Introduction: Scalable Group Decision-Making

A deliberative consensus protocol is a process that online groups can use to make decisions. It’s designed to produce good decisions that are fair and manifest the collective intelligence of the group. And it’s designed to work at scale.

This is not easy. Once a group gets large enough, people will start trying to manipulate the results. And even if everyone acts in good faith, it is hard for a large group to agree even on basic facts, let alone optimal decisions. And even if people agree on the facts, they may have vastly different values and preferences.

What is Equality?

I often don’t know what people really mean when they talk about “equality”. Let alone “equity”.

People talk about “equality of opportunity” vs “equality of outcome”. I am not even sure what either of these means.

Equality of opportunity is impossible. The accidents of our birth influence the opportunities we will have in life, and the choices we make along the way will influence them further.

Equality of outcome is just as impossible. We are all different. And I don’t mean just individually. Groups are different. Men and women are different. Japanese and French people are different. City people and country people are different. This group-level differences will result in different group-level outcomes.

The Mystery

Abdul wanted to see the Mekong Lights. He had seen a Thai movie eight years ago called Mekong Full Moon Party. It was a fictional story featuring one of the world’s most fascinating unexplained phenomena: mysterious balls of light that up shoot from the Mekong every year, as the full moon rises on the eleventh month of the lunar calendar. Ever since, Abdul had been saving money and dreaming of the day he would make the pilgrimage to see these lights.

Introduction

In this post, I discuss the concept of functional equality.

If two values $a$ and $b$ are functionally equal, then there should exist no function $f$ for which $f(a)$ does not equal $f(b)$. For mathematically-minded readers, we can give a more precise definition:

$$ a = b ⟺ ∀f ~ f(a) = f(b) $$

In many programming languages, the == operator does not test for functional equality. For example, the integer 4 and the float 4.0 can be equal according to the == operator, and yet an integer and a float generally are not functionally equal. For example, their string representations will typically differ. If toString(4) != toString(4.0), then 4 and 4.0 are not functionally equal by the definition above.