Posts made by cfrank

This post may be outside the scope of this forum, but I wanted to see what others thought. If this is derailing, let me know, and I’ll consider removing it.

I had a few ideas targeted to address abuses of presidential power in the form of pardons and court packing.

The idea is relatively simple: disable the current sitting executive from both initiating and finalizing pardons and court appointments.

Suggestion for judicial appointments: In the event a Supreme Court justice dies or resigns, the current sitting president should be allowed only to fill the vacancy until the following presidential election. Lifetime appointments should only be made for seats that were vacated during the previous presidential term. This should also hold for any expansion of the number of seats.

Suggestion for pardons: Presidents should be allowed to initiate clemency for federal crimes, and the clemency will be probationally enacted until the subsequent president opts in to finalize clemency. Clemency that fails to be approved by the subsequent president by the end of their term will be voided. This preserves the immediacy of pardons while disabling unchecked permanent clemency.

Obviously, each would require a Constitutional Amendment.

Food for thought.

@poppeacock a Condorcet method is defined in terms of the notion of a “Condorcet winner”, which is a candidate that beats every other candidate in a majoritarian head-to-head match up, also called a “beats all” winner. There can be at most one Condorcet winner in an election; however, there are pathological cases when a Condorcet winner does not exist at all, caused by what are known as Condorcet cycles.

The classic example is three voters using rank ballots over three candidates:

V1: A>B>C
V2: B>C>A
V3: C>A>B

You can see that A>B 2:1, B>C 2:1, but C>A 2:1. So A>B>C>A is a Condorcet cycle, which is a generalized “rock-paper-scissors” situation. Whichever candidate you choose as the winner, there is some majority of the voters who would have preferred a different candidate. That’s the unfortunate thing that happens when a Condorcet winner doesn’t exist…

Regardless, a Condorcet method is any method that guarantees electing the Condorcet winner when one exists. Condorcet methods differ in how they reconcile choosing a winner when the Condorcet winner does not exist, I.e. in effect how they determine which majority group(s) to jilt.

So for example, if Ranked Robin doesn’t specify how it resolves when there is no Condorcet winner, then it’s really a blanket term for Condorcet methods in general. Or maybe it’s a label for a particular curated subset of Condorcet methods.

There are many Condorcet methods, including Ranked Pairs, Schulze’s method, Copeland’s method, Minimax, and Bottom-Two-Runoff (by Tideman).

I like Bottom-Two-Runoff because it’s efficient and also equivalent to a seemingly (but not actually) more robust system: https://www.votingtheory.org/forum/topic/564/bottom-n-and-bottom-2-runoffs-are-equivalent

@poppeacock I see, so the site is using “Ranked Robin” as the umbrella term for any Condorcet method?

@jack-waugh I agree, PR is probably preferable in many ways to alternatives. Still, I think we’re too entrenched in the way our current system works and it may be most effective to start by modifying single-winner systems, specifically transitioning from choose-one plurality to approval plurality.

@poppeacock yes it seems to be a rebranding of Ranked Robin; from your link:

“Carmen won the most match-ups against other candidates, so she is elected the winner.”

I do notice often that these pro- rank-based voting sites almost never address the issues with reconciling the possible nonexistence of a Condorcet winner.

Is the main advantage of Ranked Robin over other Condorcet methods that it is precinct summable?

@jack-waugh it definitely conforms to Frohnmeyer balance, what is Shentrup balance?

Unfortunately it fails participation as any Condorcet method must. I think Condorcet is also incompatible with favorite betrayal, that may need checking.

@sarawolk I can envision a natural progression as: (1) implement straight approval, (2) eventually indicate the shortcomings of approval in guaranteeing election of Smith set candidates, (3) reform to include a ranked primaries to restrict to the Smith set before the final approval vote.

I agree it is not feasible to implement the kind of change needed for the mentioned kind of system all at once.

If approval were established somehow, the (rational, IMO) debate relevant to (2) and (3) would probably be about majoritarianism versus participation and maybe some tactical considerations.

Your point about tie-breaking is fair. For example, why not use Bucklin voting restricted to the Smith set, adjusting ranks to include only those candidates, which is similar to your suggestion. One major reason in that specific case is because it fails independence of clones.

I’m not necessarily just after a simple tie breaker. My concern is with reconciling majority cycles, which can destabilize the system. Something like approval in a second round enables the competing majorities to compromise more directly with full information. Otherwise a true majority may feel jilted by an arbitrary tie breaking rule.

Two-stage voting systems seem like a hard sell in the USA. However, I think a two-stage system is an extremely natural way to satisfy principles of majority rule and self governance.

My opinion is that an ideal single-winner system consists of a first round (or primary) of rank-based voting. If there is a Condorcet winner, no second round is needed. This can be decided easily by a run of B2R and checking if the winner is Condorcet.

