Friday, May 23, 2025

Proposal: Instant Runoff - Just Add Water

If there is a rule named “Ranked Choice”, add the following text to it:

There is a publicly-tracked Winning Plan, which is either empty or the name of a Drafter’s Plan, defaulting to empty.

If the Winning Plan is empty, and a quorum of Drafters have a Ballot that has a value, and no Drafter has changed their Ballot in the past 48 hours, and the Supervisor has not performed an Instant Runoff within the past 48 hours, the Supervisor should perform an Instant Runoff, which is an atomic action with the following numbered steps:

# Privately track a copy of each Drafter’s Ballot. These privately-tracked copies are considered the Runoff Ballots for this instance of Instant Runoff.
# For each Drafter’s Plan, calculate that Plan’s Top Pick as the number of Runoff Ballots in which that Plan is allocated a 1.
# If there is a single Plan with a Top Pick at least equal to a quorum of Drafters, set the Winning Plan to that Plan and skip to the last step in this atomic action.
# If there are no Plans with a Top Pick of at least 1, skip to the last step in this atomic action.
# Select the Plans with the lowest Top Picks among all Plans as the Losers.
# For each Loser, remove it from each Runoff Ballot.
# For each Runoff Ballot, re-allocate the whole numbers in that Runoff Ballot such that the order of the Plans in that Runoff Ballot does not change, but the whole numbers allocated to each Plan in that Runoff Ballot are contiguous starting at 1.
# Go to step 2.
# Make a Story Post stating the contents of the Winning Plan, and if the Winning Plan is not empty, the Drafter who authored that Plan.

If the Winning Plan is not empty, the Drafter who is the author of the Plan named in the Winning Plan has achieved victory.

I think I got the algorithm correct, but double check and make sure that I did. I’ll revise if not.

Comments

DoomedIdeas: he/him

23-05-2025 20:48:13 UTC

Wouldn’t this have an issue wherein Plan A could be everyone’s second choice, and Plan B is dead last except for one player who puts it as their top choice, meaning Plan A gets out before Plan B despite being more universally popular?

DoomedIdeas: he/him

23-05-2025 20:50:40 UTC

For another option: Instead of calculating Top Pick via number 1 picks only, it might be a bit more fair to give each plan a number based on overall ranking (Reverse the orders and add them up, perhaps?) and then remove the bottom most plan and perform the same steps you described until one is left.

ais523: Supervisor

23-05-2025 21:04:58 UTC

@DoomedIdeas: It’s been mathematically proven that every voting algorithm based purely on ranked choices has some sort of undesirable bug of that nature, so it just comes down to what sort of bugs you’re’ willing to tolerate.

Josh: he/they

23-05-2025 22:23:59 UTC

for

Josh: he/they

23-05-2025 22:24:53 UTC

D’Hondt would be slightly fairer but not worth the extra maths.

DoomedIdeas: he/him

24-05-2025 00:12:01 UTC

for

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