, calculated the probability to be that either Trump or Biden was the real winner of the election, leaving the court only to find for one candidate or the other on the unassailable basis that his calculated probability of being the real winner was greater than a half and his rival’s less than a half.

I am praying for somebody in authority to heed what I’ve been saying for many days now on Twitter, that nobody’s guess as to which candidate is the real winner counts for anything when, by using comparatively little, well-targeted, random sampling and auditing and calculating, America could find out the objective truth of the matter.  But do Americans want to find out the truth badly enough to want the authorities to take the small effort needed to find out the truth systematically and to prove the truth in court if necessary, using scientific evidence?


What evidence needs to be gathered?

At present, both Biden and Trump are scanning the horizon for “evidence” of vote fraud, the former (so-to-speak) with a telescope deliberately held to his blind eye (“I see no evidence”, to adapt a saying of Lord Admiral Nelson), the latter short-sightedly looking through the wrong end of his telescope, bogged down as he has become in detail in a proliferation of lawsuits about the minutiae rather than seeing the big picture.

Whichever of Trump and Biden has a good claim to be the real winner – something nobody really knows yet – would need to get hold of some additional data that would prove his claim objectively. The decision to do so favours neither candidate unless one candidate had more fraudulent votes than the other in a marginal state, something we don’t know yet.

It is the same data that is needed for proving or disproving both rival claims.

That data could be collected by neutral investigators, at public expense, for example, pursuant to a court order, or presidential executive order.  If the US elections are to be seen to have been free and fair, that data must be collected and used to prove whichever of the rival claims to be the real winner is discovered to be true.  However, it is not obvious that it has crossed the mind of either main candidate, still less the minds of any of the mainstream media, what readily available data it is that could be, and simply must be, collected and analysed scientifically.

What is needed is the random sampling of votes in the five marginal states, validation or invalidation of every sampled vote on the part of officials permitted to track down and to interview the voters whose apparent votes are in the samples, and the production, on the part of Bayesian statistics experts, of accurate estimates of what the counts of valid votes would be in the marginal states.

There seems to be a conspiracy afoot to portray the identity of the real winner as somehow unknowable.  But any statistician will tell you that it is established science that by counting the prevalence of some property in a random sample of a set, one can make inferences about the probabilities of different prevalences of that property in the whole set.  It is therefore not beyond the wit of mankind to find out who the real winner was, to any required degree of certainty, simply by attempting to validate a random selection of postal votes in each marginal constituency, by interviewing the voters in confidence as to whether (and perhaps how) they voted, assuming the voters exist (because they were not long dead by the time of the election, one well-used but easily-identified method of postal vote fraud) and actually live in the relevant state.  If any deny having voted, this proves a different well-known type of postal vote fraud.

Measuring how many invalid votes each candidate received in a sample enables us to gauge out how many invalid votes that candidate received in that state as a whole, to an accuracy that can also be calculated.  To have proved using such mathematics, applied to such data, that this or that candidate is more likely than not to be the real winner is to become able to prove in court that that candidate is the real winner to the civil standard of proof, which is only the balance of probabilities.  QED.  Nothing more than arithmetic justified by a few theorems in statistics and probability is needed, once one has the data from the samples.


Why not do this?

Why are Donald Trump and Joe Biden not in agreement with me, that finding out who the real winner was in this manner, which is feasible, would be worthwhile?

Rather, Trump is peddling a conspiracy theory that he is unlikely to be able to prove absent whistle-blowing, to the effect that the casting of fraudulent votes was centrally co-ordinated, whilst Democrats are (as it were) chanting a slogan “you have no evidence” that is based upon a preposterous, naive doctrine that there is no need to measure how much fraud there actually was, because the answer somehow must be zero.  Unless, that is, Trump can provide “evidence” that says otherwise without anybody measuring the true extent of fraud and telling Trump (and the courts) how much fraud there actually was, which is the only evidence that matters.

