The idea of a normal vs ideal probability distribution makes me think about coin flips following the normal curve. The coins flip distribution over a large sample size will form a normal curve. The "ideal curve activist" will attempt to attract evidence for and possibly find ways to undermine the conspiracy of injustice that flipped the coins after they landed to some non-random pattern making the coin flip distribution appear to correspond to the actual curve.

How are these coins flipped back becomes the topic of interest for the serious activist. Many leads are followed, the evidence and the picture is always murky so suspicions turn to those who deny or ignore the injustice of the actual distribution curve. An odd thing then happens. Denigrating and dis-empowering those who dispute or ignore the ideal curve becomes the mechanism of activism due to the activist's exhaustion of and the murkiness of the task of looking for the assumed malicious coin re-flippers. The coin re-flippers may exist but they may also possess impunity or obscurity such that the activists fail to act against them but it's usually much easier for the activists to direct their energy against assumed shills or fellow conspirators who's proof of membership is their disbelief or disinterest in the ideal curve.