Group Negotiation

Vitalik Buterin defined DAOs as "a virtual entity that has a certain set of members or shareholders which, perhaps with a 67% majority, have the right to spend the entity's funds and modify its code.”

But those consensus mechanisms are inefficient for numerical parameter decision making (ex Price / amount). This inefficiency is due to the increase in complexity in all types of negotiations when the number of participants increases. Groups avoid this kind of negotiation or do it behind closed doors in a centralized way. This paper highlights the complexity of decision making and introduces a collaborative way to reach agreement on the parameters that satisfy the parties involved. This will lead us to present the consensus mechanism for groups on numerical Parameters based on the median mechanism developed by Manda.

1. Complexity of negotiation increases when number of participants increase

If we consider group-to-group bargaining, where there are many participants, complexity grows with the square of the number of participants (we say it's O(N^2), where N is the number of people). This happens because every participant needs to think about their strategy in relation to every other participant, which makes things more complex as the number of participants grows.

3 ways of negotiating a price with a group: top down, bottom up or a mixture of both.

• Top-down approach: One proposes, the rest vote yes or no.

• Bottom up approach: Every participant of the group proposes his preference in a simultaneous or sequential way

• Flexible Top-Bottom approach: Every participant of the group delegate his preference in a simultaneous or sequential way

Often, DAO contributors have raised their voices about the feeling of not being represented by one proposal maker. Hence, sometimes the top-down approach is not ideal. See the communities contention around the price discovery in the FEI and RARI merger.

2. Complexity of a negotiation increases when number of possible agreements increase

One way to measure the complexity of a negotiation is by looking at the number of possible agreements (or 'states') that could be made.

For example:

If each person in a negotiation can either say 'yes' or 'no' to a proposal, then there are 2^n possible states for a negotiation among n people. This is because each person adds an additional bit of information—yes or no—to the negotiation, doubling the number of possible states.

However, negotiations often involve more than just a binary yes/no decision. If there are m options for each person to choose from, the number of possible states becomes m^n. For example, if each person can choose to acquire a good at price p in R+, p can take any of m different prices, then there are m^n possible states. This number grows extremely quickly as n and m increases.

As these numbers grow, the negotiation becomes increasingly complex, and it can take longer to reach a consensus (if one can be reached at all).

Liquid democracy, sometimes referred to as delegative democracy, aims to provide a flexible, responsive system of governance that empowers individuals when solving complex problems. With a fluid delegation process, it aims at reducing the number of n participants to reduce the number of possible states.

In the two other bottom-up-ish approaches, we will differentiate between a sequential and a simultaneous bargaining session.

Bargaining is when two or more parties negotiate terms and conditions, often related to a deal or agreement.

Sequential bargaining is like a tennis match - one player serves an offer, and then the other player returns with a counteroffer. The process continues back and forth until both players agree. An example of this in the literature of bargaining games is the Rubinstein bargaining model.

On the other hand, simultaneous bargaining is when all players make their offers at the same time, like playing the game of Odds where on the count of 3, you shout a number between 1 and 10. This method usually gets to a resolution quicker and simpler than the sequential way because everyone's offers are on the table right away.

3. Convergence time of sequential vs simultaneous bargaining method

Let’s assume it takes x amount of time for a person to react to a proposal. In a sequential model, you will have to wait n number of rounds times x. In a simultaneous model, you only have to wait 1 time x.

Manda introduces a flexible bottom-up mechanism where every actor can vote and express their voice on all sorts of parameters (like which asset to buy or the amount ready to be invested).

The Proposal maker decides the satisfaction criteria, the minimum participation Quorum, the % of satisfaction to reach and the price selection method, and if the parameters are set according to the DAOs requirement, then it is good to go!

Our infrastructure can be adapted to any type of voting power distribution, 1token-1vote; quadratic mechanism, 1wallet-1vote…

The geometric median will be the first available voting rule to be tested. The Geometric Median is an often used mechanism in capturing the Wisdom of the Crowd.

4. The Geometric Median as voting rule and it’s properties

In bargaining theory and voting, the solution to the Weber problem - the Geometric Median - can be seen as an optimal outcome. It represents a compromise that minimizes overall discontent.

Voters choose points in a space, symbolizing their preferred outcomes. The Geometric Median of these points minimizes the sum of the distances to all chosen points, yielding a compromise that reflects the least collective discontent.

Key properties include:

1. Existence: For any finite set of points in a Euclidean space, a Geometric Median exists.

Proof: The sum of Euclidean distances to a set of points is a continuous, strictly convex function, which means it has a unique minimum.

2. Uniqueness: The Geometric Median is unique whenever the point are not collinear.

Proof: The function defined by the sum of distances to the points is strictly convex, and hence the minimum is unique.

3. Robustness: The geometric median has a breakdown point of 0.5 (or up to quorum). That is, up to half of the sample data may be arbitrarily corrupted, and the median of the samples will still provide a robust estimator for the location of the uncorrupted data.

4. Fairness: All voters with equal weights are treated equally. Swapping two votes of equal weight does not change the Geometric Median. The function defined by the sum of distances to the points is symmetric, so swapping points does not change the minimum.

Limitations of the geometric median:

1. Efficiency: The Median Voting Rule is not necessarily efficient. Efficiency in the economic sense often refers to Pareto efficiency, where it's impossible to make any one individual better off without making at least one individual worse off. In the context of median voter rule, it will select the preference of the median voter, which doesn't guarantee that the outcome is Pareto efficient. It simply reflects the preference of the median.

2. Incentive Compatibility: The Median Voting Rule is not strictly incentive-compatible. While voters have no incentive to misrepresent their preferences if they believe they are at the median, voters on either side of the median do have an incentive to misrepresent their preferences to push the median closer to their true preferences.

Next steps:

1. What are the strategic properties of the median of medians? Is it strategy proof for people to report their true value? If not, what is the equilibrium of this mechanism?

2. Under this equilibrium, what is the efficiency of the outcome relative to an omniscient social planner?

Conclusion

Manda is taking it as a mission to improve DAO toolings and governance planning by bridging the gap between social choice theory and DAO governance. Better tooling means more efficiency, which is a necessary step for DAO competitiveness and future mass adoption. Manda aims to connect DAO to the world by building the infrastructure for DAO operations with every kind of actor. With us, we connect DAO, with other DAO, with Traditional Organizations and with individuals.