Wednesday, September 15, 2010

Angry Mob Equations

A problem was recently put to me. Namely, a formula for determining the productivity of angry mobs given certain parameters. Never being one to shy away from offering useless but entertaining (to me) answers to complex questions, I set to work and came up with the following:

Given a mob of N number of people, we assume their productivity P depends on the ease of identifying their objectives (O), the tools to carry them out (T), and their motivation (M) given by P=O*T*M.

Now, O depends on visual skill (V), amount of visibility given by daylight (L), and the intellectual ability to identify their targets (I). Assume V is measured as visual acuity where 20/20 vision is 1. Daylight is measured in function of ideal light conditions, given as 1. And I is given as the skill to identify the target given information about it, where 1 is 100% odds of identifying targets given V*L=1. Since V*L*I varies for every member of the mob, and we only need one member to identify the targets, O(mob) is defined as V*L*I for the member of the mob with the greatest individual score.

T depends on F (fear inspired by the mob) and S (strategic skill of the mob). F depends on the sum of all W (weapon) and C (craziness) values of each individual mobber, but because F is a matter of human perception, Weber-Fechner law applies. Therefore we define F as ln (Σ(W+C)). S is the mob's skill, which depends on the leader of the mob (defined as the mobber with the greatest Charisma (Ch) score), and is diminished by the effect of groupthink (mob mentality), which in turn is diminished by the leader's ability to manipulate the mob and increased by the mob's dumbness (D). So S=S(leader)*N^(Ch-D). Thus we define T as F*S.

Finally, M is the mob's willingness to continue pursuit, which is given by the appropriateness of the background music (B) and the clash (K) between mob ideals and that which the targets represent. B is defined such that ideal background music is 1. K depends on how much the targets deviates from accepted cultural norms, calculated as the target's value vs the mob's value and assuming a vector space of X cultural norms. Thus Tv-Mv for every value, and K=sqrt((Tv1-Mv1)^2+(Tv2-Mv2)^2...(TvX-MvX)^2). M also depends on the previously defined values of N and D, thus M=B*K*N*D.

There you have it. P=O*T*M.

This is the original wording, as posted here. A number of minor corrections for style and clarity come to mind, but I think the original text deserves to be here in its pure, unadulterated glory.

Credit for the inspiration goes to Luna May. Blame goes strictly to me.

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