Trying to come up with an even simpler non-realistic toy example based on the classic Russian roulette example everybody uses. Imagine N people playing Russian roulette with six-shooter revolvers, repeatedly.https://twitter.com/vgr/status/1234555199307407365 …
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Relative to the initial N, each round eliminates 1/6. So with N=6, 5 rounds cuts it down to 1 person left alive. With N=12, you get L=2 (last round population), etc.
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Example. There are 12 people trapped on a planet about to explode. Vogons offer to save 2 people in return for all the Altairian dollars all 12 have together. Iterated Russian roulette would be a good way to choose. Survivors take dead people's dollars. Last 2 alive take seats
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Actually, the primary candidate selection process we just went through is kinda like this. If you don't get 15% you're dead. Delegates get divided up among the rest.
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Thought of an actual fictional example... the scene in Sholay were the bandit leader Gabbar Singh plays 3-chamber Russian roulette with his 3 henchmen who messed up a raid (Hindi)https://youtu.be/8gX4rPLjpkU?t=350 …
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Here, Gabbar uses a revolver with 3 bullets, 3 empty chambers. All 3 escape the first round and everybody starts laughing that they all escaped. Then he turns around and shoots then all anyway.
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Though crucially, he empties the first 3 chambers by firing into the air, so the remaining three are in sequence, not randomly distributed. So when he randomizes by spinning the cylinder, there's only 1/6 chance of starting in a way that yields that particular outcome.
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Hmm... the first guy must estimate his survival chances at 1/2. After he survives, the second guy can actually estimate his survival chances at 2/3. After he survives too, the third guy will have estimate of 1/2 again. After all survive the first round, all 3 have 0% in 2nd.
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Ah thought of Monty Hall connection. In Sholay example, if he offers the first guy a chance to switch to second position, should he take it? Makes no difference *knowing what he knows then*. But if he offers it to 2nd guy after first one survives, he should *not* switch.
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So survival of 1st guy is non-trivial info. Survival of 2nd guy is as well, but in that case, makes no difference to the odds: value of information is balanced by increased closeness to the full sequence of barrels. So it's worth competing to be #2 *in the #1-survives scenario.*
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I bet there's a similar scene in an English-language movie. There's a whole bunch here https://en.wikipedia.org/wiki/Russian_roulette#Film …
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End of conversation
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