Summary

• I present a framework to estimate the expected value of rejecting a job offer when there are other ongoing applications.
• I illustrate how to apply the framework with a real world example involving applications of mine.

Framework

If one has to accept/reject now a job offer for opportunity 0, but has N other ongoing applications whose results will only be known in T_results years, assuming one always works for at least 1 year on an opportunity T_start years after accepting an offer for it, and the time until starting to work on an opportunity has no value, the expected value over the 1st 1 + T_results + T_start years after deciding on opportunity 0 is as follows. If one:

• Rejects the offer, p_1*V_1 + p_2*V_2 + … + p_N*V_N + EV_other, where p_i is the probability of accepting an offer for opportunity i if one rejects that for opportunity 0, V_i is the value of working for 1 year on opportunity i, V_1 >= V_2 >= … >= V_N without loss of generality, and EV_other is the expected value from opportunities outside the ongoing applications.
• Accepts the offer, V_0*(1 + T_results).

p_i is equal to the probability of receiving an offer for opportunity i, p_offer_i, but not for any better ones, which is (1 - p_offer_1)*(1 - p_offer_2)*...*(1 - p_offer_{i - 1})*p_offer_i.

V_i should account for the impact of direct work, donations, and career capital. The contribution from donations is:

• For opportunities besides 0, I_i - S_i, where I_i is the net income from the 1st year working on opportunity i, and S_i is the spending excluding donations in the 1 + T_results + T_start years after deciding on opportunity 0 if one accepts opportunity i.
• For opportunity 0, I_0*(1 + T_results) - S_0.

Real example

Context

I applied to join Anonymous Organisation as a founding researcher of a project aiming to steer the giving of philanthropists in India towards cost-effective interventions^[1]. I completed the 1st 2 stages, was invited to the 3rd on January 20 conditional on accepting a seemingly likely future offer, and was supposed to decide on whether I would accept such an offer until January 21. I concluded I would not accept an offer made on January 21 if I had to decide then on it. This was partly informed by my calculations below, which illustrate how to apply the framework I presented above. Some caveats:

• I only considered the applications which intuitively accounted for the most expected value.
• I did not account for the time it would take to know the results of other applications, which corresponds to assuming that T_results is 0.
• I did not quantify the value of career capital, which is relevant if it is not proportional to the value from direct work and donations.

Values

I estimated the value in terms of additional donations to the Shrimp Welfare Project (SWP) from working 1 year as (ordered from the highest to the lowest impact):

• A fund manager at the Animal Welfare Fund (AWF) was 211 k$ (= (186 + 25.2)*10^3). I got this adding:
  • 186 k$ (= 930*10^3*0.2) from direct work. I calculated this multiplying:
    • 930 k$ (= (555 + 375)*10^3) granted in 2024 to help wild animals and shrimp.
    • Annual impact relative to the 2nd best hire equivalent to moving 20 % of the above per year to SWP.
  • 25.2 k$ (= (35.2 - 10)*10^3) from donations (assuming the impact of my donations would be much larger than those of the 2nd best hire because they would not donate much to helping shrimp or wild animals). I calculated this from the difference between:
    • The net salary of 35.2 k$ (= 80*10^3*(1 - 0.56)). I assumed a gross salary of 80 k$ (= (60 + 100)*10^3/2), which was the mean between the lower and upper bound in the job ad, and a 56 % (= 0.45 + 0.11) reduction due to income tax and social security in Portugal.
    • 10 k$, which was my rough guess for my annual expenditure excluding donations.
• A research analyst at Ark Philanthropy was 45.0 k$ (= (28.6 + 16.4)*10^3). I got this adding:
  • 28.6 k$ (= 1*10^6*0.143*0.2) from direct work. I calculated this multiplying:
    • 1 M$ granted per year, as guessed by me.
    • 14.3 % (= 1/7) of the above goes towards helping farmed and wild animals, since animal welfare is one of Ark’s 7 causes.
    • Annual impact relative to the 2nd best hire equivalent to moving 20 % of the above per year to SWP.
  • 16.4 k$ (= (26.4 - 10)*10^3) from donations. I calculated this from the difference between:
    • The net salary of 26.4 k$ (= 60*10^3*(1 - 0.56)). I assumed a gross salary of 60 k$, as guessed by me, and a 56 % (= 0.45 + 0.11) reduction due to income tax and social security in Portugal.
    • 10 k$, which was my rough guess for my annual expenditure excluding donations.
• An operations associate at Epoch AI was 21.9 k$ (= (0 + 21.9)*10^3). I got this adding:
  • 0 from direct work, as I guessed the impact from donations to be way larger.
  • 21.9 k$ (= (31.9 - 10)*10^3) from donations. I calculated this from the difference between:
    • The net salary of 31.9 k$ (= 72.5*10^3*(1 - 0.56)). I assumed a gross salary of 72.5 k$ (= (65 + 80)*10^3/2), which was the mean between the lower and upper bound in the job ad, and a 56 % (= 0.45 + 0.11) reduction due to income tax and social security in Portugal.
    • 10 k$, which was my rough guess for my annual expenditure excluding donations.
• A founding researcher of Anonymous Organisation’s project was 12.8 k$ (= (7.78 + 5.00)*10^3). I got this adding:
  • 7.78 k$ (= 3.1*10^6*0.00251) from direct work. I calculated this multiplying:
    • 3.33 M$ granted per year (= 10*10^6/3), given their goal of influencing 10 M$ over 3 years.
    • An annual impact relative to the 2nd best hire equivalent to moving 0.251 % (= 0.01*0.251) of the annual amount granted per year to SWP. I obtained this multiplying:
      • 1 % (= 10*0.001) of the amount granted per year going towards helping farmed and wild animals, which is 10 times ChatGPT’s and Claude’s guess that 0.1 % of the donations of Indian philanthropists help farmed and wild animals in India. For reference, 3 % of donations in the United States help farmed animals.
      • An annual impact relative to the 2nd best hire equivalent to moving 25.1 % of the above to SWP, as, among AWF’s grants in 2024, 25.1 % (= 930*10^3/(3.7*10^6)) went towards helping wild animals and shrimp.
  • 5.00 k$ (= (15.0 - 10)*10^3) from donations. I calculated this from the difference between:
    • The net salary of 15.0 k$ (= 28.0*10^3*(1 - 0.465)). I assumed a gross salary of 28.0 k€, as mentioned in the job ad, and a 46.5 % (= 0.355 + 0.11) reduction due to income tax and social security in Portugal.
    • 10 k$, which was my rough guess for my annual expenditure excluding donations.
• An operations associate at Giving What We Can (GWWC) is 12.0 k$ (= (0 + 12.0)*10^3). I got this adding:
  • 0 from direct work, as I guessed the impact from donations to be way larger.
  • 12.0 k$ (= (22.0 - 10)*10^3) from donations. I calculated this from the difference between:
    • The net salary of 22.0 k$ (= 50.0*10^3*(1 - 0.56)). I assumed a gross salary of 50.0 k$ (= (35 + 65)*10^3/2), which is the mean between the lower and upper bound in the job ad, and a 56 % (= 0.45 + 0.11) reduction due to income tax and social security in Portugal.
    • 10 k$, which was my rough guess for my annual expenditure excluding donations.
• A freelance math tutor of high school students is negligible. I conclude this because:
  • I guess the impact from direct work is negligible.
  • I estimate the impact from donations is negligible:
    • I calculate a net salary of 10.0 k$/year (= 15.0*10^3*(1 - 0.33)). I assume a gross salary of 15.0 k$/year (= 1*10^3*15), which is 1 kh/year times 15 $/h, as guessed by me having a quick look into what people listed on Superprof charge in my area, and a 33 % (= 0.22 + 0.11) reduction due to income tax and social security in Portugal.
    • The above matches my rough guess of 10 k$/year for my annual expenditure excluding donations.