The Democrats’ “presumption of zero fraud” doctrine is already refuted by anecdotal evidence.  We already know that there was some fraud.  With postal voting, there more-or-less always is.  But anecdotal evidence cannot tell us how much fraud there was and whether the amount (and direction) of (net) fraud was enough to flip this or that state from Trump to Biden or vice versa.  The USA therefore ought to measure how much fraud there was, wherever fraud is likely to affect the output from the algorithm (i.e. in marginal states), with an open mind as to what the repercussions will be of collecting the necessary data and calculating the truth from it.

The already discredited “presumption of zero fraud” doctrine mimics the “presumption of innocence” doctrine of criminal law.  Trump’s provocative accusation of a “stolen” election therefore gives emotional force to the fallacy that rests on the Democrats’ false “presumption of zero fraud” doctrine.  His accusation is of a huge criminal conspiracy in which even Biden himself might be complicit.  Phrases like “guilty until proved innocent” and “beyond reasonable doubt” immediately arise in the Democrats’ minds, along with the nobly indignant emotions which those phrases evoke.  From that indignation there may spring an unreasonable demand that Trump provides evidence that the level of fraud is not just non-zero but enough to affect the election’s outcome, before he be allowed to measure scientifically what the level of fraud actually was.  But Trump did not need to make an accusation of criminal conspiracy and he doesn’t need to prove one to the criminal standard of proof.  He merely needs to prove that he was the real winner of the election, to the civil standard of proof.  Sampling, validation and calculation applying Bayesian statistics, will prove which candidate was the real winner far more easily than Trump could prove a conspiracy.

We don’t know who the real winner of the election was, none of us.  Formulating this first as a problem of evidence and proof as these terms are understood by lawyers has created more heat than it has shed light and must stop.  Formulating it first as a problem in mathematics and then recognising how little missing data we need to collect if we wish to solve the problem mathematically (and then show the courts our workings) is what I think Trump’s lawyers need to realise is the winning approach for them.  (But only if the missing data supports their client’s claim to be the real winner.)  Biden’s lawyers would do well to adopt this approach too, unless their client wants to lord it over a divided nation about half of whose adult population disputes his legitimacy and hates his guts, as the usurper and cheat who wasn’t willing to prove he hadn’t stolen the election when that is what it looked like to them.

I hope that both Trump and Biden pay attention to what I have been suggesting for several days now and agree to this plan to find out scientifically who the real winner is.  This would be much better than their present, baseless posturing and insulting of one another.  I shall be disappointed if the solvable mystery of who is the real winner remains unsolved, due to apathy towards truth, becoming instead like the earlier historic mysteries such as who Jack the Ripper was, or what became of the Princes in the Tower.  The doctrine that we’ll never know the truth, whether Biden or Trump is the real winner because it is impossible to find out the truth, is a big fat lie.



Postscript added 22 November 2020

Since I wrote this piece, encouraging news has broken (here: Williams College Mathematician Flags up to 100,000 Ballots in Pennsylvania) that Mr Trump’s legal team have visibly moved towards using the numerate, quantitative approach I have suggested here is necessary, for finding out whether or not the election was (so-to-speak) “stolen”; whether “stolen” (that is) as the result of a heinous central conspiracy or (perhaps just as likely) as the cumulative effect of many instances of local, small-scale cheating that were not solicited by senior officials of the Democratic Party.

Although this piece did not set out to provide any evidence that rebutted any presumption of zero fraud, simply asserting that such evidence existed and questioning the assumption, Ark has tried so hard in the comments below to make something of this omission on my part that, ex gratia, I offer him (and any others who accuse me of making a “claim” of fraud without “evidence”) the following link, which arrived in my email today, for what it is worth: ‘There Was in Fact Fraud That Took Place:’ FEC Chairman Trey Trainor.


Tweets about this topic  – please scroll past these to the reader comments if you wish



Filed under Political

22 responses to “Who really won, Biden or Trump?

  1. Ark

    Georgia officials have recently finished a manual recount and have officially declared Joe Biden Winner.
    Are you now prepared to acknowlege this or are you still adament more needs to be done to verify Biden’s presidency as legit?

    • Nobody’s “acknowledgment” of Joe Biden’s presidency as “legit” affects my argument for finding out the truth.

      • Ark

        You implied there had been fraud, based on zero evidence and nothing but spurious claims so what truth were you finding out?

