MollieTheMare
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User ID: 875
MollieTheMare
6d ago
The Fussy Suitor Problem: A Deeper Lesson on Finding Love
Inspired by the Wellness Wednesday post post by @lagrangian, but mostly for Friday Fun, the fussy suitor problem (aka the secretary problem) has more to teach us about love than I initially realized.
The most common formulation of the problem deals with rank of potential suitors. After rejecting r suitors, you select the first suitor after r that is the highest ranking so far. Success is defined as choosing the suitor who would have been the highest ranking among the entire pool of suitors (size n). Most analyses focus on the probability of achieving this definition of success, denoted as P(r), which is straightforward to calculate. The “optimal” strategy converges on setting r = n/e (approximately 37% of n), resulting in a success rate of about 37%.
However, I always found this counterintuitive. Even with optimal play, you end up failing more than half the time.
In her book The Mathematics of Love Hanna Fry suggests, but does not demonstrate, that we can convert n to time, t. She also presents simulations where success is measured by quantile rather than absolute rank. For instance, if you end up with someone in the 95th percentile of compatibility, that might be considered a success. This shifts the optimal point to around 22% of t, with a success rate of 57%.
Still, I found this answer somewhat unsatisfying. It remains unclear how much less suitable it is to settle for the 95th percentile of compatibility. Additionally, I wondered if the calculation depends on the courtship process following a uniform geometric progression in time, although this assumption is common.
@lagrangian pointed out to me that the problem has a maximum expected value for payoff at r = sqrt(n), assuming uniform utility. While a more mathematically rigorous analysis exists, I decided to start by trying to build some intuition through simulation.
In this variant of we consider payoff in utilitons (u) rather than just quantile or rank information. For convenience, I assume there are 256 suitors.
The stopping point based on sqrt(n) grows much more slowly than the n/e case, so I don’t believe this significantly alters any qualitative conclusions. I’m pretty sure using the time domain here depends on the process and rate though.
I define P(miss) as the probability of missing out or accidentally exhausting the suitors, ultimately “settling” for the 256th suitor. In that case you met the one, but passed them up to settle for the last possible persion. Loss is defined as the difference in utility between the suitor selected by stopping at the best suitor encountered after r, and the utility that would have been gained by selecting the actual best suitor. Expected Shortfall (ES) is calculated at the 5th percentile.
I generate suitors from three underlying utility distributions:
- Exponential: Represents scenarios where there are pairings that could significantly improve your life, but most people are unsuitable.
- Normal: Assumes the suitor’s mutual utility is an average of reasonably well-behaved (mathematically) traits.
- Uniform: Chosen because we know the optimal point.
For convenience, I’ve set the means to 0 and the standard deviation to 1. If you believe I should have set the medians of the distributions to 0, subtract log(2) utilitons from the mean(u) exponential result.
Running simulations until convergence with the expected P(r), we obtain the following results:
| gen_dist | r | P(r) | P(miss) | <u> | <loss> | sd_loss | ES_5 | max_loss |
|----------|---------|------|---------|-----|--------|---------|------|----------|
| exp | n/e | 37% | 19% | 2.9 | 2.2 | 2.5 | 7.8 | 14.1 |
| exp | sqrt(n) | 17% | 3% | 3.0 | 2.1 | 1.8 | 6.6 | 14.8 |
|----------|---------|------|---------|-----|--------|---------|------|----------|
| norm | n/e | 37% | 19% | 1.7 | 1.2 | 1.5 | 4.6 | 7.0 |
| norm | sqrt(n) | 18% | 3% | 2.0 | 0.8 | 0.8 | 3.3 | 6.3 |
|----------|---------|------|---------|-----|--------|---------|------|----------|
| unif | n/e | 37% | 19% | 1.1 | 0.6 | 1.0 | 3.2 | 3.5 |
| unif | sqrt(n) | 17% | 3% | 1.5 | 0.2 | 0.5 | 2.1 | 3.5 |
What was most surprising to me is that early stopping (r = sqrt(n)) yields better results for both expected utility and downside risk. Previously, I would have assumed that since the later stopping criterion (r = n/e) is more than twice as likely to select the best suitor, the expected shortfall would be lower. However, the opposite holds true. You are more than 6 times as likely to have to settle in this scenario, so even if suitability is highly skewed as in the exponential case, expected value is still in favor of the r=sqrt(n) case! This is a completely different result than the r=n/e I had long accepted as optimal. The effect is even far more extreme than even the quantile-time based result.
