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The default voting system will be token-based quorum voting. A quorum means a minimum number of available votes are required to pass. IE if a quorum is set to 50%, and there are 100 total votes, then at least 50 votes must be cast or the proposal automatically fails. Once the quorum threshold is reached, the decision with the most votes wins.
This type of voting mechanism can be difficult to get right, because if you reduce the quorum percentage to increase scalability, requiring fewer voters to pass proposals, resiliency is reduced by making it too easy to push through malicious or just ill-conceived proposals. Paideia will have balanced default values, but DAOs can adjust these through proposals after inception if they find their settings aren’t working well.
Quadratic voting uses a calculation to optimize voting power so that if, for example, 10 voters have 1 vote each, that will count for more than if 1 voter submits 10 votes. This works well for DAOs to prevent wealthy whales from controlling all the decisions.
[The] number of contributors matters more than [the] amount funded. This pushes power to the edges, away from whales & other central power brokers, [which] creates more democracy in public goods funding decisions! 🦄 
Quadratic voting is a setting that can be chosen at DAO initiation, or added later through a proposal.
Voters can allocate their entire voting power to one choice. This is the default and typical voting mechanism.
Voters may select multiple choices, and their voting power is spread equally between each choice.
In IRV, voters rank their favorite option as first choice and then indicate their second and additional back-up choices in order of preference. Votes are counted in a series of rounds to ensure that as few votes as possible are wasted.
In each round, one of two things happen: either a winner is found, in which case all votes in excess of the requirement to win will be redistributed to each voter’s second choice, or no winner is found and the lowest voted choice is removed, in which case those voter’s votes are redistributed to the next choice on their list.
The election threshold (how many votes required for victory) is determined mathematically based on the guarantee that that selection can’t lose.
Eg: three options to be selected would make the winning threshold 25%, since if one option had more than 25% of the vote, it’s impossible for three other options to get more votes than it, because that would add up to more than 100% of the votes. With four options, it’s 20%, and 17% for 5, and so on.
Any options that exceed the election threshold will be elected that round. Any votes above that threshold go to the totals of the next option on those voters' lists.
If no option has more votes than that threshold, the one with the fewest votes is removed and the next option on those voters' lists is used in the next round of counting.
How does this work for a DAO? One example would be if we had a specific budget in mind, and a few choices to spend it on. For instance, perhaps there is $10k in the treasury and we'd like to spend $5000 on marketing, $5000 on development, and $5000 on redistribution to DAO members. You could setup ranked choice voting, and each voter could rank their favorites. The top 2 would receive the funds.
With Paideia, there will always be a "No" vote as well. If you'd rather the DAO not spend those funds on any of those options, or you think the numbers don't make sense, you can say that in the discussion and vote down the proposal entirely.