A Question of Volume

[bonavada]

an interesting article today on the BBC's "The One Show" (http://www.bbc.co.uk/theoneshow/article/2007/08/mm_crowds.shtml)
it centered on the theory that when you poll enough people to guess at something (ie a persons weight, height etc) the average of their guesses will be remarkably accurate. a successful demonstration of the theory was shown on the programme (see link above) with 100+ people guessing the weight of a cake and the answers averaged out to be 99% correct. they are also running another poll at the site to guess the number of £1 coins in a jar. as seen here:-

http://forums.randi.org/imagehosting/874846b8e042065cc.jpg

anybody fancy a guess at this? btw a british pound coin is about 22 mm diameter and about 3 mm thick............
i know the volume of a cylinder is pi x r^2 x h but the question is harder because you aren't given the exact dimensions of the jar and due to its tapered shape.

BV

[Ziggurat]

anybody fancy a guess at this?

1200. Are you going to reveal the real answer sometime?

[TTLer]

Good OP; I've put a lot of thought into this myself. Here's what I think:

Of course, the "law of averages" is firstly responsible. Some people will 'overjudge' and some will 'underjudge,' so indeed a large enough sampling will iron out differences into more mean accuracy - especially for such things as a person's height or the weight of a cake, which most people can judge fairly well within the ballpark already.

Then, into the formula goes what I'd call "gravitating interest of skilled participants" (also applies to many other public participation concepts). Bakers, or people who eat lots of cake, are extremely likely to include themselves in a cake-guessing game. People who figure themselves a good judge of height will certainly assert themselves to join a guessing game of people's height.

Finally, factor in a few geniuses - very high IQ people who are simply good at anything they apply their brain power to - and the average of total guesses will indeed hover closely around the correct, exact figure.

[bonavada]

1200. Are you going to reveal the real answer sometime?

the programme was aired only yesterday, the poll is still ongoing at the site in the OP. the answer will be revealed there.
we seem to be on the same wavelength regarding our guesses though. i entered 1229...
i guessed at the size of that jar to be about 2.5 million mm^3 and the coins each about 1700 mm^3 and then estimated the empty space in between some of the coins.

factor in a few geniuses - very high IQ people who are simply good at anything they apply their brain power to

as if to prove your point they mentioned an example on the show where an aircraft was lost at sea and a number of experts were consulted. when their estimations of it's crash site were averaged out the answer pinpointed it to within 200 yards.
i am trying not to read too much into it but i think, if anything, the whole thing shows the inate basic intelligence of humans as a species. as a group at least sometimes we can come to an accurate decision.

BV

[Gord_in_Toronto]

I think this was a quite popular approach with management sometime ago. Let me Google "delphic principle" -- nope that's not it. Anybody?

[JoeEllison]

One of the things that I find interesting about this is that people have tried to incorrectly extend this little anomaly into areas like politics, claiming that whichever viewpoint is most supported MUST BE close to correct.

[fuelair]

I think this was a quite popular approach with management sometime ago. Let me Google "delphic principle" -- nope that's not it. Anybody?

I dogpiled "group guess averages correct" to get http://www.randomhouse.com/anchor/catalog/display.pperl?isbn=9780385721707&view=excerpt

a book on the topic. Saw no management form name on site though.

[Molinaro]

642 coins.

[JoeTheJuggler]

I think that's also true when you hear 20,000 or so people singing along at a pop concert. Some people sing a little off one way or the other, and some people start in too early or too late, but when you hear the entire hall, like what you hear on a live album for example, sounds pretty spot on.

[casebro]

I think you are both low. I'll say 1350.

[Ladewig]

I think this was a quite popular approach with management sometime ago. Let me Google "delphic principle" -- nope that's not it. Anybody?

I thought that the Delphi Technique involved everyone producing individual estimates before sharing all the numbers. A second estimate is then made based on a viewing of the numbers.

[Ladewig]

Good OP; I've put a lot of thought into this myself. Here's what I think:

Finally, factor in a few geniuses - very high IQ people who are simply good at anything they apply their brain power to - and the average of total guesses will indeed hover closely around the correct, exact figure.

I am hesitant to include this factor in an analysis of how the technique works. The type of genius that you describe will be a very, very small fraction of all the people involved. If you removed all the people with IQs above the 96th percentile, you could probably still produce a pretty accurate estimate.

[TTLer]

I am hesitant to include this [genius] factor in an analysis of how the technique works. The type of genius that you describe will be a very, very small fraction of all the people involved. If you removed all the people with IQs above the 96th percentile, you could probably still produce a pretty accurate estimate.

Fair enough, Ladewig, I may be guilty of adding my own subjective experience in item #3: genius guesses.

When I was 19, I was robbed at knifepoint while working the counter at 7-11. The police officer who took my report asked me to guess his own height and weight, by way of considering how accurate I was at judging such things about the robber. I guessed his exact height, and his weight within 5 pounds. He seemed duly impressed by my height guess, but he was astounded I got his weight so close - he was wearing a bulletproof vest, which he said usually makes most people guess heavier.

What can I say - I'm really good at perceiving height and weight, and other quantitative guesses - I figure there's many more people out there like me!

