Myth, Math and Michigan

Monday’s “Independent” carried this article under the headline:

“Can Donald Trump win the election? Here’s the mathematical reason why it’s impossible for him to become President”

Spot the mistake?

Yes, but apart from that.

It was written by one Bryan Cranston, an online lecturer in politics and PhD candidate at Swinburne University, Australia, because a major British newspaper couldn’t find anyone on the European continent capable of reading a graph such as this one and commenting on it? True, but that’s not what I was getting at.

Give up? OK, try this one: “Here’s the theological reason why it’s impossible for him to become President”
“Here’s the numismatical reason why it’s impossible for him to become President”

Get it now? You can see what’s wrong, because, even though you know nothing about theology or coin collecting, you know what the words mean, just as you know what “mathematical” and “reason” mean.

Lots of journalists and editors can’t do maths, or even math, but one expects them to understand the meaning of words. And if they don’t, and have to hire a PhD student to understand it for them, one hopes they could find one who understands what you can and can’t do with maths (or math.)

Maths can tell you that 49% is bigger than 48% but it can’t tell you who will get 49% and who will get 48%.

Just as maths can tell you that 0.17°C per decade = 1.7°C per century, but it can’t tell you how many feet of water Manhattan will be under, or how many Bangladeshis will be arriving in 2100, or whether there’ll be electricity cuts this winter. Only careful thought by rational human beings can do that.

Anyone out there, in the media or elsewhere, still capable of rational thought?

37 thoughts on “Myth, Math and Michigan

  1. You’d never get heart surgery from a plumber, but hey, why not get psephological advice from the dad off Malcolm in the Middle?
    Bryan Cranston objectively making fun of Donald TrumpImage: Independent mathematical consultant Bryan “Heisenberg” Cranston doing a hilariously objective impression of the President Elect.

    Liked by 3 people

  2. I regret not having kept a collection of similar howlers during the campaign – things that were just wrong on grounds of elementary arithmetic or reasoning. Here’s one from the Guardian this morning:

    “Donald Trump had a 15% chance of winning based on polling predictions – roughly the same chance of rolling a six if you have two dice.”

    ..that’s if you only roll one of them.

    Liked by 1 person

  3. Actually Geoff the chances of rolling a six don’t depend on how many dice you own. I probably have upwards of a dozen (though to be sure, some of them are d8s and d20s from my D&D days) but my rough chances of roughly rolling roughly a six are still roughly 16.666666666666667%.


  4. BRAD
    Quite. That’s why I suggested that you’d have to only roll one. Clearly the journalist didn’t bother distinguishing between how many dice you had and how many you rolled because until today, discussion of probability in the press was largely limited to trivial subjects like the coming climate catastrophe, so such precision wasn’t necessary. Now that we’re faced with something deadly serious like the possibility that opinion polls can be wrong, they’re going to have to clean up their act.

    Liked by 3 people

  5. More damning evidence calling Walter White’s impartiality into question:
    Is this drug dealer teaching your 20-year-old children probability? Probably.Image: Is this unrepentant meth dealer [right] teaching your 20-year-old child probability? Probably, say mathematicians.

    Liked by 1 person

  6. I can’t get Bryan Cranston’s criminal alias—”Heisenberg”—out of my head.

    What effect did the smug pre-election triumphalism of the izquierdist pollsters (but I repeat myself several times) have on the day? It’s hard to believe the answer is “none.” Didn’t they change that which they were observing in the very act of making their pompous observations?

    Dewey. Truman. Has the American sneering class learned nothing from the science of quantum psephology?

    A scarier question is: if the pollsters didn’t exist, would the pollsters have been right?

    Liked by 1 person

  7. Geoff, I don’t understand your complaint…The chance of rolling a (total of) six with two dice is 5/36 ~14%. Close enough to the stated 15%.

    You’re correct that the odds of rolling a six with one die is 1/6~17%, also pretty close to the stated 15%. So if he written “one die”, it wouldn’t have been wrong. But what he wrote is OK.

    Liked by 1 person

  8. Harold, I have to admit it hadn’t even occurred to me to mentally work out the probability of rolling a 1 and a 5 or a 2 and a 4 or a 3 and a 3 or a 4 and a 2 or a 5 and a 1. Would any normal reader have done so? That’s such a bizarre way of communicating odds to the unwashed masses (or even the well-washed readers of pop-pol-sci articles) that if you took all the Olympic-sized swimming pools in the world and laid them back to back, there’d be more chance of two moths colliding with each other in a 125m^3 room than there would be of a hurricane in a used-parts yard spontaneously assembling the works of noted chimpanzee expert Wm Shakespeare.