All cases yield a positive expectation value. Since we set the mean of the generating distributions to 0, this implies that on average having some dating experience before deciding is beneficial. Don’t expect your first millihookup to turn into a marriage, but also don’t wait forever.
I should probably note for low, but plausible n <= 7, sqrt(n) is larger than n/e, but the whole number of suitors mean the optimal r (+/-1) is still given in the standard tables.
One curious factoid, is that actuaries are an appreciable outlier in terms of having a the lowest likelihood of divorce. Do they possess insights about modeling love that the rest of us don’t? I’d be very interested if anyone has other probabilistic models of relationship success. What do they know that the rest of the life, physical, and social sciences don't? Or is it that they are just more disposed to finding a suitable "good" partner than the one.
first grade teacher
Based only on this, aren't the average elementary education majors IQ's 108 based on the old SAT data? The gap between 108 and 120 is still pretty healthy.
120 (80thp)
Am I messing up the IQ quantile conversion, or was there an error up-thread? Using a normal with mean 100, and SD 15 I get:
| IQ | p |
|-------|-------|
| 140 | 0.996 |
| 135 | 0.990 |
| 120 | 0.909 |
| 112.6 | 0.800 |
| 110 | 0.748 |
| 108 | 0.703 |
So a relaxation to a requirement of 120 would only be a 10x wider filter rather than 20x.
MollieTheMare
7d ago
I kind of assumed, based on a vague recollection of OP's claimed achievements, username (as implied major), and desire for a 135+ IQ partner that their (maybe self assessed?) IQ was at least 140. In that if it were "only" 135 it would be unreasonable to set a lower bound at 135.
At 140, the gap to 110 is 30 points, which is the same gap as 100 to 70. Or average to borderline intellectually disabled. I do think it's possible for 140 paired with 110 to work, which is why I put it as conditional on the relationship you expect with your children. Like there is a whole set of life experiences you likely will never be able to share with your children. That's sort of based off of a crude model of averaging parents IQ and assessing a 10 point regression to the mean, (140 + 110) / 2 - 10 = 115. I'd be pretty interested if someone has a less ad-hoc way of calculating this.
It can at least work in fiction though, season 6 episode 9 of House "Ignorance Is Bliss" has an IQ 178 married to an IQ 87.
MollieTheMare
7d ago
- Lower IQ filter down to >120 (80thp) as opposed to ~135(99p).
- Attractive.. okay keep this one, but don't be a k-drama protagonist about this
- Politics - For the most part, drop this.
I do wonder about these filters.
For IQ it depends on how much you value producing high IQ children. I assume it's pretty hard to estimate the distribution for outcomes, but if you were to go down to 110 like @2D3D suggests, it might be unreasonably hard to relate to both your wife and your children... I suppose if you're willing to go down the embryo selection road, but then you would also have to find a partner who would also be into that.
Attractive—where does 1 in 3 here conditional on 25-34 and high IQ place them on absolute attractiveness? I would assume given youth, iq, and contentiousness the person would be well above average in attractiveness to start with. Even if only from the correlated likely socioeconomic advantages they enjoyed growing up. I mean, how many ugly people do you see walking around the campus of say Stanford?
For politics a 1 in 2 filter would be compatible, but not necessarily exactly aligned? Given how niche the politics of someone who posts regularly on the Mott probably are, I suppose it would be hard to filter any more generously without admitting intolerable incompatibility.
MollieTheMare
9d ago
It is quite ironic that one of the biggest contributes to CO2 emissions reductions is fossil fuel companies fracking so aggressively they drove the price of natural gas negative at some points. Ultimately substituting NG for coal is probably a net benefit, but I'm pretty sure environmental activists are not happy with the growth of NG as a energy source.
It's been more than 15 years since An Inconvenient Truth came out and the IPPC won their Nobel Peace Prize. In that time it would have been totally possible to replace essentially all electricity production in developed countries with GEN III+ nuclear plants and make substantial progress on Gen IV plants. Instead, without utility scale storage, the focus on growing interment renewables has only entrench NG peaking plants as the dominant on-demand electricity generation source.
MollieTheMare
10d ago
That's more or less what I was gesturing at with 0.005% of GDP.
Though I would prefer they not exhaust the worlds supply of helium to do it. It's a very usefully industrial gas, and basically not renewable. Using hydrogen balloons would be much more "sustainable," though not supper feasible to do at small scale. Using their cost projections you actually get ~0.05% of gross world product per year. I assumed you could get the cost down with economies of scale by using some mix calcite substituting for the sulfur and hydrogen substituting for the helium.
