Bryan Caplan  

Converting Ordinary Language to Probabilities: CIA Edition

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Interesting email from Todd Proebsting, reprinted with his permission.


Dear Prof. Caplan,

Your recent attempt at a wager on Iran's nuclear progress, and the subsequent exchange with the author about why you wanted 10:1 odds reminded me that the CIA tried to quantify what certain claims meant:

100% Certainty

The General Area of Possibility

93%

give or take about 6%

Almost certain

75%

give or take about 12%

Probable

50%

give or take about 10%

Chances about even

30%

give or take about 10%

Probably not

7%

give or take about 5%

Almost certainly not

0% Impossibility

 

It's from a 50-year old CIA proposal.

 

It's interesting to me that "Almost certain" was only 93%.  I think the CIA would have argued that you should have been asking for even longer odds given the original claim.

Cheers, Todd Proebsting


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COMMENTS (11 to date)
Sam writes:

Bizarre that the language is asymmetric about 50%. Is there some prospect-theory justification for that?

Adam writes:

Or there's the IPCC (TS, box TS1) typology:

Virtually certain: 99–100% probability
Very likely: 90–100% probability
Likely: 66–100% probability
About as likely as not: 33–66% probability
Unlikely: 0–33% probability
Very unlikely: 0–10% probability
Exceptionally unlikely: 0–1% probability

Tom West writes:

I remember having a long debate with my wife about this early in our marriage.

It took a while to understand that we weren't using the terms the same way:

"Absolutely certain" me: 90% her: 100%
"Very certain" me: 80% her: 100%
"Pretty certain" me: 70% her: 98%
"Fairly certain" me: 60% her: 95%
"I think so" me: 25% her: 90%

Eventually, I just started using actually percentages. As for her, if she's willing to venture an opinion, then she's right (with exceptions countable on one hand in 25 years).

Al writes:

It's interesting to me that the CIA define "Probable" as approx. 75%, but "Probably Not" as approx. 30%.

The definitions are not balanced between events which are likely and other events which are equally unlikely.

There are also a few grey areas, most notably events with probability of approx. 12% to 20% have no suitable description under this proposal.

There appears to be a considerable amount of discretion involved.

Examples:

1. Using these definitions an event with probability 39% would be described as "Probably Not", but an event with probability 61% wouldn't be described as "Probable" (it's in a grey area between "Chances about even" and "Probable").

2. An event with 85% probability would be described as "Probable", but one with a 15% probability would fall in the large grey area between "Almost Certainly Not" and "Probably Not".

Al writes:

Adam: At least the IPCC definitions are symmetrical about 50%. I don't much care for their incredibly wide "About as likely as not band" which ranges from 33% to 66% though. 66% is about twice as likely as not.

Richard writes:

I think that it depends on what you're talking about. If I say "I'm absolutely sure that she has a crush on you," it probably means about 90%, since I think that's about the maximum level of certainty you can have about something like that. If I say "I'm absolutely certain that the sun will come up tomorrow," it's more like 99.999999999%, since we can be that certain about physical phenomena.

Ken P writes:

Like Al, I have a problem with the lack of symmetry between probably and probably not. It's like nails on a chalkboard.

It sounds like Watson would be answering only when almost certain.

Dick White writes:

Can someone refer me to a pithy essay on how one concludes, for example, that a given outcome is, say, 63%-87% likely (Probable)?

D. F. Linton writes:

Pretending that you can estimate a numerical probability for future events that will either occur or not occur once is at best a rhetorical device and at worst gross self-delusionary scientism. You can estimate odds for a bet or weigh whether given odds are favorable or unfavorable given your present knowledge and preferences. But such polls will vary from person to person; otherwise you would take the other side of bets? Frequentist considerations aside, how can the truth or falsity of such statements even be proven?
If I say there is a 83% chance that some event will occur tomorrow and it happens I say see! If it doesn't happen then we just experienced a 17% probability event.

_NL writes:

Tax opinions have similar methods of converting confidence levels expressed as phrases into numerical percentages, and here is one common interpretation:

“Will” opinion: 90-95% probability of position being sustained.

“Should” opinion: 70% to 75% probability of position being sustained.

“More likely than not” opinion: More than 50% probability of position being sustained.

“Substantial authority” opinion: Less than “more likely than not” but greater than “reasonable basis” (34% to 40% likelihood)

Realistic possibility of being sustained on its merits: One-in-three possibility (33%)

“Reasonable basis” opinion: Higher than “not frivolous” but lower than “substantial authority” (20-30%)

Not Frivolous: Lowest level at which there is some modicum of comfort as to a position.

These aren't exact, and the percentage level assigned will vary across situations and has varied over time. Some practitioner interpretations treat "reasonable basis" as 1 in 3 while reducing "should" to 60% chance.
Joe Topp writes:

The CIA, where even the error bars have error bars.

(e.g. give or take about 10%)

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