Liquid Democracy

The third ‘Democracy’

Current known democratic processes

Direct Democracy

poeple vote for policies directly. This type of democracy only works when each of the members are informed and can estimate the impact of each policy.

similar but different Approval Voting

(最高裁判所裁判官国民審査)

Representative Democracy

you choose a representative (usually someone) to decide for you. Cuts costs for informed concent, but trades off control.

Liquid Democracy

Democracy that you can vote for both policies and people.

Example1: Deciding Breakfast

As a family we need to decide what to have for breakfast. The options are Rice or Bread.

Minori put 0.1 points to Yasushi and Ray to deicide, and voted directy 0.1 and 0.7 points respectively to Rice and Bread. Yasushi voted 0.2 points to Minori and 0.3 points to Ray. He gave half of his vote to Rice. Ray gave 0.4 points to her parents and gave the remainder for eating Bread.

some points to consider

  • Minori contradics. She is giving 0.1 points to rice while giving it 0.7 to bread.
  • Yasushi is the only one directly voting for Rice
  • Ray has limited knowledge and may not know how Rice tastes.

  • Voting matrix

    The Voting Matrix (%V%) will be:

    -MinoriYasushiRay* Rice* Bread
    Minori0.00.20.40.00.0
    Yasushi0.10.00.40.00.0
    Ray0.10.30.00.00.0
    * Rice0.10.50.01.00.0
    * Bread0.70.00.20.01.0
  • results:

    PlanVotes
    Rice1.1725
    Bread1.8275

    so we have bread this morning.

  • influences:

    Representativeinfluence
    Minori11.0
    Yasushi4.625
    Ray3.5

    Minori has the most influence for deciding breakfast.

Math

based on [1]. ref pp 141-148

\[ \ A_{t+1} = VA_t \]

where the \(V\) is the voting matrix and \(A_0\) is \(I\). when \(A’\) is the result with enough recusive operations that convergeses, the vote result is.

\[ \ a_i=\sum_{j=1}^{M} A’_{ij} \; \textrm{for all} \; i \]

the infulence of each member can be calculated by:

\[ \ \frac{\sum_{j=1}^{H} \sum_{t=0}^{\infty} A_{ij}(t)}{\sum_{t=0}^{\infty} A_{ii}(t)} \; \textrm{for all} \; 1 \leq i \leq H \]

code can be found at github

Reference

  1. なめらかな社会とその敵 - Ken Suzuki