I was more referring to statements like (from the IPCC Climate Change 2023 Synthesis Report pp. 101)
Redistributive policies across sectors and regions that shield the poor and vulnerable, social safety nets, equity, inclusion and just transitions, at all scales can enable deeper societal ambitions and resolve trade-offs with sustainable development goals.
I'm not even saying it's wrong, but putting redistributive policies ahead of mechanical interventions is what I would argue could be perceived to be driven by a political agenda. That perception can erode trust in the institutions advocating for those interventions, even if the "Equity and Inclusion" and "Scientific Basis" sections are not logically dependent on each other.
I certainly was not making the argument that general public sector works are always bad. Even for things like highways though, there are clearly different strategies that spread the costs and responsibilities differently. For example, the primarily toll-based privately maintained and operated Autoroutes in France vs the free at the point of use Interstate Highway System in the US.
I always thought one of the paradoxes of climate science was that (1) climate modeling is sound enough to project far into the future and determine magnitude, causality, and predict ecological, social, and economic impacts. And (2) geoengineering would be too dangerous because we don't know what the long term effects will be. That's probably not the exact phrasing of the IPCC or other consensus positions, but I don't think it's unreasonably far off either. Very speculative, but I suspect some of the skepticism of climate activism is that the solution always seems to be more socialism, rather than we would like to spend 0.005% of GDP to spray some calcite into the stratosphere.
MollieTheMare
20d ago
I wonder if there should be a formal mechanism for preserving top level posts, or other important contextual bits.
On a slightly related note, what is the preferred way to request the mods to check an account for suspicious activity? It seems like there have been an unusually large number of new accounts dropping in, concern trolling/making low effort posts, then ghosting recently. Though brigading or getting linked from somewhere else seems plausible as well.
MollieTheMare
20d ago
like the fact that crime is overwhelmingly interracial
Wait is this a typo or am I missing something?
In the US context don't most statistics support violent crime being primarily intraracial?
See for example table 6 of the latest FBI Crime in the U.S. or table 13 of U.S. Department of Justice Criminal Victimization, 2021. Excluding the Hispanic origin category, Both show >75% of perpetrators of violent crime being from the same grouping as the victim.
MollieTheMare
20d ago
Yeah, there are also condensed versions if you search the agent's name, but some of the splicing and commentary might leave a little bit to be desired.
Interestingly, when searching I found several "AI" generated looking articles that seem to have incorrect information about the case. One claimed the agent had settled with the city for $440k, but links to an entirely unrelated case.
Other sources claim the agent was fired from the ATF for his part in the incident. Though, it would be pretty funny if the official policy of the agency was for plain clothes agents to scream "I'm a federal fucking agent!" when confronted by uniformed officers.
MollieTheMare
29d ago
He talks about this topic a bit here: https://youtube.com/watch?v=LKyniPMgQ94&t=2410s
Talks about noticing "Willpower and generics take you really far — at least."
My interpretation is he is at least libertarian leaning. There are strong Kolmogorov complicity vibes whenever he butts up against a topic that would get you hard core canceled. I suspect because his business is primarily selling his apps and programs/books and getting canceled would probably hurt that.
MollieTheMare
1mo ago
If you want a very powerful, but very crusty, option that will probably not have the problem of turning into an advertising platform. GnuCash has the capability of "properly" doing bookkeeping with full double-entry accounting. It's probably overkill for personal budget tracking, and comes with the expected jank of a raw GNU project, but there is a reason GAAP exists.
MollieTheMare
1mo ago
confounded by the super heavyweights with enormous fat mass
Not just that, but if you look at the methodology they do not control for any confounders. Particularity the fact that countries that focus on Olympic weightlifting typically do so because it's relatively inexpensive to have a program compared to other sports. Look at any of the medals tables and you see a bunch of North Korea, Kazakhstan, Georgia, Belarus, etc. None of which are famed for longevity of the population. That lifespan chart is absolutely useless without controlling for confounders, unless you think equestrian and sailing has some magical protective powers other than being a sign of affluence.
They also fail to quantify the likely effect of steroid use, which is absolutely rampant in top level weightlifting. "...in the past decade, more than 600 lifters have tested positive." This is particularity relevant because the steroids used are chosen for their ability to avoid doping control and make the athletes stronger not for safety
Also agree, you should probably not take training advise from someone who does not understand the difference between general strength training for health, weightlifting the sport, and bodybuilding.
