Applied Divinity Studies wrote a related post that might be of interest: How Long Should you Take to Decide on a Career? They consider a modified version of the secretary problem that accounts for the 2 problematic assumptions you noted (binary payoff and ignorance of opportunity cost); you can play with the Colab notebook if you’re curious. Interestingly, varying the parameters tends to pull the optimal starting point earlier (contra my initial intuition), sometimes by a lot. The optimal solution is so parameter-dependent that it made me instinctively want to retreat to intuition, but of course ADS anticipates this and argues against it: “formal models may be bad, but at least they can disabuse us of even worse intuitive mental models”.
Applied Divinity Studies wrote a related post that might be of interest: How Long Should you Take to Decide on a Career? They consider a modified version of the secretary problem that accounts for the 2 problematic assumptions you noted (binary payoff and ignorance of opportunity cost); you can play with the Colab notebook if you’re curious. Interestingly, varying the parameters tends to pull the optimal starting point earlier (contra my initial intuition), sometimes by a lot. The optimal solution is so parameter-dependent that it made me instinctively want to retreat to intuition, but of course ADS anticipates this and argues against it: “formal models may be bad, but at least they can disabuse us of even worse intuitive mental models”.