# Another recursive poll

## What percentage of people will have chosen the percentage chosen most often?

Poll closed Oct 29, 2009.

13.0%

6.5%

8.7%

21.7%

10.9%

17.4%

2.2%

10.9%

2.2%

2.2%
11. ### 100%

4.3%
1. Jul 21, 2009

### AUMathTutor

What percentage of people will have chosen the percentage that will receive the most votes?
(no peeking!)

For instance, if you think that the option with the most votes will be 50%, and you think 30% of the people will vote for that, you should answer 30%.

2. Jul 21, 2009

### Staff: Mentor

$$\sqrt{-1}$$

3. Jul 21, 2009

### Jimmy Snyder

I chose 0%. Most PFers are individualists and will deliberately avoid picking the most popular choices.

4. Jul 21, 2009

### turbo

Some PF'ers can visualize the distribution and make a reasonable guess. Half the people responding so far have settled on one choice, though the sample size (4) is still really small.

5. Jul 21, 2009

### DaveC426913

PFers also like to be right.

6. Jul 21, 2009

### Staff: Mentor

72% of all PF'ers would rather skew the poll than be right. But only 13% of those members will actually vote. Personally, I will just wait and vote for whatever number hasn't been selected.

7. Jul 21, 2009

### Math Is Hard

Staff Emeritus
I'll just wait and see if there is one option left over that doesn't get a vote and then I'll vote for that one. That way it won't get its feelings hurt because nobody picked it.

8. Jul 21, 2009

### junglebeast

If people voted with a uniform distribution then the answer would be 1/11 = 9%. Assuming everyone notices this, then they will assume everyone else votes 10% in an attempt to win. But if everyone votes 10%, then the answer is actually 100%. Not everyone will notice this though, so it will drive the answer upwards from 10% by some unknown amount. I haven't done the math on this, but I expect it will probably be chaotic, which would mean that nobody can really predict where the equilibrium will be. Therefore, people will end up voting by their gut instinct, which will be no better than random guessing, causing the true answer to be somewhere between 10 or 20%.

9. Jul 21, 2009

### turbo

Did you get "Miss Congeniality" at your prom? ;-)

10. Jul 21, 2009

### lisab

Staff Emeritus
For those members who have voted, please feel free to print this, and pin it on your shirt.

11. Jul 21, 2009

### Staff: Mentor

12. Jul 21, 2009

### Staff: Mentor

Put that on a sweatshirt, and I'd wear it! I don't look good in t-shirts.

13. Jul 21, 2009

### AUMathTutor

I really have no idea how this is going to turn out.

The cooperative solution would have been for everybody to bet 100%; nobody should have rationally bet 0%.

I have no idea how this is going to turn out.

14. Jul 21, 2009

### lisab

Staff Emeritus
...and yet right now it has the most votes .

15. Jul 21, 2009

### Staff: Mentor

Agreed. I don't think those lines will intersect.

16. Jul 21, 2009

### Staff: Mentor

In polls like this (like that "pick a random number" poll), I always choose the answer that got the most votes.

17. Jul 21, 2009

### Pupil

*gasp* Delete that post (and this one)! You're giving the answer away to people who haven't voted yet! :uhh:

18. Jul 21, 2009

### junglebeast

So in other words it's going a lot like a US presidential election

19. Jul 21, 2009