What is the 2/3 the Average Experiment and How Can You Help?

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In summary, the goal of this experiment is to see how many people choose a number that is not an integer, and to see how people's choices change depending on the math level chosen.
  • #1
mathematicsma
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2
I apologize if I'm posting this in wrong place.

I am the President of my college's math club, TCMC (www.touromathclub.org[/URL]).

We are running an experiment called 2/3 the average, but the results only become meaningful once there are many submissions. So we need your help.

Filling out the form takes only a few minutes, is free, and helps advance mathematics/economics/whatever field you want to call it. You don't have to part with any personal information if you don't want to. The link is below, thanks for your help.

[PLAIN]http://www.touromathclub.org/math-puzzles/2-3-the-average [Broken]
 
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  • #2
mathematicsma said:
I apologize if I'm posting this in wrong place.

I am the President of my college's math club, TCMC (www.touromathclub.org[/URL]).

We are running an experiment called 2/3 the average, but the results only become meaningful once there are many submissions. So we need your help.

Filling out the form takes only a few minutes, is free, and helps advance mathematics/economics/whatever field you want to call it. You don't have to part with any personal information if you don't want to. The link is below, thanks for your help.

[PLAIN]http://www.touromathclub.org/math-puzzles/2-3-the-average [Broken]

I used my PF username "berkeman". Seems harmless enough.
 
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  • #3
I expect most people will use pseudonyms. That's what I'd do, too. In any case, thanks for submitting your number. We'll probably run it for about two weeks, then tally the results and see how things come out.
 
  • #4
Should we, or not, discuss the strategy we used to pick our number here?
 
  • #5
This reminds me of the recursive polls we had here a year or so ago :biggrin:
 
  • #6
Hepth said:
Should we, or not, discuss the strategy we used to pick our number here?
Perhaps we should wait until the experiment is finished? I guess it's pretty much up to mathematicsma. Or we could set up a separate thread to discuss our strategies, and rely on the honor system for people to participate in the experiment before reading the strategies thread?
 
  • #7
I have no problem with people discussing strategy here. I figure that however people choose their answers, there will be a variety of ideas, and I'd like to hear discussion. Let's see how things turn out. I just request that the actual numbers remain private.

I'll start: I was the first person to choose a number, so my choice was not biased by the fact that I happen to have access to the results in real time. I also had no idea how many people would answer, and what kinds of people those people would be. The way I see it is this:

If everyone was completely rational, and everyone knew that everyone else is completely rational, then the number would obviously be driven down to the lowest possible choice, which is zero in this case. If that happens, everyone wins, because 2/3 of 0 is 0.

But of course, we're not all rational. Some people will find the whole thing too confusing, and just pick a number. If even one person picks a number above zero, the whole thing is thrown off. Which makes for another problem: How do you second guess other people's intelligence? And how do you figure in all the people who are figuring in everyone else's intelligence, and the people who are figuring in the figurers, so to speak, ad infinitum? (Kind of reminds me of an old Dr. Seuss I grew up with: there's a fellow watching a bee, and someone else watching him, and a watcher for the watcher for the watcher for the bee watcher...)

I honestly don't know. How many people around me are stupid? How many really smart? And many will get so confused by the whole figuring thing that they won't know what to do? (That's me.) I took what I consider a fairly decent guess, but I have to admit that it's not based on anything really good.

Anyway, that's how I view the challenge. Tell me how you see it.


Note: It's important to remember that people who hang out on a forum dedicated to physics tend to be a different pool of people than the average population.
 
  • #8
I filled it out, but noticed a glitch (or deliberate lock-out?) that messed it up for me. I was unable to change the entry that set the math level at "not past high-school''. My math education ended a couple of months into grade 10.
 
  • #9
Mathematicsma: is your experiment advertised in other venues (forum, media, etc.)? You might get different distributions depending on the venue. Also, even though rationality is taken as an axiom, I've long suspected that real people switch between being "rational" and "irrational" depending on the time of the day or day of the week, etc.
 
  • #10
Judging from the pie-charts, it looks like the contest has had 30 respondents at this point. Or some multiple of 30.
 
  • #11
I imagine that you are correct, no human being is either completely rational or completely irrational. I'm not even sure how to define rationality objectively, I'm influenced by my own sense of rationality. (I've never hear anyone admit that they were irrational.)

That said, I imagine some people spend more time on the rational end of the spectrum than other people do.

Anyway, thanks to all those who've replied so far. We appreciate it.

