In a vodle poll, each participant gives each option a “wap” (willingness to approve) between 0 and 100.
Based on all waps, it is calculated who “approves” which options: if i gave x a wap of r, then i approves x iff less than r% of all participants do not approve x (this coupled system of inequalities has a unique largest solution, which vodle uses).
Based on who approves what, the “share” of each option is calculated: x’s share is the fraction of participants who approve x but approve no other option y that is approved by more participants than x. In other words: each participant “owns” an equal share, and a participant’s share goes to the most-approved option among those approved by that participant.
If the poll is about distributing a budget, each option gets their share of the budget.
If the poll is instead about picking a single winner, the winner is determined by a lottery in which each option’s winning probability equals its share.
Rationale: By giving suitable waps, participants can make sure their share only goes to a good compromise option if others’ shares also go to that option. One can show that this possibility of “conditional commitment to approve” makes sure that if there is a good compromise, it will win with certainty in a strategic equilibrium between rational participants. Majoritarian methods like Plurality Voting, Approval Voting, STAR Voting, Instant Runoff Voting, Score Voting etc. cannot guarantee this whenever one faction has a majority (if only a slight one) and has thus no incentive whatsoever to seek a compromise with the other participants.
I mean, I think it is, but I need to understand it more fully. I just really like the tricks so far, and haven’t evaluated what they’re optimal for yet. :P
if i gave x a wap of r, then i approves x iff less than r% of all participants do not approve x
A wap is a measure of how much you’d be willing to let your approval of x override others’ underapproval of x? (Where “underapproval” is just assigning a wap<r)
Does the method have a name? Is it similar to anything else? The % conditional approval thing has assurance-contracty vibes, but it does more.
The method is named “Maximum Partial Consensus (MaxParC)” in the paper.
The exact meaning of giving a wap of r to option x is really just the following binding conditional commitment: “I commit to approve x if and only if less than r% of the participants do not approve x”.
All the waps for x together form an interdependent system of conditions, which has a “largest” solution in the sense that there is a unique largest set of participants such that if all of them approve, then everyone’s condition for approval is met.
One can find this solution easily with pen and paper as follows: sort all waps for x in ascending order, draw a diagonal like in the screenshot below, and find its leftmost intersection with the wap distribution. Then all participants with waps to the left do not approve and those with waps to the right do approve.
In the GUI, one can see whether one approves by checking whether one’s wap slider intersects with the light approval bar, as in this screenshot from the EA-related demo poll posted earlier:
Is there a quick summary of the mechanism somewhere?
Yes:
In a vodle poll, each participant gives each option a “wap” (willingness to approve) between 0 and 100.
Based on all waps, it is calculated who “approves” which options: if i gave x a wap of r, then i approves x iff less than r% of all participants do not approve x (this coupled system of inequalities has a unique largest solution, which vodle uses).
Based on who approves what, the “share” of each option is calculated: x’s share is the fraction of participants who approve x but approve no other option y that is approved by more participants than x. In other words: each participant “owns” an equal share, and a participant’s share goes to the most-approved option among those approved by that participant.
If the poll is about distributing a budget, each option gets their share of the budget.
If the poll is instead about picking a single winner, the winner is determined by a lottery in which each option’s winning probability equals its share.
Rationale: By giving suitable waps, participants can make sure their share only goes to a good compromise option if others’ shares also go to that option. One can show that this possibility of “conditional commitment to approve” makes sure that if there is a good compromise, it will win with certainty in a strategic equilibrium between rational participants. Majoritarian methods like Plurality Voting, Approval Voting, STAR Voting, Instant Runoff Voting, Score Voting etc. cannot guarantee this whenever one faction has a majority (if only a slight one) and has thus no incentive whatsoever to seek a compromise with the other participants.
See the theory paper for details.
This is awesome!
I mean, I think it is, but I need to understand it more fully. I just really like the tricks so far, and haven’t evaluated what they’re optimal for yet. :P
A wap is a measure of how much you’d be willing to let your approval of x override others’ underapproval of x? (Where “underapproval” is just assigning a wap<r)
Does the method have a name? Is it similar to anything else? The % conditional approval thing has assurance-contracty vibes, but it does more.
The method is named “Maximum Partial Consensus (MaxParC)” in the paper.
The exact meaning of giving a wap of r to option x is really just the following binding conditional commitment: “I commit to approve x if and only if less than r% of the participants do not approve x”.
All the waps for x together form an interdependent system of conditions, which has a “largest” solution in the sense that there is a unique largest set of participants such that if all of them approve, then everyone’s condition for approval is met.
One can find this solution easily with pen and paper as follows: sort all waps for x in ascending order, draw a diagonal like in the screenshot below, and find its leftmost intersection with the wap distribution. Then all participants with waps to the left do not approve and those with waps to the right do approve.
In the GUI, one can see whether one approves by checking whether one’s wap slider intersects with the light approval bar, as in this screenshot from the EA-related demo poll posted earlier: