Dice Decision Making
Epistemic status: I have been using dice on and off in my decision-making processes for a few years and am confident it has been a net positive for me (85%). I believe that experimenting with dice decisions would be beneficial for most people who struggle with decision-making (60%). I have a very limited understanding of IFS and quantum mechanics, so take these connections with a grain of salt. All quotes interleaved are from Luke Rhinehart.
I often find myself struggling to make decisions. It can be overwhelming to weigh the pros and cons of each option and make a choice that feels right. A while ago, I came across the concept of using dice to make decisions. At first, it sounded crazy, but the more I thought about it, the more it made sense. I read the book “The Dice Man” by Luke Rhinehart, which tells the story of a psychiatrist who uses dice to live his life. He assigns various actions to each number on the die and follows through with whatever the die tells him to do. Although the book is pretty terrible, this crazy form of decision-making made me wonder if leaving some choices up to chance could eliminate the stress and anxiety that comes with decision-making.
For example, this morning I gave the die the following six options:
Improve my draft of A Framework of Possible Minds
Improve my draft of A Framework of Possible Minds
Write a post about Dice Decision Making
Call a friend I haven’t spoken to in a long time
Apply for a job
Think of six new options and throw again
(Note that the first option appears twice. I control both the options and the probabilities.)
I believe dice decision-making relates interestingly to Multiagent Models of Mind and Internal Family Systems (IFS). These models view the mind as a system of parts, with each part having its own thoughts, emotions, and desires. To promote healing and personal growth, IFS encourages individuals to identify and communicate with their parts. When making decisions, the different options we consider can represent the preferences of different parts of ourselves. Using the dice as a coordination mechanism, we can assign the preferences of different parts to a number on the die and roll it. In this way, we can give the preference of each part a fair chance. This can help us make decisions that align with our true desires and values, allowing us to coordinate our various parts and promote inner harmony. I often feel a lot of energy and excitement when throwing the die, which might indicate that many of my parts agree with the options and proposed decision mechanism.
“The man who fights himself always
carries around a lot of sore losers.”
Also, I often feel that the sole act of thinking of six options can already be helpful. Using two dice, you can give 36 different options some probability. Sometimes, I may feel stuck or overwhelmed when faced with a decision, and simply listing out the different options can help clarify my thoughts and give me a better understanding of what my options are. It helps me to consider options I may not have otherwise thought of. By thinking about how much probability I want to assign to each option, I give myself the chance to explore my preferences further and make a more informed decision.
“Indecisive? Uncertain? Worried? Let the rolling ivory tumble your burdens away. $2.50 per pair.“
To take it a step further, we could use quantum dice. If I understand it correctly, the many-worlds interpretation of quantum mechanics suggests that if we would use a quantum die for our decisions, each roll of the dice creates multiple universes where each possible outcome is realized. This means that every option we consider when rolling the die is executed in one-sixth of the universes, giving us peace of mind knowing that all possibilities have been explored. In this way, you can basically git-branch your life! While the concept of chance is still at play from your universe’s point of view, the idea allows me to feel empowered by the fact that every option has been given a chance to play out in a large fraction of the other universes.
“In the beginning was Chance.
After that?
A series of accidents.”
To conclude, using dice for decision-making is an interesting concept that can help reduce decision-making stress, promote healing and growth by involving different parts of ourselves, and give every part of ourselves an equal chance. It is also an empowering way to explore different possibilities and consider options we might not have thought of before. Furthermore, the multiverse interpretation of quantum mechanics suggests that all options get a chance to play out, offering us peace of mind. Finally, involving some chance in your life is just a lot of fun. So go ahead, and give it a try – you may be surprised at the results.
“When we are living, we are die-ing“
Dice can help in another fairly well-known way with decision making by adding one more step:
If you have some options, and no clear preference between them, you can assign them to dice outcomes. The exact probabilities you assign are not very relevant, roughly equal is fine. Roll the dice to pick one.
Then introspect for whether you are actually satisfied with this outcome, or would have preferred some other outcome. Commit accordingly.
This strategy has never worked for me, but I can see it working for other people. If you want to try this though, it is important to make it clear to yourself which procedure you’re following.
I believe that for my mechanism, it is very important to always follow up on the dice. If there is a dice outcome that would disappoint you, just don’t put it on the list!
You can also do this with coin flips. Have heads represent 1 and tails represent zero. if you need a number between one and eight, flip the coin three times; the first flip says whether to add 1, the second flip says whether to add 2, and the third flip says whether to add 4 (three tails means eight instead of zero).