Expected values

I estimated an expected value of rejecting an offer from Anonymous Organisation over the subsequent 1st year of work of 15.3 k$ (= (11.7 + 2.12 + 0.983 + 0.511)*10^3) adding the following contributions:

• 11.7 k$ (= 0.0556*211*10^3) from joining AWF as a fund manager. I computed this multiplying:
  • A probability of joining of 5.56 % (= 1/18), since 18 people were invited to stage 2, which was the last one I had completed.
  • An expected value conditional on joining of 211 k$, as estimated above.
• 2.12 k$ (= 0.0472*45.0*10^3) from joining Ark as a research analyst. I computed this multiplying:
  • A probability of 4.72 % (= (1 - 0.0556)*0.05) for a 5 % (= 1/20) chance of joining if I did not join AWF, as I guessed 20 people, including me, would be invited to stage 2, although I had only completed stage 1.
  • An expected value conditional on joining of 45.0 k$, as estimated above.
• 983 $ (= 0.0449*21.9*10^3) from joining Epoch AI as an operations associate. I computed this multiplying:
  • A probability of 4.49 % (= (1 - 0.0556)*(1 - 0.05)*0.05) for a 5 % (= 1/20) chance of joining if I did not join AWF or Ark, as I guessed 20 people had been invited to stage 2, which was the last one I had completed.
  • An expected value conditional on joining of 21.9 k$, as estimated above.
• 511 $ (= 0.0426*12.0*10^3) from joining GWWC as an operations associate. I computed this multiplying:
  • A probability of 4.26 % (= (1 - 0.0556)*(1 - 0.05)^2*0.05) for a 5 % (= 1/20) chance of joining if I did not join AWF, Ark or Epoch AI, as I guessed 20 people, including me, would be invited to stage 2, although I had only completed stage 1.
  • An expected value conditional on joining of 21.9 k$, as estimated above.

Consequently, I arrived at a ratio between the expected value from turning down and accepting an offer from Anonymous Organisation of 1.20 (= 15.3*10^3/(12.8*10^3)).

Decision and outcome

I strongly endorse expectational total hedonistic utilitarianism (increasing happiness, and decreasing suffering), and I got a ratio higher than 1, so I decided I would not accept an offer from Anonymous Organisation. Just kidding! I did decide that, but I had other considerations in mind. I noted I underestimated the value of turning down the offer because I could get other jobs I did not include, including other ongoing applications I had. Furthermore, Anonymous Organisation’s project would overwhelmingly involve doing research on human welfare interventions that I do not know are beneficial or harmful, which would be demotivating. I suggested joining as a volunteer who would work 8 h/week on animal welfare. They replied a few weeks later saying they had figured it was best for them to focus just on human welfare, such that it would not be fair for me to join as a volunteer. So I believe I decided well.