The experiment has gotten off to a slow start, I do need to try to get it advertised in more places. I will say this: I just took a look at the data, and there are two possibilities: either people are just messing with the numbers/info for fun, or in some cases, level of education and ability to think rationally are not correlated. I kind of hope the first is the case.

By the way, a date is not a legitimate number. It will be deleted, not treated as 1/3/2011=0.000165755014.
 
  • #12
Thanks to all those who've replied so far. We appreciate it.
 
  • #13
mathematicsma said:
I just took a look at the data, and there are two possibilities: either people are just messing with the numbers/info for fun, or in some cases, level of education and ability to think rationally are not correlated. I kind of hope the first is the case.

By the way, a date is not a legitimate number. It will be deleted, not treated as 1/3/2011=0.000165755014.

I thought we were supposed to pick a whole number between 1 and 100. Did I misread the question?
 
  • #14
We're supposed to choose a number between 0 and 100, inclusive. So 0 is acceptable. I had assumed we are to choose an integer, but now realize that was not specified in the instructions.
 
  • #15
mathematicsma said:
I imagine that you are correct, no human being is either completely rational or completely irrational. I'm not even sure how to define rationality objectively, I'm influenced by my own sense of rationality. (I've never hear anyone admit that they were irrational.)

I would estimate that 99.999999% of humans are mostly irrational. For one thing, in a more primitive world, it's the irrational quick reactions that make the difference between living and dying, so the irrational always dominates with a person consciously having to make an effort to apply rational logic to a situtation.

Regardless, this is a strategy game where rational thought should outweigh irrational thought, but not so much so that everyone will pick zero. It's just tough to weigh where on the scale to guess when even rational guessers are trying to guess how many irrational guessers are guessing.

Considering most of the responses so far have been by PF members and considering the poll conducted a couple of years ago about whether PF members respond to polls and how often, I'm pretty certain my guess was spot on.

Being a rational person doesn't mean the person isn't strange.
 
  • #16
I picked zero.

If people so far voted 0, current person votes 100, the person following will try to aim for 2/3 of the new mean. So, mean will approximately settle down to 0 eventually. Anything below 10 looks good to me.
 
  • #17
I tried to pick 38 but as I clicked enter I saw I had picked 83 :redface:
 
  • #18
mathematicsma said:
I imagine that you are correct, no human being is either completely rational or completely irrational. I'm not even sure how to define rationality objectively

randomness?
 
  • #19
mathematicsma said:
I have no problem with people discussing strategy here. I figure that however people choose their answers, there will be a variety of ideas, and I'd like to hear discussion. Let's see how things turn out. I just request that the actual numbers remain private.

rootX said:
I picked zero.

If people so far voted 0, current person votes 100, the person following will try to aim for 2/3 of the new mean. So, mean will approximately settle down to 0 eventually. Anything below 10 looks good to me.

lisab said:
I tried to pick 38 but as I clicked enter I saw I had picked 83 :redface:

A couple of the responses give me great confidence in my choice. :rofl:

Plus how the "Do you answer polls?" poll turned out: https://www.physicsforums.com/showthread.php?t=68084
Since 32% of PF members never respond to polls, I think your results might get skewed (and I'm absolutely positive all members answered truthfully).
 
  • #20
BobG said:
A couple of the responses give me great confidence in my choice. :rofl:

Plus how the "Do you answer polls?" poll turned out: https://www.physicsforums.com/showthread.php?t=68084
Since 32% of PF members never respond to polls, I think your results might get skewed (and I'm absolutely positive all members answered truthfully).

Oops, I gave my number and i wasn't supposed to! Sorry, mathematicsma. I think I'll stop coming to this thread, every time I do I screw something up.

Maybe we should have a poll, Do you read and follow directions?
 
  • #21
rootX said:
I picked zero.

If people so far voted 0, current person votes 100, the person following will try to aim for 2/3 of the new mean. So, mean will approximately settle down to 0 eventually. Anything below 10 looks good to me.

I wonder what the total sample size will be though.
 
  • #22
BobG said:
A couple of the responses give me great confidence in my choice. :rofl:

Yes, but there may be a self-selecting group of people that announce their answers. I'm not sure they're representative of the rest of us.:rofl:

I also assumed that we were supposed to choose an integer between 0 and 100, inclusive. Turns out I didn't specify it in the instructions, so I guess it doesn't matter. But the person who submitted a date is disqualified. I'll assume it was a mistake. (And the 83 has been duly changed to 38. I got nervous there, you know.)
 
