AQB & Minimum Quorum

One of the most important aspects when designing a governance system is to specify under which circumstances a proposal can pass. Intuitively, a vote will pass when there are more voters in favor of the proposal than voters against it. But how many yes votes are needed?

The simplest option would be to tag a proposal as passed whenever there are more yes votes than no votes. However, this approach would not take the level of participation, or quorum, into consideration. In the case of a low voter turnout, the legitimacy of the result could be questioned.

The immediate solution is to impose a minimum quorum threshold. This mechanism imposes a minimum level of participation, such that proposals with a level of participation below the quorum threshold would be automatically marked as failed.

Although the minimum quorum threshold effectively prevents proposals that lack sufficient support from passing, it lacks flexibility. For impactful DAO decisions, a substantial voter turnout is essential, and thus, setting a high minimum quorum is justified. Conversely, imposing a high quorum for less impactful proposals could hinder their approval due to lower voter interest and participation.

Introducing AQB

The Adaptive Quorum Biasing mechanism, or AQB, excels in providing flexibility for voting processes. AQB sets a dynamic threshold for the number of affirmative votes required for a proposal to pass. This threshold adjusts based on voter participation levels, lowering the threshold as voter turnout increases to enhance the vote's legitimacy.

The exact threshold depends on three factors: the number of yes votes, the number of no votes and the number of possible votes (also called electorate). Specifically, it is controlled by the following relationship:

q=yeselectorateβˆ’noyes+noq = \frac{yes}{ \sqrt{electorate} } - \frac{no}{ \sqrt{yes+no} }

In the formula above, the value of q represents whether a proposal has passed or not. A positive q indicates that the proposal passed, while failing proposals result in a negative q.

Let us illustrate the working mechanism of AQB by providing a series of examples. For the sake of simplicity, in these examples, we will assume that there are 100 people entitled to vote, all with equal voting power.

Scenario A: 40 yes votes, 20 no votes, 40 not voting

In this first scenario, we can see that there were double the amount of yes votes than no votes. Also, there was a healthy 60% voter participation, this should likely result in the proposal passing. Now to input these numbers into the AQB formula:

40100βˆ’2040+20=1.418\frac{40}{ \sqrt{100} } - \frac{20}{ \sqrt{40+20} } = 1.418

As expected, the formula yields a positive value and a passed proposal.

Scenario B: 20 yes votes, 10 no votes, 70 not voting

Note that in this second scenario, there are also double the amount of yes votes than no votes. However, only 30% of the eligible voters participated in this poll. This result has less legitimacy than the previous one, as the opinion of a majority of voters is unknown. Should this proposal pass? The AQB formula can assist us here.

20100βˆ’1020+10=0.174\frac{20}{ \sqrt{100} } - \frac{10}{ \sqrt{20+10} } = 0.174

The proposal has been approved, but we are approaching the critical threshold. Consider the scenario where 6 out of these 30 voters had neglected to cast their votes.

Scenario C: 16 yes votes, 8 no votes, 76 not voting

The engagement in this poll has declined noticeably. Only 24% of the electorate participated.

16100βˆ’816+8=βˆ’0.032\frac{16}{ \sqrt{100} } - \frac{8}{ \sqrt{16+8} } = -0.032

This proposal will not be passed. Despite receiving twice as many yes votes as no votes, the low level of participation undermines the legitimacy of the voting outcome.

As we have seen, this proposal failed even if there were 66.6% of yes votes. But as indicated by the very small negative q number (-0.032), it was close to the AQB threshold. In fact, if just a single of the voters who voted no had voted yes, the outcome of the proposal would have been different:

17100βˆ’717+7=0.27\frac{17}{ \sqrt{100} } - \frac{7}{ \sqrt{17+7} } = 0.27

This means that with 24% of participation, the effective threshold for a proposal to pass is higher than 66.66% at 67.11%.

Considering these scenarios, one might be curious about the extremes. Let's look at a few.

Scenario D: 100% Participation

In the case where all the electorate had shown up to vote, the intuitive expectation is that the proposal would pass if there were more yes votes than no. A quick look at the formula confirms this expectation:

x100βˆ’100βˆ’x100β‡’x=50\frac{x}{ \sqrt{100} } - \frac{100-x}{ \sqrt{100} } \Rightarrow x = 50

Scenario E: 5% Participation

On the other hand, in the event that the voter turnout is poor, the intuitive expectation is that the proposal would pass if there is full consensus among the participants. Again, a quick look at the formula confirms this expectation:

x100βˆ’5βˆ’x5β‡’x>4\frac{x}{ \sqrt{100} } - \frac{5-x}{ \sqrt{5} } \Rightarrow x > 4

Indigo’s hybrid approach

Scenario E described above makes it clear that with 5 participants or less, a full consensus among the participants would be needed. However, it also uncovers a valid concern. What if, for whatever reason, voter turnout was low in a mission-critical proposal? Should a single voter be able to make a decision on behalf of the whole electorate?

The AQB formula indicates that if there is only one voter, a single yes vote would suffice for a proposal to pass. At Indigo, we find this insufficient, recognizing several valid reasons why a proposal might not receive votes from interested parties. For instance, the website from which most people vote could be down after only a few votes have been casted. This could result in a very unfair outcome for the proposal.

This is why Indigo adopts a hybrid strategy that blends the minimum quorum with AQB. For a proposal to be approved, it must satisfy two criteria: the AQB formula must produce a positive q number, and the minimum quorum requirement must be fulfilled.

Thanks to the effectiveness of AQB, the minimum quorum can be maintained at a relatively low level, serving primarily as a safeguard against unforeseen circumstances. Once this security threshold is met, the AQB takes the lead in determining whether a proposal is approved. With great power comes great responsibility!

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