Why arccos? Like ignoring diffuse horizontal irradiance, .......
The insolation is just proportional to the incident cross-section, or sin(90° - ϕ) = cos(ϕ), where ϕ is the latitude.
you can check for yourself though. The instantaneous insolation is given by
Q = S_0 * (d_bar / d)^2 * (sin ϕ sin δ + cos ϕ cos δ cos h)
In your case S_0, d_bar, and d are constant (the solar constant, mean distance, actual distance)
δ is the declination angle, 0 in your case, so sin δ -> 0, cos δ -> 1.
The hour angle h, or deviation from local solar noon you can consider for h = 0, since you can scale to the max if everyone has a 12 hour day. Or cos h -> 1
giving Q ∝ cos ϕ.
Edit: I see @JhanicManifold already answered and got the same thing. Obviously I mean like cos of degrees latitude and he was working in cos of radians and converting the degrees with the factor of 1/90 * pi/2
MollieTheMare
1mo ago
That previous discussion does look pretty much right to me.
For bands, traditional offerings are gold or silver alloys: few people are allergic to the common ones, and they have a wide array of possible coloration.
For traditional, hard to beat gold for inertness in terms of resistance to tarnish and allergen potential. Also has the pros of being easy(ish) to resize and easy(ish) to cut off in an emergency.
For non-traditional bands I would add tungsten as an option. Its density does make the ring feel "special" though it can also be a con if the the weight is bothersome to you. Tungsten is also pretty good on inertness. You should probably be able to shatter a tungsten ring in an emergency, but that assumes the person removing the ring recognizes that's the right approach. Personally, I go for a silicone band in situations where a band might be expected but I might be doing light stuff with my hands. In the shop or any other place where there is any risk of a degloving injury absolutely no jewelry. Have a dedicated place to place your ring in the shop so it doesn't get lost.
MollieTheMare
3mo ago
Just for completeness, it's probably worth mentioning that it's possible it is slightly more optimal to break up protein feeding into smaller boluses. This paper for example recommends four 0.4 g/kg/meal servings. For someone at 80 kg that puts the recommend size at 32 g.
MollieTheMare
3mo ago
Are you vegetarian? If so you will probably have to supplement, and there is an argument for going to >0.7 g/lbs lean body weight if you are primarily consuming "lower quality" sources.
If not, I can see how getting more than 150 grams could be difficult, but you should be able to hit 100 g eating mostly "normal" stuff. Two large eggs and 2 chicken sausage links ~40g. A 5 oz chicken breast should be at least 35 g. Another 5 oz of 93% lean ground beef is another 30g. That's already 105 grams not including supplements or incidental protein, i.e. if you had 1/2 cup of oats with breakfast that's another 5g. If you go out to eat and the macros aren't great, save enough calories for a casein shake before bed.
MollieTheMare
4mo ago
YMMV, but from the maybe two people I know who have researched it and tried both, hellochinese is probably slightly better than duolingo for Chinese.
MollieTheMare
4mo ago
For general introduction maybe "set your back stiff like a board, not flat like a board."
If you're experiencing frequent back tweaks maybe this series. Much more advanced. For an intermidate level reference, I guess maybe this video.
MollieTheMare
4mo ago
Almost certainly a form issue. It's possible your anthropometry isn't great for deadlifits, but the vast majority of people should be able to perform the lift safely. Wearing a belt can help, but I don't recommend relying on it to save you if you are pulling from a less-safe position.
For a novice I would recommend only owning one belt for everything. If you are not planing on competing any time soon, I would prioritize adjustability and comfort. A uniform width is generally considered better for the type of bracing you should be using for deadlifts. That is, I would personally avoid the bodybuilding style belts that have the wide part "for you back". A good intra-abdominal pressure based brace is far superior to the proprioceptive benefit of a tapered style belt.
IMO the best overall pick for a training belt is a single or double ply, 3" or 4", leather single prong belt. Something like this can be nice because of the extra adjustment. Go for the 3" if you have a short torso, or if you have a hard time getting into deadlifit position with a belt on. Single ply can be more comfy but is less supportive if you get really strong. For sure single prong for ease of use. Lever belts can be nice, but entry level models are usually too annoying to adjust to be nice training belts. Having the extra holes can be nice, as most people can get a slightly better position deadlifting with a belt ~1" larger setting than their squat setup.