  • #23
mathematicsma said:
Yes, but there may be a self-selecting group of people that announce their answers. I'm not sure they're representative of the rest of us.:rofl:

I also assumed that we were supposed to choose an integer between 0 and 100, inclusive. Turns out I didn't specify it in the instructions, so I guess it doesn't matter. But the person who submitted a date is disqualified. I'll assume it was a mistake. (And the 83 has been duly changed to 38. I got nervous there, you know.)

Whew, thanks :smile:!
 
  • #24
mathematicsma said:
By the way, a date is not a legitimate number. It will be deleted, not treated as 1/3/2011=0.000165755014.
How about a fraction, say 1/9?
 
  • #25
mathematicsma said:
I have no problem with people discussing strategy here. I figure that however people choose their answers, there will be a variety of ideas, and I'd like to hear discussion. Let's see how things turn out. I just request that the actual numbers remain private.

The question is, would the mean be 50 if the directions were simply to pick a number between 0 and 100, with no other instructions? I think not, because a substantial number of people tend to choose their birthday. For that subset of people, the mean would be 15. For those who choose the month they were born, the mean would be 6, and for those who chose the year they were born, the mean would probably be somewhere around 75 to 80.

Then there will be the crowd who chooses 50 simply because they didn't catch the fact that the winner will be the person who guesses closest to 2/3 of the mean. Obviously, this rule will drive down the guesses, but the question is, how far? I predict most people will choose 15, as that's about three levels down, but I could be wrong. Factoring in those who didn't read the directions brings the winning number up to about 26, I think.

Please share the actual results when they're in - thanks!
 
  • #26
EnumaElish said:
How about a fraction, say 1/9?

Fractions are legitimate. But it strikes me as remarkable that people are that confident in their choices that they need such precision.

I think most people think about whether it'll be in the range of, say, 15, or in the area of 35. Not whether it'll be 15 or 15.375.

If there some kind of analysis that can lead to such precise numbers, please share it with me. Personally, I just took a stab at a general area.

Mugaliens, do people really choose their birthday? I guess it's possible. I figured that there are only three kinds of people: a) those who don't understand the question, and guess something like 95 because they think it's a cool number, or can't be bothered to turn their brains on, b)those who just assume that everyone is as rational as them, and pick zero, and c)those who try to figure out how many people are in the first group, how many in the second group, and how many are in their own group.

I suppose that the birthday idea does shift things, though. We'll see.
 
  • #27
mathematicsma said:
If there some kind of analysis that can lead to such precise numbers, please share it with me. Personally, I just took a stab at a general area.

I picked a number with two decimal places, but not because of a precise calculation. I figured a lot of people would pick integers. I guess it would make more sense if there was an actual prize that would be split between people who tie, since then winning by picking an integer will result in a much smaller prize. But since some people know other people will pick integers, they can ruin other people's chances by picking a number like 15.01 so they will have the prize to themselves if the winning number is almost anywhere between 15 and 16. Picking a non-integer seems safer.
 
  • #28
Interesting thought. Oh well, there's no prize. Other than the ability to pat yourself on the back and convince yourself you're a genius.

Then, since you're so darn good at anticipating the behavior of others, become a day trader on the stock markets, or trade currency options, or something like that. Then you get to find out how good you really are. :biggrin:

We couldn't offer a prize, seeing as there isn't really any control system in place to keep people from rigging the system (multiple entries, etc.) So it's just for fun, and we assume most people aren't bored enough to actually manipulate the results on purpose.
 
  • #29
Mathematicsma said:
Fractions are legitimate. But it strikes me as remarkable that people are that confident in their choices that they need such precision.

I think most people think about whether it'll be in the range of, say, 15, or in the area of 35. Not whether it'll be 15 or 15.375.

If there some kind of analysis that can lead to such precise numbers, please share it with me. Personally, I just took a stab at a general area.
30/2 is no more precise than 15 :biggrin: Say, someone could hypothesize that the actual mean is going to be around 1, in which case they would enter 2/3 as their guess.
 
  • #30
EnumaElish said:
30/2 is no more precise than 15 :biggrin: Say, someone could hypothesize that the actual mean is going to be around 1, in which case they would enter 2/3 as their guess.

Point well taken. You're correct on both counts. I meant fractions that cannot be expressed as integers between 0 and 100.:approve:

And I guess if you're around the area between zero and one, then precision starts to matter.
 
