"Quadratic voting: a more nuanced method of expressing preferred choice"

In quadratic voting, the cost of voting for an option increases quadratically with each additional vote, meaning that the marginal cost of each additional vote increases as more votes are allocated to an option.

For example, suppose a person has 10 votes and they allocate all of their votes towards a single option. If the cost of each vote is $1, then the first vote would cost $1, the second vote would cost $4, the third vote would cost $9, and so on. Therefore, if the person allocated all 10 votes to the same option, the cost would be:

1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = $385

This means that the average cost per vote is $38.50. In contrast, if the person allocated their votes evenly among 10 options, each option would receive one vote, and the cost would be:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = $10

In this case, the average cost per vote is $1. Therefore, allocating all 10 votes to a single option is more expensive than allocating one vote to each option, and it would result in the person's preference for that option being weighted as roughly the square root of the number of votes they cast for it.
In this case, it would be the square root of 10, which is approximately 3.16.
So, it would be reasonable to assume that allocating all 10 votes towards a single choice would equate to approximately 3 votes for that particular choice under quadratic voting.

Quadratic voting allows voters to express their preferences with greater nuance and granularity, enabling them to allocate more tokens to the options they care about most, while also allowing them to express their ambivalence towards options they feel less strongly about. This results in a more accurate representation of the collective preferences of the group, and it can lead to more effective decision-making.

This can help to create more balanced and equitable outcomes, especially in situations where there is a lot of disagreement or diversity of opinions.