UDASSA

How likely is it that you exist? Not just that someone exists, but that you specifically, with your particular experiences and memories, are reading these words right now?

This seemingly simple question leads to profound puzzles in philosophy and cosmology. In a universe that might be infinite, or a multiverse where every possibility is realized, how can we even define probability?

Developed by Wei Dai in the early 2000s, UDASSA combines two powerful ideas:

• 1.Solomonoff Induction: Simpler programs that generate your observations are more likely to be true. A universe describable in 1000 bits is exponentially more probable than one requiring 2000 bits.
• 2.Self-Selection: Within any world, your probability of being a particular observer is 1 divided by the total number of observers. More observers means your "measure" is more diluted.

“The probability that I find myself to be a particular observer is proportional to the universal prior probability of the world, divided by the number of observers in that world.”- Wei Dai

Your "measure" under UDASSA depends on two factors: how complex is the world you inhabit, and how many observers share that world with you. Adjust both parameters to see how your measure changes.

Notice how both complexity and observer count reduce your measure, but the complexity penalty grows exponentially while observer dilution is linear.

UDASSA has surprising implications for which world you should expect to find yourself in. It is not simply the "biggest" world or the "most common" type of observer - it is a balance between simplicity and observer count.

This has profound implications for questions like the simulation argument, the Fermi paradox, and the nature of consciousness. A simple simulation with few observers may have more measure than a vast, complex universe.

The total measure across all observer-moments sums to one. But this measure is not distributed equally - it flows according to the UDASSA formula. Explore how different weightings affect the distribution.

Each slice represents an observer-moment. The size of the slice is their share of total measure. Hover to see how complexity and observer count determine each moment's probability weight.

At the heart of UDASSA is Solomonoff induction - the idea that shorter programs deserve higher probability. This is Occam's Razor made mathematically precise.

The Kolmogorov complexity of a string is the length of the shortest program that outputs it. The Solomonoff prior assigns probability 2^(-K) to a program of complexity K bits.

print("Hello")

UDASSA tells us how to update our beliefs when we make observations. Different observations provide evidence for or against different universe hypotheses, changing our probability distribution.

Unlike naive Bayesian reasoning, UDASSA automatically handles selection effects. You do not need to separately account for the fact that you can only observe from your location - it is built into the framework.

One of UDASSA's most controversial implications concerns copies. If someone creates a perfect copy of you, what happens to your measure? Under UDASSA, it gets divided.

This has striking consequences: creating copies of yourself might be against your self-interestfrom a certain perspective. Each copy dilutes the measure of all others.

UDASSA rests on deep foundations in algorithmic information theory and philosophy of probability. Expand the sections below for technical details.

UDASSA provides a principled framework for anthropic reasoning, but its implications are often counterintuitive. Here are the key takeaways:

You exist. UDASSA tells you how likely that was - and what it implies about the nature of reality.