This method gives true randomness for any 2^n interval, and also for any interval, so long as you’re willing to start over whenever the number returned is too high (at worst, <50% for intervals like 1-33 or 1-65).
The pedant in me wants to say that three tails means 7 (tails, tails, tails > 111 > 1 + 2 + 4 > 7).
EDIT: Ah, now I see you started with 1, so the max value is indeed 8.
Better yet, use a coin to generate a random number between 0 and 1 by generating subsequent bits. Divide the unit interval into any arbitrary set of sub-intervals you want, with arbitrary sizes (probabilities), and stop flipping once the number is squarely inside one of them. That’s your answer. It works with any probabilities whatsoever.
That involves a lot of coin flips, and that will be tiring and you develop an aversion to it. Although 10 coin flips will consistently give you an interval between 1 and 1024 and you’ll only need to reset 2% of the time, so that could work.
Two coin flips for 4 choices and 3 coin flips for 8 choices seems good to me. You can also use a dice for 4 and 5 choices, if you reroll whenever you get a number greater than 4 or 5.
Suppose you want to make a binary decision with a specified bias $p$. If, say, $p=1/8$ then you can throw a coin 3 times, and if you got, say, $HHH$, you take it as positive, else negative.
But if $p$ is a big number (say $1/1000$), or a weird number, say $1/\pi$, then this method fails. There is another really beautiful method I learned some time ago, which allows you to get any biased coin in a constant =2 expected number of throws! (I lost the source, unfortunately)
It works as follows: you throw the coin until the first time you get a head—assume this happened on your $n$-th throw. Then, you accept if and only if the $n$-th digit in the binary expansion of $p$ is 1. It is easy to show that this comes out to the bias exactly = p, and the expected number of coin throws is always 2.
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Also, here’s three quick examples for anyone still wondering exactly how this works. Remember that the chance of flipping tails until a given digit in the binary expansion, then flipping heads, is (12)n where n is the digit number (1/2 for the first digit after the decimal, 1⁄4 for the second, etc).
P=14
P2=.01
My chance to land on the 1 with a heads is exactly 14.
P=23
P2=.101010...
My chance to land on a 1 with my first heads is 12+18+132+...=23
P=17
P2=.001001...
My chance to land on a 1 with my first heads is 18+164+...
The only semi-tough part is doing the base 2 long division to get from your fraction to a binary decimal, but you can just use an online calculator for that. The coolest part is that your expected number of flips is 2, because you stop after one heads.
or you could roll a d10 for each digit. then you would have 5x fewer rolls and wouldn’t have to convert the binary expansion of an arbitrarily precise number back to decimal.
Or use an online RNG or an app to discover a number of your desired precision in one step.
If you really like the gaming feel, you could have an arbitrary number of slots for decisions and roll a die for each slot, eliminating slots that roll under a certain value. You could even have a table of modifiers for each class of option: chores get +1, self-care tasks like making a meal get +3, sending that angry email gets −1, &c.
In any case, all that is far more work than just assuming that six options of approximately equal weight is usually going to work out just fine. I don’t think we really need arbitrary precision here; we just want a process that gets an unambiguous answer and keeps the brain-goblins from having to fight it out. ;) Adding more parameters strikes me as a good way to get that fight going again but at an additional step removed from the actual decision.
That said: if navigating a binary tree with a coin or whatever is more fun for you, you should definitely do that instead. The system that we want to use is the best system!
This isn’t actually resolving the decision making problem, just turning it from “which activity do I want to do” to “how much probability do I want to assign each possible activity,” which is arguably more difficult.
True. It does however resolve internal conflicts between multiple parts of yourself. Often when I have an internal conflict about something (let’s say going to the gym vs going to a bar) the default action is inaction or think about this for an hour until I don’t have enough time to do any of them.
I believe this is because both actions are unacceptable for the other part, which doesn’t feel heard.
However, both parts can agree to a 66% chance of going to the gym, and 33% of going to the bar, and the die decision is ultimate.
Whenever I’ve attempted this it has failed. Each of my parts is so stubborn that they can’t even agree to obey the outcome of a die / coin flip. I just keep prevaricating. This seems like the sort of thing that takes willpower to succeed at.
I can see this being a problem. However, I see myself as someone with very low willpower and this is still not a problem for me. I think this is because of two reasons:
I never put an option on the list that I know I would/could not execute.
I regard the dice outcome as somewhat holy. I would always pay out a bet I lost to a friend. Partly, because it’s just the right thing to do and partly because I know that otherwise, the whole mechanism of betting is worthless from that moment on. I guess that all my parts are happy enough with this system that none of them want to break it by not executing the action.