Updated from: Live from Over the Rocky Mountains: I see that the War on Nate Silver has broken out again, with another article less appetizing than bilgewater in The New York Times, written by Jim Rutenberg:
Still more recently--as in Tuesday--the data journalist Nate Silver... gave Hillary Clinton a 90 percent chance of beating Bernie Sanders in Indiana. Mr. Sanders won by a comfortable margin of about five percentage points.... The lesson [from Eric Cantor's defeat] in Virginia, as the Washington Post reporter Paul Farhi wrote at the time, was that nothing exceeds the value of shoe-leather reporting, given that politics is an essentially human endeavor and therefore can defy prediction and reason...
Nate has his comment: Nate Silver Being Smart and Bringing the Snark: "Do You Know What 'Polling' Is? It's Talking to Voters in a Structured Way to Reduce Bias"
And Justin Wolfers says:
But I do not feel today like talking about the anti-empirical reporters--horse-race journamalists who try to avoid learning about horses, tracks, or jockeys--with their alternative methodology of source-flattering. I'm bored with their false and repeatedly disproven claims to magical expertise via choosing and flattering particular sources.
It's more fun to go back into serious and interesting thoughts about chance, uncertainty, and understanding. I will put my reading list for this at the bottom. And, meanwhile, this is what I now think:
You are seated outside at a table in the muggy, unpleasant weather of the lower Missouri River Valley in between the torrential thunder- and hail-storms that come through. You are grading your 3000 pages of Econ 1 exams that you transported here in a suitcase. A Trumpeter Swan--better make it a Black Trumpeter Swan--swims over to the bank, and waddles up:
Black Trumpeter Swan: Declare unto me: What is your maximum willingness-to-pay for a security that pays off $1 in the state of the world in which, as of the Wednesday morning following election day, Hillary Rodham Clinton is by consensus projected to receive 270 electoral votes?
Me: Uh uh. If I name a number that you think is greater than the true probability, you will then wander off. If I name a number that you believe is less than the true probability you will demand that I put my money where my mouth is--and I will either suffer reputational harm as a bloviater who will not back his opinions, or find that I have just made a negative net present value bet.
Black Trumpeter Swan: But I know no more about the election than you do! I am as likely to be wrong as right in my assessment of whether your number is above or below the true probability! It's a 50-50 bet.
Me: That is simply not true. Until a minute ago I had no knowledge that the world contained talking Black Trumpeter Swans. Your information set is therefore certainly larger than mine--and so your probability forecasts are almost surely better-informed than mine. The symmetry you appeal to simply does not exist.
Black Trumpeter Swan: That's not fair! I'm just a transparent rhetorical device!
Me: The point stands. When the situation is rife with uncertainty of any kind--when we are not playing with my own well-tested dice--any mind I bet against may well have more information and a better forecast than I do. Cf. Grossman-Stiglitz. A situation in which talking Black Trumpeter Swans waddle out of the Missouri River is one in which my information set is highly likely to be inferior--in which my Visualization of the Cosmic All is badly flawed. In such a situation I should by a good Bayesian and revise my expectations thus: my rational Bayesian-updated estimate of the HRC probability is that number at which you are no longer willing to accept the bet. So I ask you: At what number are you indifferent?
Black Trumpeter Swan: $0.70.
Me: And is that statement truthful?
Black Trumpeter Swan: Yes.
Me: And is that statement truthful?
Black Trumpeter Swan: I'm going to go eat water plants unless you stipulate that you are 100% certain that Black Trumpeter Swans functioning as transparent rhetorical devices never lie, or mislead.
Black Trumpeter Swan: Well?
Me: "Well?" what?
Black Trumpeter Swan: The answer to my question?
Me: $0.70. You are a better judge of these matters than I am...
A Missouri Riverboat steams up from the direction of St. Louis. It stops, and a group of Vulcans unload a Star Trek transporter booth. The Black Trumpeter gestures at the booth with a wing.
Black Trumpeter Swan: As you may have guessed, we are actually highly-intelligent aliens. Our transporters carry us not just through space but through time as well. I am about to visit election-day morning this forthcoming November, just before the polls open. I will there and then inform myself of the true probability of an HRC victory as of dawn on election day.