        • The truth we should find out, is whether fraud had any effect on the outcome in certain states where the majority is small. There is already enough evidence to refute your “zero fraud” hypothesis (although I’m not bringing that evidence here).

          Mathematically, the absence of fraud isn’t a different thing from the presence of fraud. It is simply an extraordinarily unlikely measurement to make, a zero where one hopes for as small a value as possible, the smaller the better, but doesn’t seriously expect a reading of zero.

          Most elections don’t calibrate the postal vote counts to adjust for the effect of any fraud because most elections have comparatively few postal votes (so a huge proportion of them would have to be fraudulent to have any effect), because there is no reason to suspect that there are more fraudulent votes for one candidate than another, and because majorities are not as thin as some of those observed in the uncalibrated vote counts in this election. None of those reasons for not usually calibrating apply here.

          Basically, you are simply chanting the discredited slogan that we don’t need to find out how much fraud there was and whether it benefited one candidate more than another, because we can safely assume that there was zero fraud, or zero net fraud (i.e. equal fraud for both main candidates). I’ve dealt with that fallacy in the post and also on your blog for days before I posted this. There is evidence a-plenty that there was some fraud. Trump needs to be ready to order neutral officials to find out how much fraud there was and whether it flipped any states, or to ask the courts to order that sort of investigation. Biden has nothing to lose from such an investigation, unless he benefited more than Trump from fraudulent votes.

          • Ark

            Basically, you are simply chanting the discredited slogan that we don’t need to find out how much fraud there was and whether it benefited one candidate more than another …

            Bollocks! That is not what I wrote at all.
            If you don’t have the integrity to respond honestly to my comment then why bother to respond at all?

            • Before I posted this post on my blog, I had already dealt with everything you had to say on this topic , on your own blog, here:

              If Trump’s lawyers manage to plan the end game of the litigation, I think there’s a small chance he could remain president. I think the approach needed must recognise that proof and probability are ideas in mathematics as well as in law. As I said,

              • Ark

                Once again, bollocks. Not a shred of evidence has been submitted or produced.
                Examples of how post-election audits and recounts have been handled are described here:

                I thought this part of the article particularly enlightening.

                Trump’s own election security agency declared the 2020 presidential election to have been the most secure in history . (Though days after that statement was issued, Trump fired the agency’s leader. )

                For goodness’ sake, if one is going to claim the earth is flat the very least one should do is sail a ship off the edge.

                • “Not a shred of evidence has been submitted or produced.”

                  I am familiar with that tired old rhetoric. Based on news coverage I have read, it is empty rhetoric that doesn’t stand up to a fact check. The BBC were already spouting the same campaigning slogan by 5th November, about court cases that had only just been filed, or which hadn’t even been filed yet, i.e. long before those cases had reached the stage at which the parties would have been directed to file and disclose the evidence in their possession.

                  We will have to agree to disagree, because I have better things to do with my time than to keep myself acquainted with the progress of court cases in the USA in which I am neither a party nor a witness, which in any case is hardly practical for me even as a citizen journalist like yourself, given that I live in the UK.

                  There was a particularly good example of an evidence-fueled court case reported yesterday, in which Dr Steven Miller at Williams University was a party or an expert witness, I forget which. That case adopted the quantitative approach I had advocated here, so my ears pricked up. I emailed Miller today and he has emailed me back saying he has passed on what I wrote to him. Find a report of that which mentions the evidence on which the pleadings in that case rely, why don’t you?

                  • Ark

                    Instead of your conspiracy theory fuelled rhetoric why don’t you simply supply the evidence? That way you could help Donald Trump retain the Presidency and maybe he will reward you for your efforts?
                    Perhaps a position on his staff?
                    So, once more …if you are going to espouse such rhetoric then at least man up and have the balls to produce evidence.

                    • I don’t have any “conspiracy theory”. You appear to have misunderstood this post. It is a post about what sort of evidence Trump needs and how to get it and nothing else.

                    • Ark

                      Based on the conspiracy theory orchestrated by Trump that the presidency was ”stolen”, a ridiculous claim in the first place and one that has not revealed a shred of evidence to support it. Neither has a shred of evidence been put forward to even warrant such a half-arsed claim.
                      Maybe you just like the sound of your own voice, John? Or believe you have some ”secret method” that will expose this fraud you continue to allude to?

