Scott Adams

Scott Adams Understands Probability

A probability expresses the observed frequency of the occurrence of a well-defined event for a large number of repetitions of the event, where each repetition is independent of the others (i.e., random). Thus the probability that a fair coin will come up heads in, say, 100 tosses is approximately 0.5; that is, it will come up heads approximately 50 percent of the time. (In the penultimate paragraph of this post, I explain why I emphasize approximately.)

If a coin is tossed 100 times, what is the probability that it will come up heads on the 101st toss? There is no probability for that event because it hasn’t occurred yet. The coin will come up heads or tails, and that’s all that can be said about it.

Scott Adams, writing about the probability of being killed by an immigrant, puts it this way:

The idea that we can predict the future based on the past is one of our most persistent illusions. It isn’t rational (for the vast majority of situations) and it doesn’t match our observations. But we think it does.

The big problem is that we have lots of history from which to cherry-pick our predictions about the future. The only reason history repeats is because there is so much of it. Everything that happens today is bound to remind us of something that happened before, simply because lots of stuff happened before, and our minds are drawn to analogies.

…If you can rigorously control the variables of your experiment, you can expect the same outcomes almost every time [emphasis added].

You can expect a given outcome (e.g., heads) to occur approximately 50 percent of the time if you toss a coin a lot of times. But you won’t know the actual frequency (probability) until you measure it; that is, after the fact.

Here’s why. The statement that heads has a probability of 50 percent is a mathematical approximation, given that there are only two possible outcomes of a coin toss: heads or tails. While writing this post I used the RANDBETWEEN function of Excel 2016 to simulate ten 100-toss games of heads or tails, with the following results (number of heads per game): 55, 49, 49, 43, 43, 54, 47, 47, 53, 52. Not a single game yielded exactly 50 heads, and heads came up 492 times (not 500) in 1,000 tosses.

What is the point of a probability statement? What is it good for? It lets you know what to expect over the long run, for a large number of repetitions of a strictly defined event. Change the definition of the event, even slightly, and you can “probably” kiss its probability goodbye.

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Related posts:
Fooled by Non-Randomness
Randomness Is Over-Rated
Beware the Rare Event
Some Thoughts about Probability
My War on the Misuse of Probability
Understanding Probability: Pascal’s Wager and Catastrophic Global Warming

The “Shy Trump Supporter” Hypothesis

Scott Adams — the creator of Dilbert — has some thoughts about the “shy Trump supporter” hypothesis:

For starters, we can say with certainty that they exist…. People feel comfortable telling me privately, and also anonymously online, that they hide their Trump support from their spouse and coworkers. So we know they exist. We just don’t know how many.

We know that sometimes robocall surveys and online surveys show more Trump support than human-to-human polling. So that might be an indicator, but we don’t know what other variables are in play.

…I’m guessing some Shy Trump Supporters “park” their votes with Gary Johnson (polling at 9.3%) or Jill Stein (polling at 3.3%).

But I wonder if the Shy Trump supporters are mostly parked with Johnson because of gender (consciously or unconsciously), whereas Stein is more of a real protest vote against Clinton. Anecdotally, Shy Trump Supporters tell me they do park their pre-vote preferences with Johnson….

Then you also have the question of turnout. Trump is clearly generating the most enthusiasm in public appearances. I would think that translates into more new voters….

I predict that 3% of voters are Shy Trump Supporters. As polls continue to tighten, especially in battleground states, that will be enough for an electoral landslide for Trump.

Here’s my take. It’s unlikely that much of Gary Johnson’s support comes from disaffected Democrats. He’s a fiscal-conservative-small-government-is-best candidate. If there are disaffected Democrats who aren’t yet ready to push the button for Clinton — or who never will be ready — they’re in the Jill Stein camp.

Johnson’s support, which is running around 9 percent, is improbably high for a Libertarian candidate. Johnson got 1 percent of the popular vote in 2012. The only Libertarian candidate to do better was Ed Clark in 1980, with 1.1 percent.

What about “respectable” (non-segregationist) third-party upstarts like John Anderson and Ross Perot, who garnered 7 to 19 percent of the popular vote in the elections of 1980, 1992, and 1996? Well, the Libertarian Party isn’t an upstart. It’s been around since the election of 1976, and has never gained traction. Johnson just isn’t making the waves that Anderson and Perot did.

So I believe that Scott Adams is right. A lot of “shy Trump supporters” are claiming that they’ll vote for Johnson, but most of them will vote — if they do vote — for Trump. My evidence? Trump’s standing in Rasmussen’s poll is strongly (r-squared = 0.6) and negatively correlated with Johnson’s standing. As voters decide that they aren’t going to waste votes on Johnson, they’ll turn (mainly) to Trump.

Does that mean a win for Trump on election day? Not necessarily. I’ve run some numbers on the polling relationships to date. Here’s what they imply:

If Johnson’s popular-vote share slips from its current 9 percent to 3 percent on election day — which is 3 times better than his showing in 2012 — Trump would pick up 3 percentage points. On the other hand, if Stein’s support slips from its current 2 percent to 1 percent on election day — 3 times better than her showing in 2012 — Clinton would pick up 0.7 percentage point. So far, so good, for Trump.

But as the “other-undecided” vote shrinks from its present level of 7 percent to 1 percent (a bit higher than in recent elections), Clinton will pick up 5.5 percentage points while Trump picks up only 1.3 percentage point.

Adding it up, there’s a likely gain for Trump of 4+ percentage points and a likely gain for Clinton of 6+ percentage points. Adding those numbers to Rasmussen’s latest results for Trump (39 percent) and Clinton (43 percent) yields something like 43 or 44 percent for Trump and 49 or 50 percent for Clinton.

That’s consistent with the results of another method. Based on trends to date, if Trump and Clinton take 95 percent of the total popular vote (leaving 3 percent for Johnson, 1 percent for Stein, and 1 percent for “other”), Clinton will get 50 percent of the total,  as against 45 percent for Trump. Clinton’s margin of 5 percent exceeds the 3-percent margin of error in Rasmussen’s polling. With 52 or 53 percent of the two-party popular vote (50 percent divided by 95 percent), Clinton would win at least 60 percent of the electoral vote. (In 2012, Obama won 62 percent of  the electoral vote with 52 percent of the two-party popular vote.) So it’s looking good for Clinton.

All of this is predicated on trends over the past several months.  Those trends might continue, allowing Clinton to “run out the clock.” But a major event could change everything. For example, Clinton might have a stroke, Assange might reveal truly damning e-mails, Trump might demolish Clinton in the debates, etc. Those are the “known unknowns.” It’s impossible to list the “unknown unknowns” — but they’re out there.

As I’ve said before, the only thing worse than a Trump victory would be a Clinton victory. There’s a chance that Trump would nominate constitutionalists to the Supreme Court; there’s no chance that Clinton would  do so.