    To put it another way, why on earth didn’t the author just say “15% chance” and leave it at that? 15% isn’t like anything else, or roughly anything else, or usefully illuminated by comparison with anything else, it’s just 15%.

    Liked by 2 people

  9. HaroldW and Brad
    I don’t want to pursue this for ever. I accept HaroldW’s correction, though I wouldn’t say “roll a six” for “roll (a total of) six.” My apologies.


  10. There doesn’t appear to be much about Michigan in this post, but as a resident, I can say it was a very exciting election, especially when the power went out for about half an hour, shortly after noon.

    Liked by 1 person

  11. The reason I linked to the realclearpolitics poll of polls page was because of an interesting fact that jumps out at anyone who looks at it for ten seconds, but which apparently hadn’t interested any of the thousands of journalists who must have consulted it.

    Since about August just one poll has stood out from the others by forecasting a Trump win – the LA Times/USC tracking poll. This can hardly be dued to a bias on the part of the very liberal LA Times. A simple click reveals that they use a rather original and complicated method, and they courageously remained confident of its value despite being out of sync with dozens of other polls. I must have read scores of articles quoting polls by professional political analysts and such, and not one seemed to have bothered to look into this. The impression one gets from just this one tiny corner of the media machine is a lot of highly skilled experts bent on not finding things out, and then not communicating what they don’t know.
    Does that remind anyone of anything?

    Liked by 3 people

  12. I do think that media/luvvie/foreigner whining has had an effect they didn’t plan for. They essentially insult one side day in, day out and frame what can be discussed or said and then expect to know how the public will react. You may be able to shut people up with satire, mockery, anger and threats but you don’t stop them thinking and in the secrecy of the voting booth, spitting in your eye.

    Incidentally, with all the luvvies who’ll leave the US and the UK, where will they all go where right wingers won’t already be there?

    Liked by 1 person

  13. In many games where one rolls two dice — e.g. Monopoly — “roll a six” (or whatever number) seems very natural to me. This may be idiomatic usage in the US, if it doesn’t sound natural to you.

    And yes, Brad, if the author really intended to talk about a total of 6 on two dice, it *is* a strange choice when one thinks about it. I’ve played enough games, and handle enough probability, that I went there at once. But such a comparison should put the chances into a more common context, easier to have a mental “feel” for, and for those who are not nerds (or craps players), the distribution of the results of rolling two dice doesn’t qualify. The 1-out-of-6 chance for one die might. Hmm…how about the chance of picking an ace or king from a deck of cards? 8/52 ~ 15% 😉

    Liked by 1 person

  14. This is already one of my favourite CliScep threads! Great point originally by Geoff and I consider his follow-up example from the Grauniad to be totally justified, for the reason that Brad states and for the additional reason that HaroldW’s a little bit odd! (But I did appreciate your comment on Climate Audit that both Clinton and Trump are big government people, in justifying voting for a third party candidate in a safe Democrat state.) Above all, the love is in the minutiae. More please.

    Liked by 1 person

  15. Canman,

    Darkness At Noon? What next, Scum Of The Earth? Dialogue With Death? The Gladiators? Roger and Me?


  16. HaroldW,

    I humbly defer to your many years of dissolute living in America’s saloons and Monopoly dens!

    Nevertheless, I still think Geoff’s broader point would have been right had he had the boldness of vision to go this far, which is why I’ll have to reiterate the generalization in his stead:

    Thinking people can only deplore the compulsion of certain pop-sci journalists to “explain” numerical constants by describing them as “like” completely different numerical constants. It’s a worse than meaningless magic ritual, no doubt contrived to baffle the rubes with counterfeit comprehension.

    “His chances of winning Michigan are 15 percent, which, just to give you a feeling for what that means, would be a bit like the probability of a different event whose probability was between 14 and 17 percent, depending on what exactly I meant by it.”

    Gee whizz paw, that cleared that right up!

    Liked by 2 people

  17. If rolling a die/dice is too complicated an analogy, picture instead the NYT’s offering – that 15% was ‘the probability that an NFL kicker misses a 37-yard field goal’. Because YouTube or something.

    (Also worth a look: the NYT’s election opinion page, and not just for Paul Krugman’s ‘blood and soil’ piece.

    Liked by 1 person

  18. Thanks Vinny. I can’t read or write so I had no idea what 15% was, but the NYT’s analogy sheds four Olympic-sized swimming pools of Hiroshimas’ worth of light on the mystery. Suddenly Hindu-Arabic numerals aren’t quite so terrifying. I guess I was just being xenophobic, 9/11 and all.


  19. Brad –
    Yes. I understand the urge by the author to try to put numerical values into context. But “rolling a 6” isn’t going to do that for most people — and for most who do get it, they’re already comfortable with a probability of 15%.

