“…professional investment may be likened to those newspaper competitions in which the competitors have to pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most nearly corresponds to the average preferences of the competitors as a whole; so that each competitor has to pick not those faces which he himself finds prettiest, but those which he thinks likeliest to catch the fancy of the other competitors, all of whom are looking at the problem from the same point of view. It is not a case of choosing those which, to the best of one’s judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees. Keynes (1936, p. 156)”.
The Beauty Contest game allows seeing different things. Adapting this game into a number picking from 0 to 100 –as in the Nagel experiment- and the participant who picks a number that is 2/3 ahead of the average chosen by the rest is the participant that wins. Numbers chosen could range from 0 to 100.
The 2/3 number ahead of the average that the rules request to each participant is in order to avoid having numbers from 67 to 100, as these numbers would be considered irrational or a trying to prank the game. There is always the case where participants could have not understood the game and just say a number randomly. Let’s pretend all participants understood the rules and no one is trying to pull the average as in the FT’s Thaler experiment.
If there are many 50s could mean that each participant picking this number believes the rest will just pick numbers randomly, and when obtaining an average, this will be 50 as this is the total average overall. This means thinking about the others as having a random and irrational way of thought so you just have to take an average in order to win, and the average from 0 to 100 is 50. In the beauty contest, this is similar to the naïve plain strategy of picking the most beautiful faces, which tells us about participants believing the others will just pick according to what they like. These participants believe they are one step further of the rest of participants that are not aware of their level of thought and just pick anything. This is the zero level of thought respect the others.
A zero level of thought would recognize that there are people that on average will pick 50, so first level participants, more sophisticated than the former, will pick 2/3s of 50 or 33 in order to win. These participants recognize that since there is a median population below them, there is the possibility to exploit this “massive market” thinking this population from below is not so aware of the big picture and the possibility of somebody anticipating their decisions. These first-level-thought participants could also recognize (or not) that there are participants more sophisticated than them, but the amount is so tinny that it wouldn’t affect the results.
Participants with a second level of thought believe that there are participants with zero level of thought that will pick 50, that there are participants with first level of thought that will pick around 33 and themselves, that are a minority from the two previous groups and will pick 2/3 of 33 or 22. This group of participants is yet more sophisticated or believes that there could be not just the average and them, but also one intermediate group, the group of the 33s. Again, these participants could be aware (or not) that there are a few participants more sophisticated that could think in a third level but not so representative in the sample. After all, the participants believe that they are unique in some way and that they are n-steps ahead of the rest.
Following this way of thinking respect of the others in a cascade way, there could be fourth, fifth, sixth levels of thought where each level is conscious that there are other “levels” of thought below them which at the same time are thinking about the rest below them.
When participants tend to pick 0, we are talking of a Nash Equilibrium where all the participants are educated on game theory and believe on the knowledge and sophistication of the rest. In an experiment made by Thaler in the Financial Times, there is a representative number of participants that picked 0 on this experiment. But the FT is a newspaper where many readers are learned in Game Theory. Similar would happen to an economics course if they had already learned the Nash Equilibrium. On other instances, maybe it could be unanticipated to pick a 0. The New York Times, for example, got less 0s than 22s, 50s or 33s. However, after explaining the participants the results and if the experiment is done again, results will be closer to the equilibrium.
So how is this applied to social networking such as Facebook? The New York Times poses the beauty contest experiment version of Nagel and Thaler with a title, “Puzzle: Are You Smarter Than 61,139 Other New York Times Readers?” (as of September the 3rd, 2017), and well, due to the confirmation bias, Facebook is full of smart people.
Picking a number is similar to make a comment in a debate context, somehow. You have made a decision to comment with a certain level of thought in relation with the rest of the participants that also post a comment on a certain topic. If you believe that your plain thought when having an opinion is a plurality, then you will not care about the others. If you believe that there is a plurality with a “sheepish way of thought” posting comments and you have identified yourself with not being part of it, then you will post a comment on a first level of thought based on these zero level participants that you perceive. However, on this scenario, the way we see the other participants as “the sheepish” could be biased as we don’t know what the other commenters really are trying to say, we just understand the comment under our own point of view.
There could be the overconfidence that a Dunning Kruger effect bias brings where a participant believes the rest is not so smart and the meaning of everything that is read in consequence will be switched to “evil” by the confirmation bias. Translated to numbers, this person would believe that everyone is a 50, while he or she is a 33, or a 23, or a 15, depending on the levels of perceived learning this person has seen on the others –the perceived levels are according to the subjective classification that the participant has made about the others-. Maybe for a very sophisticated participant 50 would be for dulls; the 33 for not so dulls but still; the 23 for almost leaving the dullness; and 15 he or she, the enlightened, and the number he or she would pick trying to anticipate the others’ number. But the truth is that mostly, participants just reach to think on the others on a first level thought.
It is worth mentioning that all these “types” of participants do not contribute to a whole universe in Facebook (even if they were measured objectively on their actual level of knowledge or ideological position and not the perceived ones); they just contribute to a certain group where there is a fixed and perceived (commonly biased) plurality as the median that is considered the benchmark for the zero level of thought. This allows having a cluster of level of knowledge in each group, as in the case of the FT. When this cluster or virtual average is translated to other groups there is a readjustment of the perceived knowledge seen on the new group after some time, or a cognitive dissonance in the meantime.
Also, as in the FT case, picking a 0 would be for perfectly rational people would be the equivalent to believing the rest is also perfectly rational, not dull, not ignorant, or a perfect market where it is believed that everyone has the same information to make decisions, and that they make them unbiased (which is a bias itself), speaking on economic terms.
Some sources:
To see the Financial Times experiment of Thaler, check https://www.ft.com/content/6149527a-25b8-11e5-bd83-71cb60e8f08c . It shows results that tend to 0 and explanations to the level of thoughts.
https://www.nytimes.com/interactive/2015/08/13/upshot/are-you-smarter-than-other-new-york-times-readers.html?mcubz=1 explains the experiment and shows results with high concentrations in the 50, 33, 22 and 0 –which I doubt will change unless somebody tries to pull the average inputting numbers above 50-, with some explanations of your results every time you type a number. The advantage of this experiment is that it is interactive and you can see your results instantly.
Keynes (1936, p. 156) from the first paragraph refers to “The General Theory of Employment, Interest and Money”. This text was taken from https://web.stanford.edu/~niederle/GuessingGames.pdf
To know more about the Keynesian Beauty Contest, Dunning Kruger Effect, Confirmation Bias, Cognitive Dissonance Bias, Colin Camerer and the k-steps, check Wikipedia articles, and this article from Wikiversity.
https://en.m.wikiversity.org/wiki/Economic_Classroom_Experiments/Guessing_Game
All sources accessed between the 3rd and 6th of September 2017.
Carlos A Rodríguez Peña 