Rational to distrust your own rationality?

I'm envisaging an alternate universe much like our own, in which there is one additional social convention. Here is a list of some famous books in that universe:

The Portrait of a Rationalist
On the Rationality of the Heavenly Spheres
Discourse on Rationalism
The History of the Rationality and Irrationality of the Roman Empire
Dr Rational and Mr Irrational
The Rationalist of Monte Cristo
The Rational Gatsby
Things Irrational Apart
How Rational is Your Parachute?

I may have an insight to this, and I thought of 2 Allais related questions that are separate scenarios than that in the OP to express my idea. I'll give them a different set of numbers to make it easier to tell apart. Here is the first scenario:

3A: You are given 2 million, with a 100% chance.

3B: You are given 2 million with 89 % chance, 1 million with 1% chance, and 5 Million with 10% chance.

4A: You are given 1 million with 89% chance, and 2 million with a 11% chance.

4B: You are given 1 million with a 90% chance, and 6 million with a 10% chance.

As far as I can tell, this is identical to the scenario, but with an extra 1 million dollars added to all positions. Personally, I now feel much better about picking 3A as opposed to 3B. (I'm worried, but not panicky/fretting.), whereas in the comparable section (1A/1B), I'm MUCH more fearful.

I was curious about why I might think this, and then thought of my second scenario:

This bet repeats 20 times. You must pick the same strategy each time. A rabbit is 1 day of Food, and a deer is 5 days of food. You begin with no food. If you go a full day without food, you will not have the energy to run from wolves at night and they will kill you. Food does not go bad.

5A: 100% chance of Rabbit.

5B: 89% chance of Rabbit, 1% chance of No food, 10% chance of Deer.

6A: 11% chance of Rabbit. 89% chance of No food.

6B: 10% chance of Deer. 90% chance of No food.

When do you die less? 5A, or 5B? When do you die less? 6A, or 6B?

This does not match how I observe my own brain to work. I see the guaranteed million vs the 1% risk of nothing and think "Oh no, what if I lose. I'd sure feel bad about my choice then.". Of course, thinking more deeply I realize that the 10% chance of an extra $4 million outweighs that downside, but it is not as obvious to my brain even though I value it more. If I were less careful, less intelligent, or less introspective, I feel that I would have 'gone with my instinct' and chosen 1A. (It is probably a good thing I am slightly tired right now, since this process happened more slowly than usual, so I think that I got a better look at it happening.)

Yes, but I doubt it explains the Allais paradox. Not even 1% of it. The math is too easy, and the effect too tenacious. It's almost as if humans are sometimes irrational.

For what it's worth, prospect theory helps explain this paradox.

The first aspect is how probability functions in the mind. In experiment one, you're comparing 1% to 10%. A 1% objective probability gets stretched drastically to a 10% subjective probability, while a 10% probability gets stretched to 15%. Functionally, your brain feels like there's a 1.5x difference in probability when there's really a 10x difference in probability. In experiment two, you're comparing 10% to 11%. The subjective probabilities are going to be almost equally stretched (say, 10%->15% and 11%->16%). Functionally, your brain feels like there's an 1.06x difference between them when there's really a 1.10x difference. In other terms your brain discounts the difference between 1% and 10% disproportionately to the difference between 10% and 11%.

The second aspect has to do with how we compress expected values. In experiment two, we're comparing an expected gain of $1m with $5m. If the most utilons we can gain or lose is 100, then $5m would be around 90 utilons (best thing ever!) and $1m would be 70 utilons (omg great thing!), a difference of 20 utilons. In experiment one, we're looking at gaining 90 utilons (win $5m, best thing ever!) or losing 90 utilons (lose $1m, worst thing ever!) for a 180 utilon difference. Basically, losses and gains are compressed separately differently, and our expect utilities are based on whatever our set point is.

Combined, your brain feels like experiment one is asking you to choose between 70 expected utilons (70 utilons @ 100%) or ~67 expected utilons (70 utilons @ 89% plus 90 utilons @ 15% minus 90 utilons @ 10%). Experiment two feels like choosing between 11.2 expected utilons (70 utilons at 16%) or 13.5 expected utilons (90 utilons @ 15%). In other words, the math roughly matches out with a being 'really close, but I'd rather have the sure thing' in experiment one and 'yeah, the better payoff overcomes less odds' in experiment two.

I'm not trying to say if this is how we should calculate subjective probabilities, but it seems to be how we actually do it. Personally, this decision feels so right that I'd err on the side of evolution for now. I would not be surprised if the truly rational answer is to trust our heuristics because the naively rational answer only works in hypothetical models.

Test method for the hypothesis: Use two samples of people: People who have reason to trust their mathematical ability more (say undergraduate math majors) and people who don't (the general undergrad population). If your hypothesis is correct then the math majors should display less of an irrationality in this context. That's hard to distinguish between them being just more rational in general, so this should be controlled in some way using other tests of rationality levels that aren't as mathematical (such as say vulnerability to the conjunction fallacy in story form)

This seems worth testing. I hypothesize that if one does so and controls for any increase in general rationality one won't get a difference between the math majors and the general undergraduates. Moreover, I suspect but am much less certain chance that even without controlling for any general increase in rationality, the math majors will show about as much of an Allais effect as the other undergrads.

SOLVED!

They are using a basic decision making process that works great in real life (uncertain probabilities) but not great in experiments like these (known certain probabilities). This decision making processes works so well in real life that it's probably become second nature for most people and they do it without thinking. People are not inconsistent!

Step 1 - Remove potential choices that could turn out bad. (choices with a significantly lower worst case scenarios than other choices)

Step 2 - Of the remaining choices, pick the choice that has the best best case scenario.

1A: WorstCaseSenario = 1 million BestCaseSenario = 1 million

1B: WorstCaseSenario = I get nothing BestCaseSenario = 5 million

2A: WorstCaseSenario = I get nothing BestCaseSenario = 1 million

2B: WorstCaseSenario = 1 get nothing BestCaseSenario = 5 million

This alone explains the decisions but there is an added effect that enhances it. 1$ DOES NOT equal 1 standard unit of happiness. The quality of life enhancement from having 1 million to having 2 million is not the same difference as the quality of life enhancement from no money to 1 million. I expect most people intuitively know this but here's an article siting a study that supports this.

http://www.time.com/time/magazine/article/0,9171,2019628,00.html

Part of what makes this difficult is that money does not translate linearly to utilons. To put it a different way, the amount of work you'd be prepared to do to make a dollar depends very greatly on how many dollars you already have.

This is the reason most people would pick a 100% chance of a million dollars over a 1% chance of a billion.

The group who probably wouldn't do so are bankers - they'd pick the 1% chance of a billion - but only because they know the overall bet, as a bet, is worth $10 million dollars as it stands, and they can sell on the whole thing as an investment to somebody else, and pocket the 10 million with 100% probability.