Question

Suppose a rare event occurs. For example, suppose someone wins two lotteries in a year. This may have happened because it was rigged or because of chance. The defender of the chance hypothesis could point to how given that thousands of lotteries are played each year, one person winning twice is not that surprising. The defender essentially compares this event to other similar events (in this case lotteries) to rationalize it having occurred by chance. But how similar can the other events be? Suppose there is a person Joe who tells you to think of a number between 1 and 1,000,000. He then says he'll try to guess correctly. Suppose he fails 1,000,000 straight times. Another person by the name of Jane comes in and says she can do the same thing. On her fifth try, she guesses correctly. Suppose you are now tasked to figure out whether that happened by chance. If you are an attacker of the chance hypothesis, you might say that the probability of Jane guessing it right within five tries is very low. Therefore, it probably didn't happen by chance. The defender of the chance hypothesis might say Well, both Joe's and Jane's events were guesses. The probability of atleast one guess being correct out of 1,000,005 guesses isn't that low. In this case, even though the events seem more dissimilar compared to the rigged lotteries case, the defender incorporates those trials. This begs the question: when can we incorporate other trials? How similar can other trials be? And is similarity an objective property? Can it be said to be objectively true that the event of the New Jersey lottery occurring on Oct 8th and the New Jersey Lottery occurring on November 10th are more similar to each other than the events of Joe and Jane guessing a number? Why or why not? What about the naturalness of certain categories? For example, suppose Adam thinks of Jane and Jane calls her. You might put this event into the category thinking of someone and calling you since it seems natural to do so. Then, you can simply recognize that tons of people have thought of someone and they didn't call. So this particular event may not be surprising. But what if say you invent some new game where you write down a word of five letters and ask another person in front of you to write it down as well. And they match. The probability of this happening by chance is of course very low. The defender of the chance hypothesis can again try the strategy of putting this into a category of events to increase the probability. But which category does this belong to if this game has not been played before? If it hasn't been played before, does this make this event more impressive than the event of you thinking of someone and having them call you? a) Relevance-based Inclusion

b) Objective Contextual Criteria
c) Familiarity and Precedence
d) Acknowledgement of Unprecedented Events

Answer 1

Determining if an event occurred by chance involves understanding statistical independence and rarity, and considering objective contextual criteria rather than subjective similarities. Familiarity and history impact how we categorize events, affecting our perception of their likelihood. Biases like the availability heuristic and the gambler's fallacy can skew our reasoning about these probabilities.

Step-by-step explanation:

In assessing the likelihood that an event occurs due to chance, it is crucial to understand the principles of probability and the context of each situation. When incorporating other trials into an assessment, like in the example of Joe and Jane guessing a number, we ought to consider the statistical independence and rarity of each event. Similarity, in this context, does not refer to the subjective nature of the trials but rather to the objective likelihood of their occurrence. For instance, the events of the New Jersey Lottery on two different dates may seem subjectively similar because they are identical in structure and process, making them statistically comparable. However, the events of Joe's million guesses and Jane's few attempts lack this statistical equivalence due to the vast difference in sample size.

The defender of the chance hypothesis attempts to categorize an event within a larger set of similar events to show that what might seem improbable on an individual level could be probable when considering a larger number of trials. However, each category must be defined by objective contextual criteria, such as the rules of the games or the processes governing the events, rather than purely subjective resemblances.

Familiarity and precedence play roles in this process as well. If a game is new and has no history, then devising a category for it becomes challenging, and its rarity might seem more striking. Moreover, because our reasoning can be influenced by the availability heuristic or the gambler's fallacy, we should be careful not to let those biases affect our assessment of whether an event is due to chance.