Null and Vetoed: Chance Coincidence?

Abstract

In late October 2009, California Governor Arnold Schwarzenegger vetoed Assembly Bill 1176 (Ammiano), sending the memo above. The fi rst letters of the third through ninth lines (ignoring the blank lines) comprise an expletive acrostic. Many have wondered whether this could be accidental. The governor’s offi ce claimed the acrostic is “a wild coincidence.” Some have said the chance the acrostic would occur accidentally is 1 in 10 million, but that calculation depends on rather contrived assumptions. I do not think there is an answer to the question, “What is the chance the acrostic would occur accidentally?” In part, this is because there is no single sensible chance model for the wording of a veto. The issue is the framing of an appropriate “null hypothesis” under which to compute the chance. While I am sure that Gov. Schwarzenegger chooses his words carefully, this colorful example invites comparing a variety of null models for how the veto might have been worded “at random.” To put the question into a statistical framework, we ask, “If a seven-line message had been worded randomly, what is the chance that particular acrostic would have occurred?” (We ignore for the moment that many other acrostics would have triggered a similar media response (e.g., b-u-g-g-e-r o-f-f). We also ignore that the governor vetoes many bills. Multiplicity issues such as these could greatly increase the calculated probabilities.) “Randomly” does not mean much by itself. We could concoct any number of models for wording the message at random. Here, I consider six. They give probabilities that span more than eight orders of magnitude.