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Unknowns comments on Open Thread: July 2010, Part 2 - Less Wrong
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http://www.usatoday.com/news/offbeat/2010-07-13-lottery-winner-texas_N.htm?csp=obinsite
My prior for the probability of winning the lottery by fraud is high enough to settle the question: the woman discussed in the article is cheating.
Does anyone disagree with this?
The appropriate question to ask is:
Given the number of people who play all the different kinds of lotteries, what are the odds of there being some person who wins four (modest) jackpots?
Incidentally, three wins came from scratch-off tickets, which seem inherently less secure than the ones with a central drawing. (And you can also do something akin to card-counting with them: the odds change depending on how many tickets have already been sold and how many prizes have been claimed. Some states make this information public, so you can sometimes find tickets with a positive expected value in dollars.)
I admit I don't know the odds of one person winning four jackpots of over a million dollars each by pure chance. However, my guess is that they are fairly low. But maybe I'm wrong.
Regardless, one can just as easily ask "What are the odds that someone who knows how to cheat at lotteries by this time would have won four of them while cheating on at least one of them?"
Surely the answer to this is: better odds than the answer to the previous question.
There is something else involved as well. We can consider the two hypotheses: 1) she won four lotteries by pure luck; 2) she won four lotteries by cheating. The first hypothesis would predict that she will never win another lottery (like ordinary people.) The second hypothesis would predict that there is a good chance she will win another in her lifetime.
Agreeing with the second hypothesis, I predict with significant probability that she will win another. If she does, your credence in the proposition that it happened by chance must take a huge blow. In fact, would you agree that in this event, you would admit it to be more likely that she cheated?
If so, then consider what would have happened if I had raised the same issue after she had won three of them...
What's your secret? ;)
See my reply to CronoDAS regarding the possibility of a fifth lottery win.
My prior that the universe is not sufficiently uniformly described by typical reductionist reasoning like the kind found in Eliezer's reductionism sequence is high enough that in order to make distinctions between such low probability hypotheses as the ones described I would need to be more sure that my model was meant to deal with the relationship between hypotheses and observed evidence on the extreme ends of a log odds probability scale. (I would also have to be less aware of emotionally available and biased-reasoning-causing fun-theoretic-like anthropic-like not-explicitly-reasoned-through alternative hypotheses.)
What are the alternative hypotheses? Magic? A simulation with interference from the simulator?
I'm not denying the possibility of alternatives, it's just that they all seem less likely the two low probability hypotheses originally considered (chance and cheating).