For the game theorists out there...
Today’s Poll of the Day at gamefaqs.com poses an “interesting” question...
Which poll answer do you think will be the most popular today?
I guess it’s sort of like the minority game? Anyone want to try to analyze this?
I find it pretty interesting that what turned out to be the right answer got the least votes.
In a place like this that should never happen. Vote up vote up.
The Nash Equilibrium is to have an equal chance of each answer.
They all form one big loop, so no option really has any distinguishing feature over the others.
The first option is most salient, by virtue of being first.
Level 0 players will tend to choose option 1. Level 1 players will realize that this is what level 0 players will do, so they will tend to choose option 2 (“the first one”). Level 2 players will realize that this is what level 1 players will do, so they will tend to choose option 4 (“the second one”). Level 3 players will realize that this is what level 2 players will do, so they will tend to choose option 5 (“the fourth one”). Apparently there are lots of level 1 & 2 players, but very few level 3 players.
But this analysis does not explain why so many people chose option 3 (“the last one”) - I doubt that they are level 4 players. Perhaps it’s that the last answer is the second-most-salient, by virtue of being last, making them level 1 players with a twist.
When trying to choose randomly, people tend to avoid options with salient features. It is not so easy to sort players into levels accurately.
You and DanielLC are right, however:
Just because a game is isomorphic to a symmetric problem doesn’t mean that it is a symmetric problem. “Scissors cut Paper wraps Rock smashes Scissors” has an equivalent formalism to “Policeman arrests Murderer kills Mayor bosses Policeman” but I’d bet with the latter (played as a single-round game) you’d see some very different game play in practice.
So what CronoDAS needs isn’t a game theorist, it’s a psychologist.
And yet, D is over twice as popular as E. Contradiction!
People’s internal random number generators are not perfect.
Might be more interesting if we replace the permutation matrix with an arbitrary 5 x 5 matrix over the reals.
Which of these expressions do you think will be the largest?
1. a[1,1]*(number of people choosing 1) + … + a[1,5]*(number of people choosing 5)
...
5. a[5,1]*(number of people choosing 1) + … + a[5,5]*(number of people choosing 5)