Hmm, do you have examples of that? If a robber holds a gun to someone’s head and says “I’ll kill you if you don’t give me your stuff”, that’s clearly a threat, and I believe it also fits the game theory definition: most robbers would have at least a mild preference to not shoot the person (if only because of the mess it creates).
In the stated terms, Alice is the robber, Bob is the victim, X is “Bob resists Alice”, Y is “Alice kills Bob and takes his stuff anyway”, and not-Y is “Alice gives up”.
It is uncontroversial that Bob is worse off under Y than not-Y, but much less certain that Alice is also worse off. If Bob resists Alice and Alice gives up, then Alice is probably going to prison for a very long time. Alice seems much better off killing Bob and taking his stuff, so this was not a “threat” under the proposed definition.
Hmm, this depends on assumptions not stated. I was thinking of the situation where Alice has broken into Bob’s house, and there are neighbors who might hear a gunshot and call the cops, and might be able to describe Alice’s getaway car and possibly its license plate. In other words, Alice shooting Bob carries nontrivial risk of getting her caught.
If we imagine the opposite, that Alice shooting Bob decreases her chance of getting caught, then, after Bob gives her his stuff, why shouldn’t Alice just shoot Bob afterward? In which case why should Bob cooperate? To incentivize Bob, Alice would have to promise that she won’t shoot him after he cooperates, rather than threaten him. (And it’s harder for an apparently-willing-to-murder-you criminal to make a credible promise than a credible threat.)
So let’s flesh out the situation I imagined. If Bob cooperates and then Alice kills him, the cops will seriously investigate the murder. If Bob cooperates and Alice leaves him tied up and able to eventually free himself, then the cops won’t bother putting so much effort into finding Alice. Then Bob can really believe that, if he cooperates, Alice won’t want to shoot him. Now we consider the case where Bob refuses; does Alice prefer to shoot him?
If she does, then we could say that, if both parties understand the situation, then Alice doesn’t need to threaten anything. She may need to explain what she wants and show him her gun, but she doesn’t need to make herself look like a madman, a hothead, or otherwise irrational; she just needs to honestly convey information.[1] And Bob will benefit from learning this information; if he were deaf or uncomprehending, then Alice would have just killed him.
Whereas if Alice would rather not shoot Bob, then her attempts to convince Bob will involve either lying to him, or visibly making herself angry or otherwise trying to commit herself to the shoot-if-resist choice. In this case, Bob does not benefit from being in a position to receive Alice’s communications; if Bob were clearly deaf / didn’t know the language / otherwise couldn’t be communicated with, then Alice wouldn’t try to enrage herself and would probably just leave. (Technically, given that Alice thinks Bob can hear her, Bob benefits from actually hearing her.)
There is an important distinction to be made here. The question is what words to use for each case. I do think it’s reasonably common for people to understand the distinction, and, when they are making a distinction, I think they use “threat” for the second case, while the first might be called “a fact” or possibly “a warning”.
For a less violent case, consider one company telling their vendor, “If you don’t drop your prices by 5% by next month, then we’ll stop buying from you.” If that’s actually in the company’s interest—e.g. because they found a competing seller whose prices are 5% lower—then, again, the vendor is glad to know; but if the company is just trying to get a better deal and really hopes they’re not put in a position where they have to either follow through or eat their words, then this is a very different thing. I do think that common parlance would say that the latter is a threat, and the former is a (possibly friendly!) warning.
Incidentally, it’s clear that people refer to “a thing that might seriously harm X” as “a threat to X”. In the “rational psychopath” case, Alice is a threat to Bob, but her words, her line of communication with Bob, are not—they actually help Bob. In the “wannabe madman” case, Alice’s words are themselves a threat (or, technically, the fact that Alice thinks Bob is comprehending her words). Likewise, the communication (perhaps a letter) from the company that says they’ll stop buying is itself a threat in the second case and not the first. One can also say that the wannabe-madman Alice and the aggressively negotiating company are making a threat—they are creating a danger (maybe fake, but real if they do commit themselves) where none existed.
Now, despite the above arguments, it is possible that the bare word “threat” is not the best term. The relevant Wikipedia article is called “Non-credible threat”. I don’t think that’s a good name, because if Alice truly is a madman (and has a reputation for shooting people who irritated her, and she’s managed to evade capture), then, when Alice tells you to do something or she’ll shoot you, it can be very credible. I would probably say “game-theoretic threat”.
[1] Though in practice she might need to convince Bob that she, unlike most people, is willing to kill him. Pointing a gun at him would be evidence of this, but I think people would also tend to say that’s “threatening”… though waving a gun around might indeed be “trying to convince them that you’re irrational enough to carry out an irrational threat”. I dunno. In game theory, one often prefers to start with situations in which all parties are rational...
