I think what Justin is saying is that finding a single monogamous partner is not significantly different from finding two, three, etc. For some things you only care about succeeding once. So a 63% chance of success (any number of times) means a .63 expected value (because all successes after the first have a value of 0).
Meanwhile for other things, such as polyamorous partners, 2 partners is meaningfully better than one, so the expected value truly is 1, because you will get one partner on average. (Though this assumes 2 partners is twice as good as one, we can complicate this even more if we assume that 2 partners is better, but not twice as good)
Sure: For a monogamous partner, finding a successful partner has a value of 1 Finding 2 successful partners also has a value of 1, because in a monogamous relationship, you only need one partner. The same holds for 3, 4, etc partners. All those outcomes also have a value of 1. So first, let’s find the probability of getting a value of 0. Then let’s calculate the probability of getting a value of 1. The probability of getting a value of 0 (not finding a partner):
(1−110)10≈0.349
There is one other mutually exclusive alternative: Finding at least one partner (which has a value of 1)
1−(1−110)10≈0.651
So we have a 34.9% chance of getting a value of 0 and a 65.1% chance of getting a value of 1. The expected value is:
0.349∗0+0.651∗1=0.651
If you did this experiment a million times and assigned a value of 1 to “getting at least one monogamous partner” and a value of 0 to “getting no monogamous partners,” you would get, on average, a reward of 0.651.
For the sake of brevity, I’ll skip the calculations for a polygamous partner because we both agree on what the answer should be for that.
I know I am a parrot here, but they are playing two different games. One wants to find One partner and the stop. The other one want to find as many partners as possible. You can not you compare utility across different goals. Yes. The poly person will have higher expected utility, but it is NOT comparable to the utility that the mono person derives.
The wording should have been: 10% chance of finding a monogamous partner 10 times yields 1 monogamous partners in expectation and 0.63 in expected utility. Not: 10% chance of finding a monogamous partner 10 times yields 0.63 monogamous partners in expectation.
and: 10% chance of finding a polyamorous partner 10 times yields 1 polyamorous partner in expectation and 1 in expected utility. instead of: 10% chance of finding a polyamorous partner 10 times yields 1.00 polyamorous partners in expectation.
So there was a mix up in expected number of successes and expected utility.
I think what Justin is saying is that finding a single monogamous partner is not significantly different from finding two, three, etc. For some things you only care about succeeding once. So a 63% chance of success (any number of times) means a .63 expected value (because all successes after the first have a value of 0).
Meanwhile for other things, such as polyamorous partners, 2 partners is meaningfully better than one, so the expected value truly is 1, because you will get one partner on average. (Though this assumes 2 partners is twice as good as one, we can complicate this even more if we assume that 2 partners is better, but not twice as good)
I do not understand your reasoning. Please show your calculations.
Sure:
(1−110)10≈0.349For a monogamous partner, finding a successful partner has a value of 1
Finding 2 successful partners also has a value of 1, because in a monogamous relationship, you only need one partner.
The same holds for 3, 4, etc partners. All those outcomes also have a value of 1.
So first, let’s find the probability of getting a value of 0. Then let’s calculate the probability of getting a value of 1.
The probability of getting a value of 0 (not finding a partner):
There is one other mutually exclusive alternative: Finding at least one partner (which has a value of 1)
1−(1−110)10≈0.651So we have a 34.9% chance of getting a value of 0 and a 65.1% chance of getting a value of 1. The expected value is:
0.349∗0+0.651∗1=0.651If you did this experiment a million times and assigned a value of 1 to “getting at least one monogamous partner” and a value of 0 to “getting no monogamous partners,” you would get, on average, a reward of 0.651.
For the sake of brevity, I’ll skip the calculations for a polygamous partner because we both agree on what the answer should be for that.
I know I am a parrot here, but they are playing two different games. One wants to find One partner and the stop. The other one want to find as many partners as possible. You can not you compare utility across different goals. Yes. The poly person will have higher expected utility, but it is NOT comparable to the utility that the mono person derives.
The wording should have been:
10% chance of finding a monogamous partner 10 times yields 1 monogamous partners in expectation and 0.63 in expected utility.
Not:
10% chance of finding a monogamous partner 10 times yields 0.63 monogamous partners in expectation.
and:
10% chance of finding a polyamorous partner 10 times yields 1 polyamorous partner in expectation and 1 in expected utility.
instead of:
10% chance of finding a polyamorous partner 10 times yields 1.00 polyamorous partners in expectation.
So there was a mix up in expected number of successes and expected utility.
Yeah, I suppose we agree then.