Bucky
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My experience is that nurture culture is far more common than combat culture (possible exceptions: Law, science?).
This means that almost everyone has experienced nurture culture at some point. They know how to act within it and have common knowledge of how to interpret each other. Even if they prefer combat culture they at least understand the rules of the game.
I think there is a significant minority of people who have no experience of combat culture and so are left confused when they come into contact with it. Over and above being upset at being told “You’re absolutely wrong”, such a person may not understand how anyone could ever say such a thing to another human being. They don’t even understand that such a game can exist.
Maybe others have a different experience, I can imagine people who only know combat getting very confused when they first enter a nurture environment—“Why is everyone getting offended at me?“. Probably this happens relatively early in life if nurture culture is dominant in the wider culture.
I use it to determine the relative probabilities of each μ,σ pair which in turn create the pseudo cdf.
For μ,σ I effectively created a quasi-cumulative distribution with the parameter pairs as the x-axis.
μ1,σ1. μ2,σ1. μ3,σ1 … μ1,σ2. μ2,σ2. μ3,σ2 … μn,σm
The random number defines the relevant point on the y-axis. From there I get the corresponding μ,σ pair from the x-axis.
If this method works I’ll probably have to code the whole thing instead of using a spreadsheet as I don’t have nearly enough μ,σ values to get a good answer currently.
Birnbaum-Saunders is an interesting one. For the purposes of fatigue analysis, the assumptions which bring about the three models are:
Weibull—numerous failure modes (of similar failure speed) racing to see which causes the component to fail first
Log-normal—Damage per cycle is proportional to current damage
Birnbaum-Saunders—Damage per cycle is normally distributed and independent of previous damage
My engineering gut says that this component is probably somewhere between Log-normal and Birnbaum-Saunders (I think proportionality will decay as damage increases) which is maybe why I don’t have a clear winner yet.
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I think I understand now where my original reasoning was incorrect when I was calculating the expected worst in a million. I was just calculating worst in a million for each model and taking a weighted average of the answers. This meant that bad values from the outlier potential pdfs were massively suppressed.
I’ve done some sampling of the worst in a million by repeatedly creating 2 random numbers from 0 to 1. I use the first to select a μ,σ combination based on the posterior for each pair. I use the second random number as a p-value. I then icdf those values to get an x.
Is this an ok sampling method? I’m not sure if I’m missing something or should be using MCMC. I definitely need to read up on this stuff!
The worst in a million is currently dominated by those occasions where the probability distribution is an outlier. In those cases the p-value doesn’t need to be particularly extreme to achieve low x.
I think my initial estimates were based either mainly on uncertainty in p or mainly on uncertainty in μ,σ. The sampling method allows me to account for uncertainty in both which definitely makes more sense. The model seems to react sensibly when I add potential new data so I think I can assess much better now how many data points I require.
I can (a bit).
I have good programming skills compared to a typical mechanical engineer but poor compared to a typical programmer.
Is there any introductory text on the theory which you would recommend (forgetting about the programming for the moment)? I wouldn’t want to try to use a programming language where I didn’t understand the theory behind what I was asking the program to do.
Thanks John, that’s just the kind of thing I was hoping for.
The point about behaviour for the very worst components not following the same distribution as the population which I’m studying is a very good one.
I should have given a little more background to the task.
Firstly, the task is to compare a new component with an old one. Data is available for the old one and data is being collected for the new one. The new one has much higher average life but also much higher variance between samples which led to the question as to which will have the worst one-in-a-million performance.
Secondly, the number of data points is very small. Time cost per data point is ~1 week. I’ll be lucky if I have 10 data points in total. Essentially, I’m tasked to try to approve the component with the fewest possible data points.
(This means that so far I don’t have a favoured model (although Weibull is lower than the other 2) and I also don’t have a firm impression of μ and σ.)
I guess all I can achieve with limited data is to say that for components which fit the typical failure mechanism the worst one-in-a-million is better for the new component than the old. However, we don’t have any information on Black Swan events caused by a different failure mechanism for either component and I definitely need to make this clear in any presentation I make on the subject. With such a lack of data points I don’t think I can use rare event modelling to fill in the gaps.