                      And why on earth was there no evidence of fraud in the states Trump won outright?
                      And why were the results in these states not even brought into question, John?
                      As noted by Trump’s own team, this election was the most secure in history.
                      And the head of that particular team was fired for his trouble!
                      Seriously , enough already. You are coming across like a puppet in an episode of Joe 90 or Captain Scarlet and the Mysterons.

                      As the Yanks like to say – Either put up or push off.

                    • You are missing the point of this post completely. Please stop going on about things I haven’t mentioned. If you’ve got a problem with Trump, write to him about it. Don’t bore me with the details of your grievance. I’m not associated with Trump in any way.

                    • Ark

                      No, I am not missing the point at all.
                      You have suggested that, to counter allegations of fraud an audit should be done in states where the winning margin for Biden was small enough to warrant suspicion of fraud.
                      This suggests/implies that where the winning margin was considerably larger for either party there was likely no fraud and the result was legit.
                      Trump’s own election team stated it was the most secure election in history.
                      And I reiterate, to date you have produced not one scrap of evidence to support your claim.
                      Let me put it in terms that you may be able to more easily grasp.
                      The bible is riddled with enough errors across almost every major discipline to determine is thoroughly unreliable.
                      We even know that the claims of evidence supporting an historical character named Jesus of Nazareth are so weak to warrant healthy scepticism of his existence at all.
                      If one is of a mind, then under such conditions serious investigation is warranted.
                      But as for an illegally manipulated/fraudulent US election ….
                      well, John, you are going to have to do a lot better than merely cry ”Wolf”, I’m afraid.
                      Your blog. You get the last word.

                    • “you have produced not one scrap of evidence to support your claim”

                      That seems to be one of your favourite jibes. This reminds me of the saying that when the only tool in one’s toolbox is a hammer, every problem starts to look like a nail.

                      I am not making any “claim”. (That is the point you have missed.) I don’t need to produce evidence of anything to make the observations I have, in a context that is none of my making.

                      “an illegally manipulated/fraudulent US election”

                      In particular, I am not making that particular claim.

                      At the cost of repeating myself, the opinion I am expressing can summarised thus:

                    • Ark

                      Again …. at the cost of repetition. Produce evidence that warrants any further enquiry to support that:,”on the balance of PROBABILITIES, that he is the real winner of the presidential election IF AND ONLY IF neutral officials collect the data to prove MATHEMATICALLY that he is the real winner.”

                    • You’ve quoted only part of my tweet, thus destroying completely its meaning. The tweet you misquoted isn’t making a factual claim, so your demand for “evidence” to “support” that tweet is inappropriate. Please stop wasting my time and yours.

                    • Ark

                      You’ve quoted only part of my tweet, etc

                      Actually I omitted only the words ….will be able to prove in court,
                      which does not detract from the meaning of the Tweet in the slightest.
                      And any court will require evidence before rendering judgment and evidence is the one thing that has been absent from every single claim since this whole nonsensical debacle began, which is why the claims have been dismissed.
                      But if you feel you have evidence to demonstrate the veracity of your claims then why not show us your bona fides and offer it here?
                      How hard can that be?

                    • I didn’t write this post in order to make any factual claims, so I don’t need “evidence” to “demonstrate the veracity” of anything. I suggest you find somebody else to argue with, somebody who wants to take the opposite side from yours in whatever argument it is you are so desperate to have.

    • John Droz

      Recounting ballots is simply checking totals. It does not involve seeing whether machine results have been changed. It does not involve seeing whether people voted more than once. It does not involve whether non-citizens or other ineligible voters voted. It does not involve whether a vote was submitted in someone else’s name (e.g. a nursing home patient). It does not involve verifying that the “voter” was actually alive, etc.

      The sampling proposed in this article is certainly an improvement over a basic recount — however it would not catch all of the items I identified above (e.g. machine totals manipulated, duplicate votes, etc.).

      What is needed is an audited recount, especially of locations that are statistically suspicious.

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