Me: Are you sure you will not go to any time later than that Tuesday morning in November, or receive any information, directly or indirectly or through any chain of intermediaries, from any entity that has been or will go to any time later than that Tuesday morning in November?
Black Trumpeter Swan: I am certain: my information set when I return such as to give me the true knowledge of the true probability as of dawn on election day.
Black Trumpeter Swan: Will your offer to pay me $0.70 for a $1.00 HRC security still open when I come back, in a minute?
Me: NO!! Of course not. Over the next six months our information about the HRC-victory probability will approve, and our estimate of that probability will either go up or go down.
Black Trumpeter Swan: But there is a sum of money that I could pay you now to agree to hold the bet open, yes?
Me: Not clear. Your information set as of the true value right now of the call option to buy HRC at $0.70 at dawn on election day is more comprehensive than mine...
The Black Trumpeter Swan gestures at the transporter booth. It shimmers. I appear in the booth.
Black Trumpeter Swan: This is an exact copy of you as of the instant you said "more comprehensive than mine..." His information set is exactly yours. He is about to go through to election morning, inform himself, and then come back. What price would he have to pay you to get you to hold the bet open?
Me: Ah. I see. You want to identify the generally-accepted probability at which people are making bets at dawn on election day with the true probability, and identify the spread between the value of an HRC-contract today and the value of a call at that price that expires at dawn on election morning with the current uncertainty about the true probability.
Black Trumpeter Swan: Exactly: if we were going to roll your own well-tested and well-understood dice on election day, that call value would be zero because the value of the underlying would not drift either up or down between now and dawn on election day: it would stay at $0.70.
Me II: But we are not rolling my--his--own well-tested and well-understood dice now, are we?
Black Trumpeter Swan: And it is in recognizing that that call option has a value that a Bayesian can express his or her recognition that although his current estimate of the probability of an HRC victory is sharp--that he or she is willing to buy below $0.70 and sell above $0.70 to an equally well-informed counterparty--that current estimate is also uncertain.
Cosma Shalizi: Haven't you just constructed an enormous and pointless intellectual apparatus involving, in increasing order of implausibility, speaking intelligent aquatic waterfowl, options pricing, Vulcans, teleportation, Bayesianism, and time-travel just in order to be able to say the obvious thing: "The probability of an HRC victory is uncertain: it might be as low as 0.45 or as high as 0.95, and we will be able to sharpen our estimate as election day comes closer"?
Sam Wang: Historically from 1952 to 2012, the likely range of movement in two-candidate margin from this time until Election Day has been 10 percentage points, which is the standard deviation from the 16 past elections. Therefore, even though Clinton currently leads by a median margin of 7 percent (12 national surveys) and would certainly win an election held today, she could still lose the lead, and from a purely poll-based standpoint, is only narrowly favored to be elected President in November (probability: 70%).... Her ‘plus-one-sigma’ outcome (current polls plus one standard deviation) is a popular vote win of 58.5%-41.5%. Trump’s plus-one-sigma outcome is a narrower win, 51.5%-48.5%.... The last four elections, from 2000 to 2012, have been far less variable... a standard deviation of 4 percentage points. These have been polarized years.... Considering the upheaval in the Republican Party, a little voice tells me to open my mind to a wider range of possibilities...
- Elementary Philosophy of Probability and the War on Nate Silver: The (Not Very) Honest Broker for the Week of August 2, 2014
- Tuesday Virtual Office Hours: Follow-Up Questions on the Philosophy of Probability: Live from Cafe Milano CCXXXIII: August 5, 2014
- Tykhe's Nonexistent Urn and Senate Election Probabilities: Over at Equitable Growth: Philosophy of Probability III: the Philosophizing: Tuesday Focus for August 26, 2014
- Live from Over the Rocky Mountains: I see that the War on Nate Silver has broken out again, with another article less appetizing than bilgewater in The New York Times, this one written by Jim Rutenberg...
- An Ear Full of Cider... :
- Adam Elga (2010): Subjective Probabilities Should Be Sharp
- On the Certainty of the Bayesian Fortune-Teller (2009):
- Praxis and Ideology in Bayesian Data Analysis :
- Philosophy and the practice of Bayesian statistics :
Read everything? Good! What did you think?