Hmm, do you have examples of that? If a robber holds a gun to someone’s head and says “I’ll kill you if you don’t give me your stuff”, that’s clearly a threat, and I believe it also fits the game theory definition: most robbers would have at least a mild preference to not shoot the person (if only because of the mess it creates).
In the stated terms, Alice is the robber, Bob is the victim, X is “Bob resists Alice”, Y is “Alice kills Bob and takes his stuff anyway”, and not-Y is “Alice gives up”.
It is uncontroversial that Bob is worse off under Y than not-Y, but much less certain that Alice is also worse off. If Bob resists Alice and Alice gives up, then Alice is probably going to prison for a very long time. Alice seems much better off killing Bob and taking his stuff, so this was not a “threat” under the proposed definition.
Hmm, this depends on assumptions not stated. I was thinking of the situation where Alice has broken into Bob’s house, and there are neighbors who might hear a gunshot and call the cops, and might be able to describe Alice’s getaway car and possibly its license plate. In other words, Alice shooting Bob carries nontrivial risk of getting her caught.
If we imagine the opposite, that Alice shooting Bob decreases her chance of getting caught, then, after Bob gives her his stuff, why shouldn’t Alice just shoot Bob afterward? In which case why should Bob cooperate? To incentivize Bob, Alice would have to promise that she won’t shoot him after he cooperates, rather than threaten him. (And it’s harder for an apparently-willing-to-murder-you criminal to make a credible promise than a credible threat.)
So let’s flesh out the situation I imagined. If Bob cooperates and then Alice kills him, the cops will seriously investigate the murder. If Bob cooperates and Alice leaves him tied up and able to eventually free himself, then the cops won’t bother putting so much effort into finding Alice. Then Bob can really believe that, if he cooperates, Alice won’t want to shoot him. Now we consider the case where Bob refuses; does Alice prefer to shoot him?
If she does, then we could say that, if both parties understand the situation, then Alice doesn’t need to threaten anything. She may need to explain what she wants and show him her gun, but she doesn’t need to make herself look like a madman, a hothead, or otherwise irrational; she just needs to honestly convey information.[1] And Bob will benefit from learning this information; if he were deaf or uncomprehending, then Alice would have just killed him.
Whereas if Alice would rather not shoot Bob, then her attempts to convince Bob will involve either lying to him, or visibly making herself angry or otherwise trying to commit herself to the shoot-if-resist choice. In this case, Bob does not benefit from being in a position to receive Alice’s communications; if Bob were clearly deaf / didn’t know the language / otherwise couldn’t be communicated with, then Alice wouldn’t try to enrage herself and would probably just leave. (Technically, given that Alice thinks Bob can hear her, Bob benefits from actually hearing her.)
There is an important distinction to be made here. The question is what words to use for each case. I do think it’s reasonably common for people to understand the distinction, and, when they are making a distinction, I think they use “threat” for the second case, while the first might be called “a fact” or possibly “a warning”.
For a less violent case, consider one company telling their vendor, “If you don’t drop your prices by 5% by next month, then we’ll stop buying from you.” If that’s actually in the company’s interest—e.g. because they found a competing seller whose prices are 5% lower—then, again, the vendor is glad to know; but if the company is just trying to get a better deal and really hopes they’re not put in a position where they have to either follow through or eat their words, then this is a very different thing. I do think that common parlance would say that the latter is a threat, and the former is a (possibly friendly!) warning.
Incidentally, it’s clear that people refer to “a thing that might seriously harm X” as “a threat to X”. In the “rational psychopath” case, Alice is a threat to Bob, but her words, her line of communication with Bob, are not—they actually help Bob. In the “wannabe madman” case, Alice’s words are themselves a threat (or, technically, the fact that Alice thinks Bob is comprehending her words). Likewise, the communication (perhaps a letter) from the company that says they’ll stop buying is itself a threat in the second case and not the first. One can also say that the wannabe-madman Alice and the aggressively negotiating company are making a threat—they are creating a danger (maybe fake, but real if they do commit themselves) where none existed.
Now, despite the above arguments, it is possible that the bare word “threat” is not the best term. The relevant Wikipedia article is called “Non-credible threat”. I don’t think that’s a good name, because if Alice truly is a madman (and has a reputation for shooting people who irritated her, and she’s managed to evade capture), then, when Alice tells you to do something or she’ll shoot you, it can be very credible. I would probably say “game-theoretic threat”.
[1] Though in practice she might need to convince Bob that she, unlike most people, is willing to kill him. Pointing a gun at him would be evidence of this, but I think people would also tend to say that’s “threatening”… though waving a gun around might indeed be “trying to convince them that you’re irrational enough to carry out an irrational threat”. I dunno. In game theory, one often prefers to start with situations in which all parties are rational...