A bit more about whether Leia lied and Vader reasoning process.
For Vader there are two options, either Leia lied, and therefore Alderan is to be destroyed or she told the truth, but her decision algorithm for telling the truth was not correlated with Vaders not destroying Alderan as Vader has precommited to destroying Alderan, and therefore Alderan is to be destroyed.
Vader could’ve calculated all this beforehand which makes his initial precommitment to destroy Alderan rational. He looses nothing as he doesn’t care about Alderan, but wins in case Leia tells the truth, which probability is non-zero. It’s not rational for Leia to tell the truth, but she is put into a much more stressful situation where she is likelier to make a mistake than when dealing with Trakin from the comfort of confidence that Alderan is safe.
Its easy to ignore threats when all their effects are purely counterfactual. Much less so, otherwise. Next time when she will be dealing with Tarkin who will make a threat Leia may want to reconsider her superior rationality of ignoring threats, because otherwise she will have to deal with Lord Vader BATNAs.
A bit more about whether Leia lied and Vader reasoning process.
For Vader there are two options, either Leia lied, and therefore Alderan is to be destroyed or she told the truth, but her decision algorithm for telling the truth was not correlated with Vaders not destroying Alderan as Vader has precommited to destroying Alderan, and therefore Alderan is to be destroyed.
Vader could’ve calculated all this beforehand which makes his initial precommitment to destroy Alderan rational. He looses nothing as he doesn’t care about Alderan, but wins in case Leia tells the truth, which probability is non-zero. It’s not rational for Leia to tell the truth, but she is put into a much more stressful situation where she is likelier to make a mistake than when dealing with Trakin from the comfort of confidence that Alderan is safe.
Its easy to ignore threats when all their effects are purely counterfactual. Much less so, otherwise. Next time when she will be dealing with Tarkin who will make a threat Leia may want to reconsider her superior rationality of ignoring threats, because otherwise she will have to deal with Lord Vader BATNAs.