I will have a look at the ideas about:
1. Taking multiple random samples of a million to get a better estimate of CI. I’m pretty sure this is comfortably within my limited programming skills.
(My limited programming skills are the main reason that my method is a bit long winded – doing it step by step was my way of trying to stop myself making a mistake which I didn’t notice. I did make a mistake with my application of the scale parameter for Birnbaum-Saunders at one point which this method helped me spot.)
2. Looking at how adding extra data points affects my result. I think I can use this to compare value of information with cost of information to get a good impression of when we have enough.
Bayes Questions
Sorry, that’s my poor phrasing—the 53% and 29% are directly comparable. 10⁄19 GS people scored 2-5, compared to 6⁄21 non-GS.
From the report:
The percentages of subjects who offered aid by situational variable were, for low hurry, 63% offered help, intermediate hurry 45%, and high hurry 10%; for helping-relevant message 53%, task-relevant message 29%.
I’ve changed the phrasing in the OP.
Good Samaritans in experiments
In terms of how relative status works out in practice, I see it as affecting people’s first, instinctive reactions to many (probably most) social circumstances.
In an argument between Bob and Carol, who should I support?
If someone criticises me, how do I react?
If someone praises me, how good does it make me feel?
If I disagree with someone, how likely am I to fight my corner?
How do I react when someone takes something which I don’t feel they deserve?
Who do I want to spend time with?
Would this be a good person to date?
If Dave does this, should I do it too?
Other things will also affect these decisions such as liking the person or system 2 thinking—status is just one model of many required to explain human behaviour. These other models aren’t zero-sum. I personally find it helpful for predictive power to have a separate model for relative status:
What would Dave’s decision be if he only cared about relative status?
What would Dave’s decision be if he based it entirely on whether he likes me?
If Dave just thought about this logically what would he decide?
...
How do I put these answers together to predict Dave’s actions?
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I’d argue that apparently absolute questions such as buying Dave a Birthday present would include relative status considerations as there’s a relative status between you and Dave to consider. This might or might not have a big effect on the final decision but it would probably change how you feel about spending time/money on Dave which could easily subconsciously move your actions one way or the other.
Certainly if you’re higher status than him you’d expect him to be more grateful than if he was higher status (within the status model alone).
I wouldn’t be surprised if the model were to be less predictive as the group gets large enough that people can’t keep track of everyone’s relative status or where someone’s status is far away from your own.
In that case I would model people as giving people a placeholder status. e.g. “so high that I don’t have to worry about precisely how high” for VIPs or “just assume roughly average status” when we encounter new people. At this point zero sum might break down.
This is about right.
To truly attack my own position I’d add that I would define RankOrder(A, B) as A’s opinion of their relative rank. If RankOrder(A, B) <> RankOrder(B, A) then it might be arguable that this is no longer zero sum (provided A and B care more about their own opinions than each other’s).
In my experience this is fairly rare—people are very keen to ensure that everyone knows their place.
Obviously I think this is fairly predictive otherwise I wouldn’t believe it. I am aware that the model isn’t perfect but I certainly find it better than any other model I’ve tried. Does anyone have an alternative model?
Let me say I’m incredibly jealous! Functioning this way is a lot of work—that’s why I was trying to decrease the amount of work required with my simplified rule.
The wish for social circles to be more about value than rank was one of the main reasons I started posting on Less Wrong. It’s conversations like this which reassure me that it was a good idea—differences of opinion resolved without acrimony where both parties are better off the end. This does happen elsewhere in my life but not nearly often enough.
I agree that it should work like that but I don’t think that this is how it works in practice.
1. Examples of when ordinal social rank matters
Choice work assignments is an interesting example—I’d say that this is a case where ordinal social rank is the thing which matters most—there is generally no universe of possible employees to consider.
Promotions theoretically include a universe of possible employees. In practice I would say that there’s a minimum level of competence that you need to achieve to be considered for a promotion. Provided that at least one person has achieved that level of competence, the company is likely to just choose between the people they already have in the company rather than looking externally. Even if the company also looks externally the internal applicants start with a huge advantage in that they are a known quantity and know lots about the company already.