[lionking]

1500 for me. Don't know why, but can't avoid a contest.

[cloudshipsrule]

897

[Cuddles]

I think that's also true when you hear 20,000 or so people singing along at a pop concert. Some people sing a little off one way or the other, and some people start in too early or too late, but when you hear the entire hall, like what you hear on a live album for example, sounds pretty spot on.

I take it you're not a musician? Large groups of people singing almost always sound absolutely terrible because many, if not most, will be out of tune. Taking the mean of all the pitches might give the right pitch, but that isn't what you hear so it isn't really relevant.

742

[brodski]

One of the things that I find interesting about this is that people have tried to incorrectly extend this little anomaly into areas like politics, claiming that whichever viewpoint is most supported MUST BE close to correct.

How do you objectively determine when a political viewpoint is incorrect?

[bonavada]

One of the things that I find interesting about this is that people have tried to incorrectly extend this little anomaly into areas like politics, claiming that whichever viewpoint is most supported MUST BE close to correct.

must admit that i considered similar applications. ie gambling. but of course if you go into a bookies it's allready done for you. just looking at the sp for a horse race will tell you straight away what nag people think will win.......
this process will only be worthwhile when people are guessing at an exact measure. millions of people "guess" every week at what the lotto results will be and relatively very few are fully correct. sadly, so far, i am not one of the few.
btw the orginal feature in the bbc programme was a book plug for

"the wisdom of crowds" (http://www.amazon.co.uk/Wisdom-Crowds-Many-Smarter-Than/dp/0349116059/ref=pd_bbs_sr_1/203-2759138-1899153?ie=UTF8&s=books&qid=1186567858&sr=8-1)

you can read more at that link.

BV

[666]

I was almost tempted to start a thread on this myself. There's more info on the theory here: The_Wisdom_of_Crowds
On review, I see bonavada also supplied a good link.

I do miss the lovely Myleene, though. :drool:

[Ivor the Engineer]

1000

[Deetee]

Unfortunately we cannot recreate the experiment here, as our guesses have been visible to others before they make their own guess, and that will influence what they pick.
So what could have been an interesting exercise will fail because of lack of proper controls.

I think it's 685

[SomeGuy]

812

[JoeEllison]

103

[Myriad]

I guess that there are negative 137,000,000,000 coins in the glass.

So much for the average of everyone's guesses being close to accurate!

Unless, of course, I arrived at that guess because I intuitively sense that everyone else's guesses are trending high...

Respectfully,
Myriad

[Ladewig]

1120

[geoman]

I think there are positive 137,000,001,000 coins in the glass.

[tsg]

How do you objectively determine when a political viewpoint is incorrect?

It's one the government agrees with.

[slyjoe]

I think this was a quite popular approach with management sometime ago. Let me Google "delphic principle" -- nope that's not it. Anybody?

Generally, this is a prediction market. http://en.wikipedia.org/wiki/Prediction_market

In Engineering, a Delphic principle is where you get an estimate by going to an expert (the "oracle") instead of doing an analysis on your own. Based on the experts qualifications, it is assumed his estimate is better than yours.

[Michael Redman]

2000

(doing math is cheating.)

I guess that there are negative 137,000,000,000 coins in the glass.

So much for the average of everyone's guesses being close to accurate!

Unless, of course, I arrived at that guess because I intuitively sense that everyone else's guesses are trending high...

Respectfully,
Myriad

I'm going to go out on a limb and say this probably works when you average "guesses", not "numbers thrown in for the purpose of spoiling the results".

[bonavada]

from the BBC site (http://www.bbc.co.uk/theoneshow/article/2007/08/mm_crowds.shtml):-


1760 of you made a guess - and the average came out at 982 pound coins - making you 88.83% accurate. Not bad... oh, and the correct amount of pound coins is 1,111.


so well done Ladewig ..........only 9 out.
here's our ( uncontrolled :-] ) totals
1200
1229
642
1350
1500
897
742
1000
685
103
-137000000000 :-]
1120
137,000,001,000 :-]
2000
haven't got time to tally our average. got to go out. but i'm betting it's roughly the same..........

BV

[blutoski]

btw the orginal feature in the bbc programme was a book plug for

"the wisdom of crowds" (http://www.amazon.co.uk/Wisdom-Crowds-Many-Smarter-Than/dp/0349116059/ref=pd_bbs_sr_1/203-2759138-1899153?ie=UTF8&s=books&qid=1186567858&sr=8-1)


A good book, because it delves into a very skeptical topic: the value of experts in certain situations, and also a review of common reasoning errors.

It should be noted that the author also dedicates a great deal of the book to situations where collective estimates are reliably wrong.

I'd be curious to see the estimates for a prediction market on, say, the price of oil, in comparison to actual outcomes.

[insomneac]

700

[rockoon]

I demand a recount

[Cuddles]

I guess that there are negative 137,000,000,000 coins in the glass.

I think there are positive 137,000,001,000 coins in the glass.

By my count that makes the average 0. Since the average is usually correct, this means I can steal all the coins and no-one will notice.

Edit: The above would be true if geoman had typed what I read and not what is actually written there. It's a conspiracy I tell you.