There are a couple problems with this set-up, which is why I didn’t send my friend a bet distribution. The nit-pickiest is that I would be really quite happy with $200,000, so I would be betting somewhere between my true expected probability distribution and a simple even split. But the bigger problem is that I don’t think these five buckets are clearly defined enough that I’d feel comfortable betting at all (unless I really trusted the bookie).
In this thought experiment you are a contestant on a gameshow. The host of the gameshow (let’s call him Alex) has a notecard that says whether or not god exists and to what extent he is involved in the affairs of mankind. You start with $1,000,000 that you must allocate across five possible categories:
- Scriptural literalism. Bet into this category if you believe that one of the religious texts is precisely accurate.
- God is omnipresent. Bet into this category if you believe that god is everywhere and intimately involved in our lives.
- God as a guide. Bet into this category if you believe that god is only there for the major turning points in life and/or when we reach out in prayer.
- God as a watchmaker. Bet into this category if you believe that god set the universe in motion but is no longer around.
- Atheism. Bet into this category if you believe that god does not exist.
You can distribute the money however you like (e.g. all $1,000,000 in one category or $200,000 in each). After you’ve allocated your $1,000,000 Alex flips over the notecard and reveals which of the five categories is correct. You keep any money that you’ve allocated into the correct category.
Starting with the first category “Scriptural Literalism,” I’m a little chary of how the bookmaker is defining “precisely accurate.” I’d put pretty much no money down on the proposition that the earth is 6000 years old or that the stars are painted on the inside of a celestial globe, which is what I think this category is meant to encapsulate. However, some holy books (or subsections) are meant to be read as parables or allegories and they might be accurate in that sense. There must be a better way to frame this section.
Categories 2-4 are too vague and probably need to be coupled with a definition of ‘God.’ Otherwise, a undefined First Cause definitely satisfies 4, but so does a computer science grad student if we’re all living in a simulation that has not been modified since start conditions. Category 2 is so vague that I have no idea what satisfies it.
If you guys can come up with a better way to to divvy up the sample space, I’ll place my bets, and I’ll put together a google form so that the readership can weigh in, too.