The ‘Monty Hall Problem’ Sam (can I call you Sam?) on page 86 of The Moral Landscape is a problem for me. I had to sign up and post it here.
Sam claims this scenario shows how people can be logically confused and irrational even when they clearly intend to choose the most rational/logical choice.
He describes the “Let’s Make a Deal” game show and the idea that you’re given the choice of 3 doors to choose from. One has a car behind it and two have a goat. In other words…one is a ‘winner’ and two are ‘losers’.
He tells you you’ve chosen door #1 but instead it’s revealed that door #2 has a goat—is a ‘loser’. Since there are two loser doors, the show is eliminating one of them AND one choice.
You’re now allowed to ‘switch’ from door #1 to door #3. Most people, as Sam points out, say that it’s a 50/50 bet now so there’s no reason to switch (or switching doesn’t make any difference), but he claims you ‘should’ switch for a better chance.
He says it violates ‘common intuition’ to switch, but claims if you stick with door #1 your chances are 1 out of 3 but if you switch to door #3 your chances are 2 out of 3. This is all on Wikipedia if you want to look it up.
It’s NOT true though that you’d switch to a 2 out of 3 chance. And it’s not based on the grounds of ‘common intuition’.
You start the game with a 1-in-3 chance of picking the winner. When you ‘pick’ door #1 (or ANY door), it doesn’t count because they don’t accept your pick. Because there are two losers, they can show you one of them without revealing if your attempted pick was the winner or not (door #2 in this case).
If door #2 had the car, by revealing it you’d simply lose the game—the end.
But because door #2 has a loser the game STARTS OVER.
You can ‘stay or switch’ from #1 to #3, but this is exactly the same as saying you can just choose #1 or #3. There is no more door #2 because it was revealed as a loser. So you now have, for a fact, a 50/50 chance now.
If you picked something and then the game again didn’t accept the pick but changed the game again then all new odds would be created as the game once again started over. But this is beyond the scope of the scenario Sam presents.
In starting over, you do not know which door has the winner and you only have two choices. Your ‘first pick’ of door 1 was an illusion. You never actually picked it. It never counted. It’s a flaw in semantics to call it a ‘first pick’ that then wrongly gets placed into an otherwise correct mathematical display of probability.
To have Harris use this flawed example to explain how other people use poor logic even when trying to think rationally becomes ironic and does damage to the points he tries to make.
I very much support the vast majority of what Sam says and wish I had the rhetorical skill he has so I could also be out there chopping down the irrational as surgically as he so often does.
But this book about the possibility of science based morality is a bit of a mess IMO and this Monty Hall Problem is just one little facet of it.
Note- I think his basic premise is probably true. That we should be looking to science to work on and develop the most appropriate paths based on facts to guide our moral lives. But so far his book isn’t doing it.
I also highly recommend Richard Carriers ‘Sense and Goodness Without God’ which has addressed this same subject of a rationally-based morality several years ago. It’s a bit collegiate and certainly dry, but actually lays out a path to rational morality whereas Sam seems to just keep saying that science should work on this issue. That’s good, but there are actually lots of answers available now and Sam I’m sure could easily and brilliantly present them.
Also Carrier’s book presents a hierarchical list of ‘ways of knowing’ with ‘faith’ being the one ‘invalid’ way (and specifically why that’s true). It’s been of great use to me and I wish he would write a more commercial/shorter/mainstream version of it. We need lots of ‘horesmen’ out there.