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The Gemara Sanhedrin 50a writes the order of the death penalties.

It starts with Stoning, proving that Stoning is more severe than any other form of death penalty. Then it moves to Burning, proving that it's more severe than any other form of death penalty. Then it moves to Decapitation ...

Why?

All you have to prove is that Decapitation is stricter than Strangulation, Burning is stricter than Decapitation, and Stoning is stricter than Burning, we'd know the order by a simple syllogism.

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  • I am not sure what your question is asking...who cares if you start from top down or bottom up? Same amount of steps it seems?
    – David Kenner
    May 26, 2017 at 3:49
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    @DavidKenner No. What I'm saying instead of proving A > B & A > C & A> D & B > C & B > D & C >D, you prove A > B & B > C & C > D. Three proofs instead of 6.
    – ertert3terte
    May 26, 2017 at 4:46

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Ever play scissor paper rock...?

Sometimes if A is greater than B and B is greater than C then certainly A is greater than C. This is true if we compare something like mathematical amounts (like weight).

However, it sometimes works out that A is greater than B; B is greater than C; and C is in fact greater than A!

Scissors cuts paper, and paper covers rock. Now, shouldn't scissors beat rock, because it beats the thing that beats rock? NO! Rock blunts scissors.

The Gemara for instance asks that strangulation be considered more severe than burning. Burning was singled out for a daughter of a cohen; But strangulation was singled out for someone who strikes a parent. The Gemara was able to show that since a daughter of a cohen got her punishment upgraded from strangulation to burning, then obviously burning is the more severe punishment.

If we didn't go through that logical step, we may have come to the conclusion that burning is more severe than the sword and the sword is more severe than strangulation, but perhaps strangulation is more severe than the sword?? The same logic applies to stoning if we didn't walk through the steps of proving it was more severe than each of the other three.

The difference of course would be concerning someone who was convicted of two sins. One deserving of burning and the other deserving of strangulation. You can only give the condemned the death which is more severe. Which one?

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  • I'm not sure a non transitive system is possible even a priori. What if someone did an action which deserved all four punishments? Also in a strictly cyclical ordering of order 4 you'd have to address the "cross" values (ie if a<b<c<d<a we need to still know about a vs c and b vs d) unlike rock paper scissors
    – Double AA ♦
    May 26, 2017 at 11:59

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