Formalizing longtermism

Longter­mism is defined as hold­ing that “what most mat­ters about our ac­tions is their very long term effects”. What does this mean, for­mally? Below I set up a model of a so­cial plan­ner max­i­miz­ing so­cial welfare over all gen­er­a­tions. With this model, we can give a pre­cise defi­ni­tion of longter­mism.

A model of a longter­mist so­cial planner

Con­sider an in­finitely-lived rep­re­sen­ta­tive agent with pop­u­la­tion size . In each pe­riod there is a risk of ex­tinc­tion via an ex­tinc­tion rate .

The ba­sic idea is that eco­nomic growth is a dou­ble-edged sword: it in­creases our wealth, but also in­creases the risk of ex­tinc­tion. In par­tic­u­lar, ‘con­sump­tion re­search’ de­vel­ops new tech­nolo­gies , and these tech­nolo­gies in­crease both con­sump­tion and ex­tinc­tion risk.

Here are the pro­duc­tion func­tions for con­sump­tion and con­sump­tion tech­nolo­gies:

How­ever, we can also de­velop safety tech­nolo­gies to re­duce ex­tinc­tion risk. Safety re­search pro­duces new safety tech­nolo­gies , which are used to pro­duce ‘safety goods’ .

Speci­fi­cally,

The ex­tinc­tion rate is , where the num­ber of con­sump­tion tech­nolo­gies di­rectly in­creases risk, and the num­ber of safety goods di­rectly re­duces it.

Let .

Now we can set up the so­cial plan­ner prob­lem: choose the num­ber of sci­en­tists (vs work­ers), the num­ber of safety sci­en­tists (vs con­sump­tion sci­en­tists), and the num­ber of safety work­ers (vs con­sump­tion work­ers) to max­i­mize so­cial welfare. That is, the plan­ner is choos­ing an al­lo­ca­tion of work­ers for all gen­er­a­tions:

The so­cial welfare func­tion is:

The plan­ner max­i­mizes util­ity over all gen­er­a­tions (), weight­ing by pop­u­la­tion size , and ac­count­ing for ex­tinc­tion risk via . The op­ti­mal al­lo­ca­tion is the al­lo­ca­tion that max­i­mizes so­cial welfare.

The plan­ner dis­counts us­ing (the Ram­sey equa­tion), where we have the dis­count rate , the ex­oge­nous ex­tinc­tion risk , risk-aver­sion (i.e., diminish­ing marginal util­ity), and the growth rate . (Note that could be time-vary­ing.)

Here there is no pure time prefer­ence; the plan­ner val­ues all gen­er­a­tions equally. Weight­ing by pop­u­la­tion size means that this is a to­tal util­i­tar­ian plan­ner.

Defin­ing longtermism

With the model set up, now we can define longter­mism for­mally. Re­call the in­for­mal defi­ni­tion that “what most mat­ters about our ac­tions is their very long term effects”. Here are two ways that I think longter­mism can be for­mal­ized in the model:

(1) The op­ti­mal al­lo­ca­tion in our gen­er­a­tion, , should be fo­cused on safety work: the ma­jor­ity (or at least a size­able frac­tion) of work­ers should be in safety re­search of pro­duc­tion, and only a minor­ity in con­sump­tion re­search or pro­duc­tion. (Or, for small val­ues of (say ) to cap­ture that the next few gen­er­a­tions need to work on safety.) This is say­ing that our time has high hingey­ness due to ex­is­ten­tial risks. It’s also say­ing that safety work is cur­rently un­crowded and tractable.

(2) Small de­vi­a­tions from (the op­ti­mal al­lo­ca­tion in our gen­er­a­tion) will pro­duce large de­creases in to­tal so­cial welfare , driven by gen­er­a­tions (or some large num­ber). In other words, our ac­tions to­day have very large effects on the long-term fu­ture. We could plot against for and some sub­op­ti­mal al­ter­na­tive , and show that is much smaller than in the tail.

While longter­mism has an in­tu­itive foun­da­tion (be­ing in­ter­gen­er­a­tionally neu­tral or hav­ing zero pure time prefer­ence), the com­monly-used defi­ni­tion makes strong as­sump­tions about tractabil­ity and hingey­ness.

Fur­ther thoughts

This model fo­cuses on ex­tinc­tion risk; an­other ap­proach would look at tra­jec­tory changes.

Also, it might be in­ter­est­ing to in­cor­po­rate Phil Tram­mell’s work on op­ti­mal timing/​giv­ing-now vs giv­ing-later. Eg, maybe the op­ti­mal solu­tion in­volves the plan­ner sav­ing re­sources to be in­vested in safety work in the fu­ture.