Social Contagion theory

[Dominique R. Poirier]

Nat,
There is something that disturbs me in all this and I explain why.

The fact that a number X of persons chose the wrong way because they tend to rely in priority to what they see, and not to what they have been told cannot be summed up in a unifying branch of science or theory we would name “information cascade.”

In other words, I perceive it as a deductive fallacy.

Game theory doesn’t apply to your problem since there is no game in that case. If the first person takes the wrong way, then it doesn’t change the value of the winning prize, according to the rules you set up. While persisting, with a bit of humor, on using the game theory terminology one might say that this case is a “multi-player unlimited-sum non-game.”

Also, another missing element in that problem to make it a case relevant to game theory at some point is the notion that “win” implies “loss” for others. Actors involved in that case scenario may win or lose, individually and it doesn’t entail further consequences for the others. In this sense, and in supposing that we would like to find solutions through hard sciences such as logics or mathematics, then we might find them in theory of gambling or statistical logic. For, when the person 3 chooses to rely on what he witnessed instead of what he learned or was told before, then he is just gambling!

I justify my point.

Consider for a while that the person 3 is a “player” I’ll name P3, and that the precedent actions of the players 1 and 2 may be assimilated to “events” I’ll name E1, E2, and En if ever we were eventually considering the case of the persons 4, 12, 97, or more.
Equally I temporarily consider that the cues the player 3 has been provided with constitute an event too since notions of space, time, and history may apply the same way (he has been told or learned this information somewhere, sometimes). So I’ll name this last event E0. The sole difference between E0 and the events E1, E2 and En is a formal difference. The former is a told event of uncertain value while the latter constitute seen events of equal uncertain value.

In all cases, E1 and E2 may be considered as randomly generated events since there is no clear cut indication that these previous events constitute in themselves reliable sources of information, indeed.
If P3 chooses to rely on E1 and E2, then he relies on assumptions since E1 and E2 constitute informations discrepant to E0. In other words, he is gambling; and his choice to take the left (wrong) way because, at least, he witnessed E1, demonstrates that he acted in compliance with the bandwagon effect theory or with human tendency toward mimetic. If mimetic or bandwagon effect apply to our problem, then we must turn to other fields we name crowd behavior or mass psychology or even consumer behavior, all fields that provide satisfactory answers to our question. And since there is a probability for that P3 may chose to rely on P0 and to take the right way then statistical logic applies too as it applies to consumer behavior.

Since E1 and E2 constitute sources of information whose value are similar to this of E0, then P3 is confronted to the same situation in which a consumer is; as in the frame of another discipline called marketing and communication.
From the standpoint of this other discipline I do not name science the greater the number of occurrence for a given message A (A meaning En since it may encompass E1, E2, and more) the greater the odds that P3 (or Pn, if ever the case arises) will chose A instead of B (B meaning N0, or Nn if the case arises). This fact is no mere theory since applied marketing and communication prove it on a daily basis.

I see another way to tackle this problem which will consist in turning upside down the situation so as to make it relevant to the realm of game theory. In that case, E1, E2, and En would be summed up under the form of a mere message sent by a notional player we would name X; and, equally, EO would be a message sent by a second player we would name Y. The stake would be the number of persons successfully convinced (and so “won”) by each of these two players.

Well, I could go on with other examples, possibly. But all we would learn from it is that there is no way to find solutions through the use of a new discipline we would name “information cascade” since such terminology would pretend to take precedence over already well known other fields which provide satisfying and verifiable explanations.

Unless I missed something at some point, that’s the way I see it, Nat.

Regards,