Best posts made by ChocoPi

I'm just going to recenter that the entire basis of Approval as an effective and potentially-immediate compromise is that it doesn't require new ballots, machines, meaningfully different LEO procedures, noteworthy voter education, federal process certification, revised audit procedures, etc.

You just flip a switch. Uncheck the "discard overvotes" box, rewrite one sentence on the instructions line (in each language), and make sure the LEO guidance on tabulation reflects all this. The end. $0.

Extending the proposal to anything that actually requires a new ballot/process/everything defeats the entire point of the exercise. For that implementation cost, you could do practically any constitutionally valid single-winner system.

@casimir

A BTR monotonicity failure is pretty specific (4+ cycle dependent) and requires a plurality (first-rank) standing like so:

1. Paper Sr.
2. Paper Jr.
3. Scissors
4. Rock

The Paper candidates are both currently relying on Rock to take out Scissors early for them.

However, if some of Paper Jr. supporters switch their first-ranks to Paper Sr. (with no other changes) the first-ranks may now look like this:

1. Paper Sr.
2. Scissors
3. Paper Jr.
4. Rock

In this new ordering, Paper Jr. takes out Rock early, preventing Rock from taking out Scissors. Now Scissors wins.

This is, of course, an extremely specific scenario--and a good illustration of why focusing on absolute criteria is misleading. No one should care that something like BTR or Stable Voting are non-monotonic one-in-a-gazillion elections.

(On the other hand, competitive partisan primaries are egregiously non-monotonic all the time and no one bats an eye.)

@jack-waugh

Sort of; engineering is famously quantitative, wrestling with the myraid and complex nuances of reality. Most engineering constraints are built on pragmatic operational assumptions, like a realistic range of environmental conditions.

Constraints compete with standard criteria when they are too broad or abstract--"there should be absolutely no radioactive material allowed on premise" without specifying a tolerable level is banning all foods containing potassium, such as bananas. A set of food safety guidelines that that obsesses about radioactivity instead of saturated fat, processed sugars, overall caloric intake, or the many other more relevant factors would be pretty useless. So would a set of dietary standards asserting one-size-fits-all solutions that do not account for one's age, body composition, physical activity, or health conditions.

In programming, we see this with algorithm analysis a lot. Much academic emphasis is placed on a complexity classes on various algorithms, such a proving that mergesort has a O(n log n) worst-case performance while quicksort suffers from O(n^2). Yet in most empirical applications a software engineer knows they can get better performance out of a quicksort; the lower memory usage significantly decreases the circumstances that would require cache misses. (Just as your procedure for sorting papers might change depending on the size of your desk or how many hands you can use; these "harder" and more relevant constraints might be overlooked if one is fixated on comparison efficiency in a theoretical vacuum.)

So that brings us back to voting.

One of the more classic "absolute" criteria is participation: "Your participation in voting (at all) must never hurt your favorite candidate(s)."

The issue is that reality fails the participation criterion.

A Condorcet cycle is a thing that could conceivably exist in reality--it's super rare, but it could. And if it does, it's a consistent truth in that reality regardless of how you count the votes--it's a property of the electorate, not the method of measuring it.

And whenever there is a Condorcet cycle, it's possible that your vote for Scissors > Rock > Paper could be the pivotal deciding vote that makes everyone realize that Paper doesn't beat Rock. If this new information you have provided reveals that Rock beats everyone, your vote implies Rock should win--even if Scissors (your favorite) was winning before.

Any method sufficiently sensitive/accurate enough to reflect the possible existence of cycles in reality will automatically fail the participation criterion. This means that all Condorcet methods fail the participation criterion and all methods that pass the participation criterion must willfully ignore the possibility of cycles.

Another similar criteria is monotonicity--does improving your vote for a candidate never possibly hurt them, and reducing it never possibly help them? This one is more complicated. Methods that eliminate candidates one-by-one are typically non-monotonic. However, eliminating candidates one-by-one grants the most resistance to strategy and full immunity to clones.

Broadly speaking, I believe the latter is more important than monotonicity, and by several orders of magnitude. This is in part because simply being non-monotonic does not automatically imply a certain frequency of non-monotonic violation. I mentioned that BTR and Stable Voting are technically non-monotonic (both eliminate candidates one-by-one after all), but the odds of either exhibiting a non-monotonic situation are nearly astronomical. (And zero unless there are 4+ competitive candidates, or if the electorate preferences are single-peaked.)

I also mentioned the partisan primary elephant-and-donkey-in-the-room. It's frankly exhausting to discuss monotonicity's relevance in rare edge cases when our existing competitive partisan primaries are outright non-monotonic around a full 33% of the time. (That's about how often some of the primary votes hurt themselves, and would be ultimately more effective if cast "backwards" for candidate(s) in the other party.)

It's like hearing people argue over which brand of premium gas to buy for their car, when they are 6000 miles overdue for an oil change.

@jack-waugh

BTR with a cardinal ballot is the functionally the same as BTR with a ranked ballot so long as you have enough score options to distinguish all candidates. It will only resolve differently in cases where you both have a cycle and the ordering of iterated scores is different than iterated top-ranks, which is extremely specific.

And BTR is, pretty good. It's natural results are identical to Smith//Plurality outside of a 4+ cycle. This means the strategy resistance is the same as Smith//Plurality with 3 competitive candidates, and similar-but-slightly-better with 4+. It's functionally cloneproof and effectively monotonic.

I would categorize BTR as a hybrid method, and it continues a pattern of virtually all serious hybrid methods holistically outperforming all non-hybrid methods. Hybrid vigor truly is the law of the jungle.