At this point the ordinal social rank of those who are sufficiently competent becomes the thing which matters.
2. How social emotions work in practice
Irrespective of the above, my general experience of people is that they consider ordinal social rank to be hugely important and that zero-sum games are common in this respect. I don’t argue that this is always a good idea (quite the opposite as I mentioned in the OP) but from observation of how people act.
Look at any group of teenagers and you will see them engaging in just this conduct. When we get older we generally decrease this behaviour (possibly because we get put into clear-ish hierarchical structures). However, the same emotions seem to govern much of the conduct which I witness—maybe my workplaces are just unusually dysfunctional in this regard.
If I may delve into evolutionary history (not an expert, ignore if you like!), our status emotions evolved when we were in a fixed-ish group of 50 odd people. Ordinal social rank would have been one of the main drivers of reproductive fitness (essentially like any chimps/wolves etc. competing to become the alpha). I don’t think we’ve had enough time in civilised society to de-evolve the tendency to act as though ordinal social rank is incredibly important, even when this is not advantageous to us.
You have me about right I think. Maybe I should rephrase:
“Relative social rank is, within a fixed group, to a close approximation, according to my observations, a zero sum game.”
This isn’t quite as snappy but may be more precise.
I’ll take Said’s advice into account if I ever try to make a formal model.
Do either of those things prevent it from being zero sum?
A fixed set of people in a fixed branching structure even with flat levels still has no way to add utility that I can see—I feel like I’m missing something.
Can you give an example?
I will add that theoretically flat structures generally don’t feel that way to those inside them and this is actually where the fiercest fighting seems to happen. Having difficult to compare social ranks doesn’t seem to stop people trying to outdo each other either!
Edit: Wait, I think I know what you mean now—if the ranking structure isn’t fixed then you can get additional utility, provided that when people are equal rank you e.g. list the top two both as rank 1 instead of averaging the available ranks and saying they both have rank 1.5.
I’m not sure we disagree on anything other than the definition of “status” so let’s taboo it.
I am using the common meaning of “relative social rank”. Within a fixed group this is zero sum from the fact that it’s relative—for me to go up someone else has to go down.
If you replace “status” with “relative social rank” in the OP do you disagree with it?
In praise of heuristics
My intuitions worked slightly differently.
The first one my intuition comes from the Falkirk Wheel (https://en.m.wikipedia.org/wiki/Falkirk_Wheel—see operations section)
For the stone in the boat, when the stone is floating (in the boat) it displaces it’s weight of water, when it is at the bottom of the water it displaces its volume. It is more dense than water so it displaces more in the boat.
Interesting to see how other people deal with the same problem. The one in the OP is probably more generally applicable than mine.
I guess I was including that default in the “nurture culture” box rather than a separate entity—I had it mentally listed as “nurture culture at its worst”. Maybe this is an unhelpful categorisation as you’re right that often there is no underlying truth-seeking goal.
(My experience in purely social circumstances is often the same as yours, in the workplace I’d say I find semi-functional nurture culture quite often, as the default gets somewhat modified to actually get stuff done)
I think the original point stands that many people are not used to being involved in a combat culture and will simply not know how to react when exposed to it. A functional combat culture may make the uninitiated think the culture is just rude, a functional nurture culture will not seem that far removed from a normal conversation without a truth-seeking goal. As such a combat culture will tend to exclude people who are not used to it and has an optics problem.
If I grant that combat culture at its best is the ideal for efficient truth seeking (which I would agree with) there is still the problem of getting from here to there which seems like a co-ordination problem. Possibly a functioning nurture culture is a good start which then allows the culture to move towards combat as people become more comfortable (similarly to your second point here?). But that leaves a problem when you have moved to a combat culture and want other people to join.
(This is not purely theoretical. I encourage a relatively combative approach in my department and it does often make newcomers a little uneasy. Going full combat would likely be even more difficult)
It may be that scaring away those who are not used to combat culture is worth it for the benefits of a good combat culture. It might also be arguable that exposure to combat culture would help people understand it, although I think there’s a danger of this going the opposite way and putting people off combat culture completely.