    I’m not sure I can come up with a great example (drawing an ace or king is also not common enough). Maybe say it’s as likely as getting 3 heads in a row — I think a lot of people “get” coin flipping comparisons.


  20. Any game I’ve ever played with two dice, you have to roll two sixes (to start, or win, or whatever.)

    But here’s another example of statistical obfuscation from CNN this week – a journalist saying something like: “She’s two points ahead, which translates as either a 60:40 chance of winning, or maybe 90:10, depending on your point of view…”

    On one level this is insane, because (leaving aside the electoral college business) being ahead means winning – 100%. But we, and the viewers, sort of understand what the journalist meant. Just as we understand what it means to say that something that’s just happened (a hurricane for instance) was made 17.5 times more likely to have happened by global warming.

    Or do we?

    One can imagine a world (the one we live in now, for instance) where every statement uttered would be accompanied by a probability statement (“I’m 95% sure that…” etc.) In this world, saying something wrong accompanied by a 100% certainty would be viewed as a heinous crime, while announcing that you were 50% certain would condemn your views to irrelevance. Most people would probably settle for “I’m 75% certain that..” and that would become a kind of standard exclamation like “You know, like…” Only experts would dare go to 95%
    Welcome to IPCC World, the land of plausible (p≤0.05) denial.

    Liked by 1 person

  21. Off-topic, but I can’t help but think of the greasy, sleazy slope from “97% of scientists are convinced that…” to “scientists are 97% convinced that…”


  22. Ah greasy slopes and scientists… is that like one of those TV game shows where people try to navigate a slippery obstacle course? Is this the point where the big padded arm sweeps them all into the cold water, while the crowd laugh?


  23. Except there’s no water. The trough at the bottom of this ethical snakes-and-ladders board is filled with cold hard cash, it chagrins me to say.


  24. But the “crowd laughing” bit is right. All the way to the bank—where the laughs abruptly stop.


  25. In light of the clear Bryan Cranston angle (and the absence of a clear Michigan angle) in this story, why not change the title to Myth, Math and Meth?

    Liked by 1 person

  26. Pingback: Mythe, maths et Michigan | Mythes, Mancies & Mathématiques

  27. Polls hit the icebergs of polling booths when the official calendar says so. In a functioning republic, you don’t get to postpone that: the date is well defined.

    Climate is never on the official calendar. There is no “free of ice” day on the official calendar. Some people make this rookie mistake, but these are individual errors, and don’t harm the official climate consensus.


  28. “Anyone out there, in the media or elsewhere, still capable of rational thought?”

    More evidence today that the answer to this question is no.
    The Times has got hold of a “leaked memo” saying that 30,000 new civil servants are going to be needed to cope with organising Brexit, or something like that, and that
    Cabinet split threatens to derail May’s Brexit talks.

    This story was unquestioningly promoted across the media, particularly the BBC this morning.

    Nobody seems to have thought to ask where the memo came from. Now it emerges that it was written by a consultancy firm, Deloitte’s.

    Liked by 1 person

  29. Geoff,

    Just as we understand what it means to say that something that’s just happened (a hurricane for instance) was made 17.5 times more likely to have happened by global warming.

    That example seems different from guessing/computing the chances of a Hillary win. The hurricane example can be worked out quite easily from changes in the distribution of multiple real events over the decades. Working out the probability of a single future event when there is no existing distribution to act as guidance is not at all the same (and/or I just have no idea how it is done).


  30. NINO
    I think anthropogenic hurricanes, like Hillary Clinton presidential election victories, probably come under the heading of “future events when there is no existing distribution to act as guidance.” But how would I work out the probability of that being the case? We’re caught in a circular argument powerful enough to blow us right out of Kansas.


  31. Geoff, anthropogenic hurricanes (or any other events) are easy (within the limits of my perhaps questionable understanding). Plot the frequency of hurricanes in, say, 1965-1975, with intensity (x) against frequency (y). You’ll get something like a bell curve. The probability of some rare extreme hurricane intensity x1 (or greater) is given by the area of the tail under the graph to the right of the selected intensity x1.

    To see how much change there has been since that period, plot the same graph but with data for, say, 2005-2015. Again you’ll get a bell curve, but if hurricane intensities have changed it will be shifted rightwards relative to the earlier graph. If the area under the graph to the right of the same x1 intensity is bigger than before, the probability of hurricanes of that intensity or greater has increased. Divide the areas to see by how much.

    Maybe one of the mathematicians can correct me if this is wrong.

    For voting, the same procedure doesn’t seem possible because there is only one event (the 2016 election), not multiple events that can be accumulated to plot a graph.


  32. Note that by ‘easy’, I mean conceptually, not that I could actually do it 😉 Gathering the data would be the biggest challenge I suspect.


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