For every added conspirator, the chances of success fade:
This can be formulated in a model. Let n be the number of conspirators and let p= probability that a single conspirator will not cause failure, either through disloyalty or incompetence. Then
Where A is a proportionality constant. “Effectiveness” is a nebulous concept because I haven’t specified the conspiracy. You can think of it as some measure of success appropriate to a particular conspiracy. The simplest case is to assume Effectiveness is proportional to the number of conspirators, but one can imagine alternatives.
So for a typical example, A=1/10 and p=.75. These give a Chance of Success (for Effectiveness=1) of 6%. If the conspirators are in a Prisoner’s Dilemna situation where it’s advantagous to turn on the others, then p=.1 and the Chance of Success is
, which nicely explains why conspiracies rarely work.
The Dish 