The Prosecutor's Fallacy Framed as a Sample Space Substitution

The Prosecutor’s Fallacy has been described as a particular error in statistical reasoning that exaggerates a defendant’s probability of guilt, although it also occurs in other settings. When it occurs at trial, the listener must quickly detect and deflect it. This article reviews the Fallacy’s form and history (§§1-3), explains logical errors that may be imputed to it involving Bayes’s theorem with base and incidence rates, likelihood ratios, and logical form (§§4-5), and recasts them graphically (§6). But the logical and graphical errors are too abstruse to be psychologically real or to call out in a trial courtroom. Something is operating closer to consciousness, more easily exposed and rebuffed (§§7-10). Often an opportunistic subtraction from 1 sets up complementary numerical probabilities. With or without explicit subtraction, in all cases of the Prosecutor’s Fallacy and of the fallacy of the transposed conditional a probability substitution fallacy acts as an inverse straw man to illicitly shift an empirical or complementary numerical probability onto one of a different pair of complementary outcomes. Revealing the correct complement exposes this substitution and breaks any direct link to guilt. Synthesis of narrow (transposition) and broad (subtraction) paradigms into a coherent entity unites diverse, including personal, cases. Analytical and synthetic modes prepare witnesses and attorneys to avert or correct this fallacy. Probability symbols and formulas, and tabular diagrams, are offered not for courtroom use but as background to inspire readers and listeners to efficiently recognize and neutralize the Prosecutor’s Fallacy in any of its guises.