# Quadratic Range Voting

Persistent Voting fundamentally alters the dynamics of group decision making. Persistent Voting however only addresses the schedule in which elections are conducted, but not how the votes are solicited or counted. This means Persistent Voting is merely a container for some other "inner" voting method, which we also must select intelligently, taking care to make sure it optimally interacts with the persistent schedule.

My best idea so far for an optimal method is one I've named Quadratic Range Voting.

## Description

Quadratic Range Voting is simply a combination of Quadratic Voting and Range Voting (and its simplest variant Approval Voting).

• At any time, a polity would have some set of elections, and each voter some finite number of Quadratic voting "weights". I call them weights rather than credits since the persistent schedule means voters allocate weights rather than spending them, so they always have the same fixed amount at any time.
• To cast a vote in an election, they must place at least one weight on that election, which allows them to cast a traditional range ballot in that election, giving some candidates a score on a positive fixed scale (such as from 0 to 10). Separately, they can place another weight to cast a negative range ballot to give candidates negative scores on the same fixed scale. Requiring separate weights for positive and negative weights is done to neutralize a potential strategy I'll discuss later.
• The final amount of votes given to any candidate for any ballot is defined as: `votes = score * sqrt(weights)`. This means the voter can increase the strength of all the scores on their ballot for an election by placing more weights on that ballot, but in a quadratically limited way. This is done separately for positive and negative ballots.
• At any time, voters could place "nomination" weights on specific individual candidates to nominate them for a particular election, with some as yet undetermined rule for how much weight a candidate would need to enter the election. Voters could also place "anti-nomination" weights that count against an individual candidate, potentially causing them to be removed from the election if they at any time fall below the entry threshold.

## Benefits

• This voting method quite nicely combines the expressiveness and resistance to voter strategy of Range Voting with the balancing of preference intensity of Quadratic Voting. Range Voting is intentionally chosen because of its "consensus candidate" bias, with the intent on producing welfare-optimizing and democratically legitimate outcomes.
• Separating negative votes both in nomination and scoring retains the high expressiveness of Quadratic Voting without incentivizing highly strategic votes in which a voter marks even neutral candidates as negative.
• The weighted nomination process keeps elections from becoming noisy and crowded, and likely discourages some potential instability which could arise in persistent voting.
• Separating nomination and scoring likely nicely mirrors the real patterns of voter behavior. Issues almost always have a small number of activists and a much larger number of less passionate voters who merely wish to express which candidates they find acceptable. Only occasionally do voters have positive or negative outliers.

## Potential Objections

• The method is quite complicated, partially due to the persistent schedule, but also merely by itself.
• Mixing a more "honest" method with Quadratic Voting might be unnecessary, since the entire statement of Quadratic Voting embraces a voter's strategic thinking to guide them towards decisions where their input is more likely to be pivotal, making the mechanism more market-like. However I feel for democratic legitimacy and consensus building reasons, a more expressive method would fare better with a real electorate.

## Open Questions

• Is a nomination threshold actually beneficial? If so, what rule can we select that won't be arbitrary? How do the candidate incentives of the election change with different nomination rules? If we use a nomination threshold, should nomination votes in excess of the threshold count toward a candidate's votes? Should they be scaled in some way? In what direction? By how much? To balance the strength of nomination weights relative to those placed on score ballots, should they be scaled in some way, or required to remain "locked" for some period of time where they can't be moved?
• What voting strategy is optimal for voters in this system?
• What types of result will elections tend to converge toward, if any?