Algorithms
Dominique Merle edited this page 2 years ago

Algorithms for Delegative (Liquid) Majority Judgment

Introduction

Majority Judgment without delegations

Each Participant may give one Grade to each Candidate.

The default Grade is the worst (ie. most conservative) Grade (eg: To Reject).

Candidates are sorted by their median Grade.

In case of median Grade equality between two or more Candidates, remove one judgment of the median Grade from each of the Candidates, recompute their median Grades, and recompare. Repeat as needed.

Majority Judgment comes from french 🍷 wine contests.

Secret Ballots

For the sake of simplicity, we're not going to consider secret ballots in the following models, right now. We're going to assume that the algorithms know the delegation graph and the given grades, and not care about how they know that.

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Let Participants Choose

Since multiple delegation algorithms are available, Participants should be given the choice of their delegation algorithm as well as its settings if it has any.

Since such a feature can be expensive to implement its UI can be postponed but the core architecture should be carefully designed to be forward-compatible with it.

Algorithm: Expanding Social Circles

My judgment is, by order of precedence:

1. My direct judgment
2. The median of the direct judgments of my 1st degree delegates
3. The median of the direct judgments of my 2nd degree delegates
4. The median of the direct judgments of my ... degree delegates
5. The default grade To Reject (no delegations, or no judgments)

Pros

• Strongly favors direct judgments over delegations
• Also works without any change when delegations are disabled
• The maximum delegation degree (ie. delegation reach) can be a setting

Cons

• We need to figure out which delegation reach will be the default (thankfully, we have a tool for that)

Computation cost

Let n be the number of participants. Let m be the number of proposals. Let d be the number of delegations.

Good luck.

Algorithm: Weighted Social Graph

Left as an exercise for the reader…

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