Chris Lehane, the inventor of the original term ‘vast right wing conspiracy’ back in the 1990s to dismiss the (true) allegations against Bill Clinton by Monica Lewinsky
This is inaccurate in a few ways.
Lehane did not invent the term “vast right wing conspiracy”, AFAICT; Hillary Clinton was the first person to use that phrase in reference to criticisms of the Clintons, in a 1998 interview. Some sources (including Lehane’s Wikipedia page) attribute the term to Lehane’s 1995 memo Communication Stream of Conspiracy Commerce, but I searched the memo for that phrase and it does not appear there. Lehane’s Wikipedia page cites (and apparently misreads) this SFGate article, which discusses Lehane’s memo in connection with Clinton’s quote but does not actually attribute the phrase to Lehane.
The memo’s use of the term “conspiracy” was about how the right spread conspiracy theories about the Clintons, not about how the right was engaged in a conspiracy against the Clintons. Its primary example involved claims about Vince Foster which it (like present-day Wikipedia) described as “conspiracy theories” (as you can see by searching the memo for the string “conspirac”).
Also, Lehane’s memo was published in July 1995 which was before the Clinton-Lewinsky sexual relationship began (Nov 1995), and so obviously wasn’t a response to allegations about that relationship.
Lehane’s memo did include some negatives stories about the Clintons that turned out to be accurate, such as the Gennifer Flowers allegations. So there is some legitimate criticism about Lehane’s memo, including how it presented all of these negative stories as part of a pipeline for spreading unreliable allegations about the Clintons, and didn’t take seriously the possibility that they might be accurate. But it doesn’t look like his work was mainly focused on dismissing true allegations.
Explanation:
Hypothesis 1: The data are generated by a beta-binomial distribution, where first a probability x is drawn from a beta(a,b) distribution, and then 5 experiments are run using that probability x. I had my coding assistant write code to solve for the a,b that best fit the observed data and show the resulting distribution for that a,b. It gave (a,b) = (0.6032,0.6040) and a distribution that was close but still meaningfully off given the million experiment sample size (most notably, only .156 of draws from this model had 2 R’s compared with the observed .162).
Hypothesis 2: With probability c the data points were drawn from a beta-binomial distribution, and with probability 1-c the experiment instead used p=0.5. This came to mind as a simple process that would result in more experiments with exactly 2 R’s out of 4. With my coding assistant writing the code to solve for the 3 parameters a,b,c, this model came extremely close to the observed data—the largest error was .0003 and the difference was not statistically significant. This gave (a,b,c) = (0.5220,0.5227,0.9237).
I could have stopped there, since the fit was good enough so that anything else I’d do would probably only differ in its predictions after a few decimal places, but instead I went on to Hypothesis 3: the beta distribution is symmetric with a=b, so the probability is 0.5 with probability 1-c and drawn from beta(a,a) with probability c. I solved for a,c with more sigfigs than my previous code used (saving the rounding till the end), and found that it was not statistically significantly worse than the asymmetric beta from Hypothesis 2. I decided to go with this one because on priors a symmetric distribution is more likely than an asymmetric distribution that is extremely close to being symmetric. Final result: draw from a beta(0.5223485278, 0.5223485278) distribution with probability 0.9237184759 and use p=0.5 with probability 0.0762815241. This yields the above conditional probabilities out to 6 digits.