For general training, or if you plan on doing Olympic style lifts, a nylon velcro belt (never tried that brand, just an illustrative link) can be good. Cheaper and easier to deal with than a leather belt, but not quite a stiff or durable as a leather belt.
MollieTheMare
4mo ago
I find getting any sleep at all on the flights helps enormously on the other end. If I were unable to sleep on the first flight I would probably use a over the counter sleep aid like diphenhydramine for the second. If the meal service is right after takeoff I might eat, but I would brush teeth and try to sleep right after that. If the meal service is latter I wouldn't bother. To avoid being woken up for mid-flight service, try to make it as clear as possible you intend to sleep. Earplugs, blanket, eye-mask, etc. Assuming you are flying economy a neck pillow worn "backwards" can help with your head falling forward and snapping you back awake.
Pretty reasonable deadlift. Seems like a pretty elaborate setup if you pull like that every time. If you don't set up the same way every time, being more consistent with the setup for every set can help a bit.
Antifungal
Yes, the active ingredient, pyrithione zinc, is supposed to be anti-fungal. I think people are pretty sure it works for fungal acne, though I suspect it also helps with random dryness and itchiness. What causes dandruff after all, if not scalp dryness.
Edit: Personally, Head and Shoulders every day is too harsh for me. I also see you did mentioned acne in a different part of the thread. I think the other common remedy people try, not already on your list, is changing your pillow case every night or every other night. Some people use a fresh towel to wrap their pillow every night. If you have acne from oily skin, it's supposed to help keep your skin oils from clogging pores while you sleep. Fortunately I've never needed to try it, so no first hand experience on that one.
MollieTheMare
5mo ago
This. We need way more information to understand what's going on here.
including copious amounts of SPF to block out the sun
Are you 100% sure you do not have eczema, psoriasis, acne, or atopic dermatitis? If you do one of the standard treatments is phototherapy. Specifically UV phototherapy. The dose and spectrum are carefully controlled, but blocking 100% of UV may not be doing yourself any favors, given you seem to have some sort of condition. Of course UV can also damage your skin and cause skin cancer, so finding a knowledgeable dermatologist is highly recommended over blasting yourself with sun.
If you want to add another random item to your list though, some people report good results with dandruff shampoo. Like regular 2-in-1 classic head and shoulders. Just using it as body and face wash 1-2 times a week. Lather up, let dwell for 30-90 seconds, and rinse.
It's interesting what you suggested is almost the opposite of the scenario @Felagund suggested. I suppose a hopeless romantic would not want to risk the potentially corrosive effect of having knowingly settled. I assume that in practice you would combine some knowledge of the current rate, the steepness of the expected falloff, some pure romantic inclination, and some fear of missing out into some heuristic.
In the scenario where we keep n from above, but keep going if we still haven't found the one I do think is interesting. If we set our benchmark at r=sqrt(n), 83% of the time you find your partner before n/e. Assuming (offset) exponentially distributed utility, the expected utility in this case is about the same as in the case where we assumed halting. I guess this is like the plethora of people who marry someone they meet in college? In about 10% of the cases there you manage to find a partner before the expected window closes, and patients is rewarded with about 50% more utility (4.5 vs 3).
I then assumed some very questionable things to set the next boundaries. First, we can transpose to time as above. Second, that we care about marriage with respect to producing children. Putting geriatric maternal age at 35-40, and assuming you would just offset paternal age so we don't have to deal with an extra set of scenarios, I find a new cutoff of 320/256. I think this sort of accommodates @jeroboam's point. In that case not stopping, but being willing to continue into the danger zone, 1.3% of the runs find the one by "40." Of course expected utility is higher at 5.2, but being willing to push age, but unwilling to settle only picked up a small number of additional "successes."
In the remaining 5% cases you eventually find your soulmate with an expected utility of 6.4. You do have to wait exponentially long though, with a median age equivalent of 67, and a mean of 343!
Setting the high water mark at n/e, but being unwilling to stop is similar in utility. Now you've eliminated the 3 unit of expected utility bucket, and the 4.5 unit utility bucket has 63% weight. Your willingness to go into the (questionably) age equivalent 35-40 bucket also preserves 7% of the trials. By setting your benchmark so late though, 30% of the time you miss the critical window. The higher expected utility, I guess, represents it being totally worth it to find your soul mate, assuming there was no penalty for waiting past geriatric pregnancy age.
@self_made_human don't worry I know these simulations are entirely irrelevant to us denizen of themotte, thus the fun thread and why I included the note on n <= 7, ಥ_ಥ
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