  • #31
Okay, the experiment is over. I thank everyone who participated, you all helped. I ended it about a week ago, but then finals caught up with me, and I didn't have a chance to follow up. So here it is:

The official results:

http://www.touromathclub.org/math-puzzles/2-3-the-average/23-average-outcome [Broken]

A few points: obviously, it is impossible for 2/3 the average to be over 66.6, because even if you assume everyone else is supremely stupid and picks 100, the correct answer is still a bit under 2/3 that (under, because your own choice skews the number a bit).

That said, there were still some selections way up there. So I presume there are four categories of people playing this game:

1) Those who take a random stab. They get confused by the question, and just decide to choose a number and forget it, or they can't be bothered. (Or decide to do it for a joke). Included in this group are the people who misunderstand the question.

People in this group have an expected mean of 50. I'd assume anybody who picks a number like 68 is in this group. But it's just as possible that someone who chose 17 was randomly guessing, too.

2)Those who think about the problem very mathematically. They assume that they're playing against a bunch of people as smart as they are, and that everyone will think about the problem the same way. They choose zero.

3) Those who start trying to figure out what everyone else is doing. This group is further broken down by the degree they take it to. One person may figure that the mean will initiallly be 50, so 2/3 that is 33. Factor in a few people who realize this, and pick 33, so the mean is a bit lower. But another person will take it a step further, and another even further, etc.

4)Those who think about it for a little while, and realize that they have absolutely no way of figuring it out. So they do a google search. They find wikipedia says that in at least one case, it fell around 21. So they take a stab around there.

Anyway, I'm not sure I fully digested the results yet, I need to think about them a little more and see if there's anything noteable.

Comments, anyone?
 
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  • #32
ip7ale.png


Results of the experiment, for those of us who are visual :smile:.

edit - fixed x axis
 
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  • #33
Hey, thanks for getting back to us mathematicsma.

I picked 0 -- using the logical reasoning that, if everybody chose 0, we could ALL be winners!

After it was too late, I realized two things
1. Some people are bound to pick nonzero numbers.
2. The instructions did not specify that you had to pick an integer. Just a number between 0 and 100.

If I had it to do over, I would have picked 0.001, or something like that, expecting an average just slightly over 0 -- in which case I would be the closest. Now that the results are in, I see I would still have been way off. :redface:

Thanks again, the experiment was fun and the results interesting.
 
  • #34
Redbelly: when I first heard the experiment, I immediately thought I should choose zero. Then, like you, I realized that if even one person doesn't think like me, and chooses another number, my results are off. Like you, until I did some research, I never imagined it would be so high. Note that at the http://museumofmoney.org/exhibitions/games/guessnumber2.htm" [Broken], the average is 23, so the correct guess is 15.3. So our experiment is pretty close to theirs, which presumably has a much larger sample space.

Lisab: thanks for the edited chart. It's much better than the one I have on my website, especially because it highlights the fact that the most chosen range is the centered around the correct choice in a much clearer way. (That sentence was clumsy. Sorry.)
 
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1. What is the 2/3 the Average Experiment?

The 2/3 the Average Experiment is a thought experiment that involves a group of people trying to guess the average of a set of numbers. The twist is that the person who guesses closest to 2/3 of the actual average wins a prize. This experiment is used to demonstrate the concept of strategic thinking and the importance of considering other people's thought processes.

2. How does the 2/3 the Average Experiment work?

The experiment starts with a group of people being asked to guess the average of a set of numbers. Each person writes down their guess on a piece of paper and hands it in. The person who guesses closest to 2/3 of the actual average wins a prize. This experiment can be done with any set of numbers, but the most common version uses numbers between 1 and 100.

3. Why is the 2/3 the Average Experiment important?

The 2/3 the Average Experiment is important because it demonstrates the concept of strategic thinking and the importance of considering other people's thought processes. It also highlights the idea that sometimes it is more beneficial to think about what others might do instead of just focusing on your own actions.

4. How can the 2/3 the Average Experiment help in real life situations?

The 2/3 the Average Experiment can help in real life situations by teaching individuals to think strategically and consider the perspectives of others. This can be useful in decision-making processes, negotiations, and problem-solving situations. It can also help individuals understand the importance of cooperation and compromise in group settings.

5. Are there any variations of the 2/3 the Average Experiment?

Yes, there are several variations of the 2/3 the Average Experiment that have been used in different settings. Some variations involve multiple rounds of guessing or changing the rules to see how it affects the outcome. Others use different types of numbers or different prizes to make the experiment more interesting. However, the basic concept of strategic thinking and considering others' thought processes remains the same in all variations.

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