Voting power needed for DAO/DO decisions

In the latest DAO design jam, we discussed voting systems, and how to make decisions. It was good, but a bit less focussed than i’d like.

Every decision is sort-of a vote, it is just from a single person. The question is how much voting power is needed for a decision. I reckon it is affected by the following:

(1) Utility of outcome

I think the utility is sub-linear relative to units of money or other assets. If utility is some function U(A) where A is an amount.

A simple model is a set cost and binary outcome with probability p is a result with B for bad, G for good and initially I. A rational agent decides to go for a decision if: p < (U(G) − U(I)) / (U(G) − U(B)). Where U is the sublinear function with U'(x)>0.

If you look at that model with U(x)=x, you see a problem that the absolute values dont matter, which does not make sense. Sublinearity doesnt explain it, because the function will be approximately linear given small values relative to the total.

The reason this happens is that investing more into something, you get diminishing returns from the extra investments. By investing more B decreases but G doesnt increase much more.

(2) Chance of stolen private keys and ‘betrayal’

Higher levels of stake increases the chance that stolen private keys, for instance.

‘Betrayal’ could be simple theft, or much higher level.

(3) Fairness of ability to use risk−taking ability

People that are first to try take some risk with the DO/DAO assets arent the ones that should.

(4) Voting frequently shouldnt increase your effective voting power

However, not voting much should only accumulate to some point. This is not only from the point of view it doesnt give you more power, it is also that if someone makes multiple decisions, the failure/success of them cannot assumed to be independent, so the distribution of outcomes wider.

(5) Getting decisions through should not be overly hard

Of course, this is largely a trade-off between security, efficiency of people who have to learn about the topics, and democracy, decentralization of decision taking.

An approach

Perhaps take this approach with a grain of salt. It favors utility as seen by voters over representation.

The idea is to take the equation, and have classes of decision with a cost C, potential benefit βC, and then each voter has voting power n corresponding to a ‘probability to be wrong’: pn then the equation is used to decide:(same as above)

p∑n < (U(I + βC) − U(I))/ U(I + βC) − U(I − C)

That does not completely describe it though, as it doesnt take care of all the issues.

(1) Take account of the sublinearity

This means we need to figure a U that represents it well. This is hard, but then, the value of the things decided about itself is also hard to estimate.

U can be dependent on the current state. For instance for a ‘conservative’ U, any possibly lowering value is taken as very negative, making it very risk averse. However, in my opinion this does not make sense; there are reasons for being conservative in cases, whereas building it into U means you just presume it.

Three reasons being those diminishing returns, and ability to assess choices, and managing culture/ability in expansion. Some do relate to the state, for instance if more people are involved ‘low on funds’ is more money.

(2) Voting that pay just yourself isnt possible, ≥2 voters

Of course big changes may necessarily affect the voters themselves directly, so those are allowed, however for smaller ones, you should have to convince someone else.

Secondly perhaps there should be some review of decisions. Formal or informal, but it must be possible to find review from the decision itself.

For stealing of keys, well you could simply depress the voting power a bit, and try keep things secure as much as possible.

(3) Keep risk-taking ability in reserve

When any other combination can produce a ∑n, that cannot be done due to the staked amount, the vote either requires more voters so that is no longer true, or the vote is prolonged, for long enough for other approaches to compete, and then the winner is the one that passes through the main rule with the highest ∑n. (possibly there is an automatic notification when this happens)

This is triggered if below becomes true if the decision were accepted:

∃ n ≤ remaining: pn < (U(I + βr⋅n) − U(I))/ U(I + βr⋅n) − U(I − r⋅n)

Of course ‘do nothing’ should be an option in such a election of choices.

(4) Voting power is used, and grows back with time after use

Simplest is to have it just increase linearly with time up to a limit. More complex approaches, like increasing logarithmically, or reaching toward a limit are options aswel.

(5) Giving voting power to others

However, i reckon there should be a limit. The possibility of strong voters getting their private keys stolen must be dealt with. One obvious way to deal with it is to simply instruct/invest in increasing the security of those private keys.

However, i feel the need to compensate nevertheless. p being the probability that the voter is wrong or that somethings else happened. I.e.

p = P(Wrong ∪ Other) = P(Wrong) + P(Other) − P(Wrong ∩ Other)

p = pw + po − pw⋅po

Where it is assumed the two are independent. You can only pass along the bit of your vote that is given by your mind, not your loyalty or private key.

Instead of using pn, we keep track of pwn that way instead;

pn → pwn + po − pwn⋅po

And multiply these numbers from different people together. If po becomes limiting, security might be improved, maybe some background checks to warrant an increase.

Many parameters

The above approach needs to figure out quite a few parameters and functions; the utility, U(A). For the fairness mechanisms β, and r. The classes of decisions are also open, and may affect p=p(C) too.

p and the total amount of voting power given n is given too. Assuming U is at a point approximately linear and p=0.5 and someone has vothing strength n=1, if he had an action that paid out ×2 the input, he alone vote to do that action.(except the ≥2 rule) So p cant quite be the probability a person is wrong in this approach, unless you give people too much power, or think they are ridiculously unlikely to be correct about anything. It really is just a cumulative voting power n, and each sort of decision needing some amount, and there is interpretation with probabilities. (though it comes out a lot when you modify it for po.

Caveits of this discussion

Suggestions are welcome, also wholly different approaches. I tried not being ad-hoc, but that isnt a prerequisite, imho an approach should either start from principles or be simple.

The voting mechanism in the competition case is completely open. The ‘simple’ approach may cause spoiler effects, but i tend to think it is adequate for the forseeable future.

A single parameter of voting power (two if you count po) probably doesn’t capture enough of the situation? There is little respect for who knows what. A DO/DAO might have different stakeholders and knowledgables on different topics, so it is possible to give people different voting power about different things.

More can be said on for instance:

  • Decisions having effect on voting powers.
  • Reviews of decisions.
  • The role of communication. I suppose there could be a ‘second voting power’ about bringing up ‘mandatory’ discussions/responses.
  • Decisions that have continuous effect after, rather than just going one or another way.

It would be nice if there was a way to make votes anonymous. (also against timing analysis) It would make robust against buying votes and threats.