Sanhedrin 50: Why Ranking the Severity of the 4 Executions Matters

Coming back to the order of the death sentences of the court - descending order of severity: stoning, burning, beheading, and strangulation, plus the biblical sources for the rabbis' ratings. It would seem that the severity of the act would indicate the severity of the sentence, but which is more severe is not always intuitive. In the end, the conclusion is that stoning is the most severe, and the logic is followed through for each of the executions. But defining the worst execution by what is already thought to be the worst violation seems like a given -- until the Gemara goes on to explain why this ranking is important. Also, a dispute over the execution of a betrothed daughter of a kohen who commits adultery - stoning or burning? What about the illicit sexual relations without the daughter-of-the-kohen factor (e.g., incest)? The root of that dispute is exactly the reverse of setting up the "worst" execution by the worst sins, because it determines the execution according to whichever death is worse. So that hierarchy indeed makes a difference (among other examples that demonstrate the need for this ranking)