I get a strong “our physical model says that spherical cows can move with way less energy by just rolling, thereby proving that real cows are stupid when deciding to walk” vibe here.
Loss aversion is real, and is not especially irrational. It’s simply that your model is way too simplistic to properly take it into account.
If I have $100 lying around, I am just not going to keep it around “just in case some psychology researcher offers me a bet”. I am going to throw out in roughly 3 baskets of money : spending, savings, and emergency fund. The policy of the emergency fund is “as small as possible, but not smaller”. In other words : adding to the balance of that emergency funds is low added util, but taking from it is high (negative) util.
The loss from an unexpected bet is going to mostly be taken from the emergency fund (because I can’t take back previous spendings, and I can’t easily take from my savings). On the positive side (gain), any gain will be put into spendings or savings.
So the “ratio” you’re measuring is not a sample from a smooth, static “utility of global wealth”. I am constantly adjusting my wealth assignment such that, by design and constraint, yes, the disutility of loss is brutal. If I weren’t, I would just be leaving util lying on the ground, so to speak (I could spend or save).
You want to model this ?
Ignore spending. Start with an utility function of the form U(W_savings, W_emergency_fund). Notice that dU/dW_emergency_fund is large and negative on the left. Notice that your bet is 1⁄2 U(W_savings + 110, W_emergency_fund) + 1⁄2 U(W_savings, W_emergency_fund − 100).
I have not tested, but I’m ready to bet (heh !) that it is relatively trivial to construct a reasonable utility function that says no to the first bet and yes to the second if you follow this model and those assumptions about the utility function.
(there is a slight difficulty here : assuming that my current emergency fund is at its target level, revealed preference shows that obviously dU/dW_savings > dU/dW_emergency_funds. An economist would say that obviously, U is maximized where dU/dW_savingqs = dU/dW_emergency_funds)
I get a strong “our physical model says that spherical cows can move with way less energy by just rolling, thereby proving that real cows are stupid when deciding to walk” vibe here.
Loss aversion is real, and is not especially irrational. It’s simply that your model is way too simplistic to properly take it into account.
If I have $100 lying around, I am just not going to keep it around “just in case some psychology researcher offers me a bet”. I am going to throw out in roughly 3 baskets of money : spending, savings, and emergency fund. The policy of the emergency fund is “as small as possible, but not smaller”. In other words : adding to the balance of that emergency funds is low added util, but taking from it is high (negative) util.
The loss from an unexpected bet is going to mostly be taken from the emergency fund (because I can’t take back previous spendings, and I can’t easily take from my savings). On the positive side (gain), any gain will be put into spendings or savings.
So the “ratio” you’re measuring is not a sample from a smooth, static “utility of global wealth”. I am constantly adjusting my wealth assignment such that, by design and constraint, yes, the disutility of loss is brutal. If I weren’t, I would just be leaving util lying on the ground, so to speak (I could spend or save).
You want to model this ?
Ignore spending. Start with an utility function of the form U(W_savings, W_emergency_fund). Notice that dU/dW_emergency_fund is large and negative on the left. Notice that your bet is 1⁄2 U(W_savings + 110, W_emergency_fund) + 1⁄2 U(W_savings, W_emergency_fund − 100).
I have not tested, but I’m ready to bet (heh !) that it is relatively trivial to construct a reasonable utility function that says no to the first bet and yes to the second if you follow this model and those assumptions about the utility function.
(there is a slight difficulty here : assuming that my current emergency fund is at its target level, revealed preference shows that obviously dU/dW_savings > dU/dW_emergency_funds. An economist would say that obviously, U is maximized where dU/dW_savingqs = dU/dW_emergency_funds)