What is the Sleeping Beauty Paradox?
The Sleeping Beauty Paradox, also known as the Newcomb’s Paradox, is a thought experiment that has intrigued philosophers, logicians, and scientists alike. It revolves around a scenario involving a sleeping beauty who is put to sleep and then woken up multiple times, each time having to make a decision about whether to accept or reject a bet. The paradox challenges our understanding of probability, rationality, and decision-making.
In this paradox, Sleeping Beauty is placed under anesthesia and awakened three times, each time with the option to accept or reject a bet. Before she is put to sleep, a coin is flipped, and the outcome determines her fate. If the coin lands on heads, she is given $1,000; if it lands on tails, she is given $0. However, she is only told about the outcome after the third awakening. The paradox arises when considering the probability of the coin landing on heads or tails and the rational decision Sleeping Beauty should make based on this information.
Proponents of the “halfer” view argue that Sleeping Beauty should assign a 50% probability to the coin landing on heads and a 50% probability to it landing on tails. This is because she has no information about the coin’s outcome until after the third awakening. Therefore, she should choose to accept the bet each time, as the expected value of the bet is positive.
On the other hand, the “thirder” view posits that Sleeping Beauty should assign a 1/3 probability to the coin landing on heads and a 2/3 probability to it landing on tails. This is based on the idea that she is effectively in the same situation after each awakening, as she has no new information about the coin’s outcome. Therefore, she should only accept the bet once, as the expected value of the bet is negative after the first two awakenings.
The Sleeping Beauty Paradox has sparked a heated debate among scholars, with both sides presenting compelling arguments. The paradox highlights the complexities of assigning probabilities and making rational decisions in situations with incomplete information. It also raises questions about the nature of probability itself and whether it is objective or subjective.
In conclusion, the Sleeping Beauty Paradox is a fascinating thought experiment that challenges our understanding of probability and decision-making. While the debate between the halfer and thirder views continues, the paradox serves as a reminder of the intricacies involved in reasoning about uncertainty and the importance of considering all available information when making rational choices.
