I thought it would be interesting to bring this recent poll on the web to Cornell Info 204 blog

Slashdot poll gets Cognitive Dailyed gets Info 204-ed

How Many People Will Select The Same Option As You?

# 0%

# 1-25%

# 26-50%

# 51-75%

# 76-99%

# 100%

Before you click on the results at the bottom of the post to see what most people have chosen, I would like us to consider the options with our game theory hats on. Don’t look yet!

First let us consider the question itself.

“How Many People Will Select The Same Option As You?”

Although there is no payoff per se, we can treat this as a game where you win if the percentage of people who pick the same choice corresponds to the percentage range. Thus, this is essentially a coordination problem, where a group of people have to solve a problem without being able to communicate with each other. From game theory class, we may have learned about Schelling games and focal points. This game, however, has the additional property in which the choice you make not only relies on coordination but directly affects the distribution of results and hence the “correctness” of your answer. At one moment, you choice may be right, but at a later time, it may be wrong and vice versa. This also raises the question of whether you want early victories, late victories, short-term or long-term victories. Alright, let’s delve into the various choices themselves.

0%

This option will only be right if you are the one and only person choosing it. What are the odds? If you are the first person on the poll and you choose this option, you win trivially. But every subsequent person will not be able to choose this option and win. The next “rational” person might reason that the first person would have chosen this option to win on the first round. Thus he will not choose this option but rather one of the other five options. If he chooses 1-25%, he will not win until the next 3 people come and only one of them chooses the same option, giving him the 25% victory. At any rate, we can reasonably say that choosing 0% and expecting to win is a very unorthodox strategy as it relies on thinking that no one else would adopt such a strategy.

This brings us to the point of simultaneous-choice games versus turn-based games. The type of game choice mechanic can affect the chance of winning greatly. In this case, we have an ongoing choice game where it is assumed to be almost simultaneous if all the results are collected and only tabulated at the end. So 0% is a very unlikely victory choice, since the more people are polled, the higher the chance of there being people who wish to seek unorthodox 0% victories there will be.

1-25%

Since there are 6 choices, assuming an even probability of each choice would make some hasty thinkers choose this option. It is also very tempting indeed as it provides a high chance of short term and long term victories. If we assume a normal distribution we can almost safely choose this option and hope that in the long run there will be less than 25% of the people choosing this altogether. Here we come to the interesting bit where many people choose to adopt this seemingly victorious strategy and hence driving up the percentages, and ultimately resulting in defeat for the >25% who happily picked this. So this poll is not as straightforward as it might be. We will come to see as we explore the other options. (Gosh this option is unpopular again!)

26-50%

Using the same normal distribution argument, we might expect a sizable percentage of people to end up here. Rational people who rejected the previous option might also end up here as it provides a very stable long term victory option despite the fact that it might take awhile for the polls to reach the 25% required for victory.. To have >50% of a polling population choose this option would take a longer time than to have >25% of the people choose the second option. We should also note that it is perfectly possible that there is more than one winning strategy as 25% pick this option, 1 person pick the 0% option and >50% pick the 51-75% option. If the cards fall right we can have a sizable percentage of people winning despite different choices. Isn’t that just awesome.

At this point we should begin to realize that our notion of rational behavior is being challenged. There is no pure rational equilibrium strategy for this game. We should instead rely more on psychology, reasoning and intuition.

51-75%

This is quite a bad choice to pick as it has no noticeable focal properties, and 51% is a very hard target to reach, whether distribution-wise or from reasoning psychologically. I intuit that it is very unlikely that this choice would even exceed 20%. From our previous reasonings, it is better to pick the previous 2 options. We are relying on those more reasoning challenged individuals to pick this option. (Well some people reason differently after all.)

76-99%

This option is even worse than the previous. The only saving grace is that perhaps, there seems to be a good Nash-like equilibrium where if a sizable population somehow manages to end up here, it is very hard to deviate from this range. So if cooperation were somehow telepathic, we could have at least 75% of the people victorious. But I feel it unlikely. There are other more compelling options which relegate this option to a slim chance of victory. People are pretty much selfish and not all that cooperative on small or large scales.

100%

This might be considered the Nash equilibrium or most socially optimal solution to this problem where we can have 100% victory. It might also be considered a focal point of this poll. Perhaps if there were a sizable incentive, a great number of people might decide to miraculously (or rationally) cooperate and ALL choose this option. But if that is the case, some might feel that the previous option provides just as great a chance for massive cooperation since a small number of dissidents will always be present to screw up the population.

Alright go ahead and see what people picked to see if you have “won”. Here are the poll results results from the original Slashdot poll.

I would like to comment that this poll is not as trivial as it appears and its results can be applies to various fields of studies, especially in terms of the market economy, where the distribution of people’s choices has great impact on prices, profits, etc. We can also apply it to politics and society, where unanimity is rare, cooperation sporadic, and falling in with like-minded groups a considerable advantage. To sum up, game theory and analysis of networks are essential for modeling a system but oftentimes, it is more important to consider the psychology and reasoning dynamics of the people playing the game.