What Percentage of People Will Pick the Most Voted Option?

[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%.

 

[Borek]

$$\sqrt{-1}$$

 

[Jimmy Snyder]

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

 

[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.

 

[DaveC426913]

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

PFers also like to be right.

 

[Evo]

PFers also like to be right.

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.

 

[Math Is Hard]

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.

 

[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%.

 

[turbo]

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.

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

 

[lisab]

But only 13% of those members will actually vote.

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

 

[Borek]

 

[Evo]

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

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

 

[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.

 

[lisab]

(snip)...nobody should have rationally bet 0%.

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

 

[russ_watters]

$$\sqrt{-1}$$

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

 

[russ_watters]

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.

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

 

[Pupil]

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

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

 

[junglebeast]

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.

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

 

[Pinu7]

About to pick an option.

Hmmm... there are 11 options, so each one must have about 9.1% which is close enough to ten. But wait, I bet more Pfers knew that so 30% would have picked 10%. But how many PFers will know that Pfers knew to pick 10%.

Hmmmmm...
*Shoots Myself*

 

[moose]

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

Hahaha I was just thinking "0% is impossible and 10% is extremely unlikely" so then I thought "hmm I should choose 0%" but then I decided to go with 100% since if everyone chose 100% everyone would be right.

 

[Loren Booda]

I chose 50%. "Ad captandum vulgus."

 

[Huckleberry]

PFers also like to be right.

If everyone gets the right answer then the right answer should be 100%.

 

[junglebeast]

60% is the loneliest percent
80% can be as bad as 60%, but not really, because
60% can be the worst grade that you'll ever get
60% is the loneliest percent, whoa, worse than you
percent
60% is the loneliest
percent

 

[Huckleberry]

Great, now I have that song stuck in my head. Now I have to sing it or I won't be able to sleep tonight. Thanks a lot.

 

[rootX]

closed my eyes and picked one of them ...

 

[Borek]

Check if it doesn't fold in armpits.

 

[Evo]

Check if it doesn't fold in armpits.

Oooh, perfect! I want one.

 

[BobG]

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%.

I'm always so naive when it comes to assessing how people with an above average math background will respond.

Naturally, you get a lot of noise which will push the percentage down from a Nash equilibrium (for example, picking 0% is completely irrational since the only way that could be true is if no one picked any options at all; a possibility that disappears as soon as one picks 0%). I always underestimate just how much noise there is in these.

Maybe I should start from your point of view and try to visualize how much the results will vary from random chance rather than how much the noise will push the results down from the theoretical equilibrium.

I wonder if Evo's estimate will turn out to be right and about 24% pick 0%.

 

[junglebeast]

Of course, it's easy to get the correct answer by simply delaying one's vote until looking at how the result turns out. Several members have already stated that they intend to cheat in this way, which really defeats the purpose of the poll in my opinion...because they are just cherry-picking the right answer after the votes have been cast. The challenge is trying to guess what will happen in advance, or without looking at the results.

 

[BobG]

What percentage do you think will cherry pick the right answer?

Hopefully, over half, because I need some help if my pick is going to be correct.

Actually, I need a lot more than half. Based on the 36 already completing the poll, if the next 36 people cheat, the winning percentage will be 30% (barely less than 35%).

It takes a whole lot of cheating (or just a lot if they all cheat at the same time and don't know about the other cheaters) to ever reach 60%