4 ms·

I feel like there's a general puzzle here about statistics and decision theory: if the penalty for basing a bad decision on a false alarm is so high, does that

I feel like there's a general puzzle here about statistics and decision theory: if the penalty for basing a bad decision on a false alarm is so high, does that mean that every alarm should be treated as a false alarm? And in that case, if you are resolved not to trust your sensors, what's the point of installing sensors in the first place?

rtpg 10y ago
I feel like this is the sort of thing that comes up a lot in business in general. You have some strong signal about something, but it's usually hard to take anything as gospel. Instead, you take it as a datapoint and investigate further. You can try treating every alarm as a false alarm (because, historically, nuclear wars have never been started), but still investigate what is happening. The alarm isn't useless, just not decisive.
beejiu 10y ago
Game theory is probably more relevant in the nuclear war scenario.
- marcosdumay 10y ago
  The most interesting part is that no party wins anything by retaliating, only loses more. It must be very interesting how this fact in included on strategies.
  - tlb 10y ago
    Not true. If country A launches a fraction of its missiles, country B has a motivation to launch tactical missiles towards A's launch sites to prevent them launching more. And you never want to launch all your missiles, because then you have no bargaining power. So any nuclear conflict is likely to involve several exchanges.
- eli_gottlieb 10y ago
  Game theory applies to rational, intelligent agents. In real life, unfortunately, the people with their fingers on the nuclear buttons are fanatical idiots these days. And no, I'm not just referring to the one in my own country.
Jabbles 10y ago
It's still more likely that you need to react given that the alarm has gone off. P(attack | alarm) >= P(attack) Unless the alarm is literally random, or even anti-correlated with being attacked. The alarm is still useful. Remember that the penalty for missing a true alarm is possibly even worse that reacting to a false alarm.
- sandworm101 10y ago
  >> Remember that the penalty for missing a true alarm is possibly even worse that reacting to a false alarm. That depends on the scenario. The US for a few years advocated a "total" nuclear response to any use of nukes against western nations. The theory went that any limited nuclear exchange would inevitably escalate. So to win you want to fire everything in the first round. In such scenarios ignoring a true alarm, not triggering the planned world-ending response, may be the safer choice. One nuke in the US, and zero in the USSR, may be the better outcome than hundreds landing on each side. (See "The Sum of All Fears" for how that plays out.)
- duaneb 10y ago
  More likely, but how much more? That seems necessary to discern to make that decision rationally.
- tachyonbeam 10y ago
  I'm not so sure about that. It's called "mutually assured destruction" for a reason. If you have an alarm, there is some probability that it's a false one. If the US were to respond to a false alarm by say, nuking Russia, they could expect a 100% chance that Russia would retaliate. The retaliation would be extremely severe if either the US or Russia gets nuked. You have to think that in addition to all ground-based silos (some of which would definitely survive a nuclear strike), there are stealth subs with nuclear capabilities going around. Even if the US or Russia "lost" a nuclear war, these subs would be there to exercise some kind of vengeance, and make sure that the other side is destroyed as well. If some alarm goes off and there is some chance that nukes are going to hit the US, the safest course of action is probably to prepare to retaliate, but wait as long as possible to confirm that there is an incoming nuclear strike. This might even mean waiting to confirm that some US targets have been hit before retaliating. You also should be pretty god-damn sure you know who initiated that strike before you retaliate. China, for instance, has a limited number of ICBMs. They couldn't destroy the US even if they wanted to. Russia, on the other hand, could nuke the entire world multiple times.
dllthomas 10y ago
Every alarm should be treated as a false alarm. Except, it's also imperative that your opponent not be able to rely on that.

rtpg 10y ago

I feel like this is the sort of thing that comes up a lot in business in general. You have some strong signal about something, but it's usually hard to take anything as gospel. Instead, you take it as a datapoint and investigate further. You can try treating every alarm as a false alarm (because, historically, nuclear wars have never been started), but still investigate what is happening. The alarm isn't useless, just not decisive.

beejiu 10y ago

Game theory is probably more relevant in the nuclear war scenario.

marcosdumay 10y ago
The most interesting part is that no party wins anything by retaliating, only loses more. It must be very interesting how this fact in included on strategies.
- tlb 10y ago
  Not true. If country A launches a fraction of its missiles, country B has a motivation to launch tactical missiles towards A's launch sites to prevent them launching more. And you never want to launch all your missiles, because then you have no bargaining power. So any nuclear conflict is likely to involve several exchanges.
eli_gottlieb 10y ago
Game theory applies to rational, intelligent agents. In real life, unfortunately, the people with their fingers on the nuclear buttons are fanatical idiots these days. And no, I'm not just referring to the one in my own country.

Jabbles 10y ago

It's still more likely that you need to react given that the alarm has gone off. P(attack | alarm) >= P(attack) Unless the alarm is literally random, or even anti-correlated with being attacked. The alarm is still useful. Remember that the penalty for missing a true alarm is possibly even worse that reacting to a false alarm.

sandworm101 10y ago
>> Remember that the penalty for missing a true alarm is possibly even worse that reacting to a false alarm. That depends on the scenario. The US for a few years advocated a "total" nuclear response to any use of nukes against western nations. The theory went that any limited nuclear exchange would inevitably escalate. So to win you want to fire everything in the first round. In such scenarios ignoring a true alarm, not triggering the planned world-ending response, may be the safer choice. One nuke in the US, and zero in the USSR, may be the better outcome than hundreds landing on each side. (See "The Sum of All Fears" for how that plays out.)
duaneb 10y ago
More likely, but how much more? That seems necessary to discern to make that decision rationally.
tachyonbeam 10y ago
I'm not so sure about that. It's called "mutually assured destruction" for a reason. If you have an alarm, there is some probability that it's a false one. If the US were to respond to a false alarm by say, nuking Russia, they could expect a 100% chance that Russia would retaliate. The retaliation would be extremely severe if either the US or Russia gets nuked. You have to think that in addition to all ground-based silos (some of which would definitely survive a nuclear strike), there are stealth subs with nuclear capabilities going around. Even if the US or Russia "lost" a nuclear war, these subs would be there to exercise some kind of vengeance, and make sure that the other side is destroyed as well. If some alarm goes off and there is some chance that nukes are going to hit the US, the safest course of action is probably to prepare to retaliate, but wait as long as possible to confirm that there is an incoming nuclear strike. This might even mean waiting to confirm that some US targets have been hit before retaliating. You also should be pretty god-damn sure you know who initiated that strike before you retaliate. China, for instance, has a limited number of ICBMs. They couldn't destroy the US even if they wanted to. Russia, on the other hand, could nuke the entire world multiple times.

dllthomas 10y ago

Every alarm should be treated as a false alarm. Except, it's also imperative that your opponent not be able to rely on that.