Otherwise, the Smith set can be computed and made public. Once known, a second round of approval voting can be run over the Smith set.

Does this have any objectionable properties other than requiring two rounds of voting?

@gregw I think Condorcet is great when a Condorcet winner exists, but when one doesn’t exist it’s really troublesome. Ideally, we would have a method to check whether one exists without unearthing the Condorcet cycle that reveals the jilted majority upon the choosing of any winner, but that is essentially impossible.

I think it makes sense to do Condorcet//Approval, in two separate rounds, the approval round restricted to the Smith set. But two round voting outright is a difficult sell in the USA (even though two-round voting is pretty common all over the rest of the world…).

People try to put the two together in a single round vote, but the strategic incentives of casting rank and approval/score indications on the same ballot cause issues.

My personal belief is that this system of two-round voting for single winner elections, I.e. approval conditional on already knowing the Smith set, would be most ideal. I think actually implementing the approval aspect first however is an easier sell than implementing the Condorcet aspect first. I can envision a natural progression as: (1) implement straight approval, (2) eventually indicate the shortcomings of approval in guaranteeing election of Smith set candidates, (3) reform to include a ranked primaries to restrict to the Smith set before the final approval vote.

I feel even having rank/Smith-based primaries makes way more sense than what we have if the subsequent system is approval. There’s no issue with vote splitting in that instance, and it fits at least partially into the political system we already have (although this would also require substantial changes).

@gregw hm I’m just not sure how well-studied this method in particular is, as in, why it needs to be “most wins, fewest losses.” It makes as much intuitive sense as anything else, and it’s Condorcet so that’s fine.

Also it’s obviously susceptible to potentially unfortunate results when the Condorcet winner does not exist (which the above has ignored in their last step of the “how it works” section as “the candidate who beats all the others wins.”)

I still think rank-based methods are going to be much more difficult to gain firm ground on than approval. IRV got some traction but now it’s facing backlash (some rightfully so). Approval on the other hand seems relatively hard to argue against. I think it would yield a more lasting forward step.

@toby-pereira I’m sure the courts will conjure up whatever question-begging definition of vote they need to for whatever ruling they decided on beforehand. I think getting the reasonable notions settled on to facilitate progress without constitutional amendments will require more lawyering than only appeals to reason. It’s unfortunate that Maine’s constitution encoded plurality into its state voting law, I think it’s important to know what other states might have this same kind of language issue in their constitutions.

@sarawolk makes sense. “Ranked voting” (or rank-based voting?) is a good way to refer to the ballot format rather than IRV. I’ll use something like that from now on, not “ranked choice voting.”

@sarawolk that’s unfortunate, but is this about ranked ballots in general or about instant runoff voting? I hope the latter.

I still think approval is the best path forward.

@jack-waugh I’m imagining the decisions could be automated by making assumptions about the group utility and computing the mixed strategy Nash equilibria of the game.

The deepest problem there is the utility function, since it would be an aggregate utility of some kind that we would have to presume emerged somehow from the individual utility functions of the voters that constitute the group.

All of that is definitely questionable, I don’t believe in utility functions, but I’m unsure how else to proceed in putting this kind of situation into an analytical framework.

I have an idea I’m trying to flesh out properly, maybe some others’ thoughts can help.

The idea is to group voters by ballot type (or latent preference but that’s not observable), and then view the issue of participation as an adversarial game among those groups.

As a strategy, each group chooses how many of their ballots to cast (and how many to abstain). In a more complicated scenario, the groups could also choose how to distribute the ballots they cast among the other ballot types, but that’s probably too much.

This is a large game but it’s finite, so it has a Nash equilibrium over mixed strategies. Any equilibrium induces a lottery over decisions.

In principle, this is something that could be simulated. Say as a big ask that group utility functions were set up normatively or faithfully enough. Then under certain assumptions, a method that simulated the equilibrium strategies over groups would “essentially” satisfy participation, since casting a ballot would only give one’s group an extra pure strategy to sample from.

Roughly, I’m considering whether the no-show/abstention problem can be all but artificially removed under certain assumptions about group utility functions, and whether those assumptions are reasonable enough or not.

It could be that there is some recursive issue of meta participation. In fact, I think that even casting a ballot and allowing it to be a strategic option for one’s group can change the game globally as other groups adjust, which may mean the problem persists unless perhaps other conditions are met… In a zero-sum situation, I don’t think increased optionality can reduce the equilibrium payoff for a group.

@toby-pereira I see, it seems that the properties of maximal lotteries related to participation aren’t what I believed they were. Looking into this, I misunderstood the definition of an (x,y)-improvement, this is swapping the adjacent positions of x and y in a ballot that already exists in the election, not introducing a new ballot where x>y.

That’s unfortunate, but also makes sense.

@cse4129 no problem, that’s what forums are for! Your idea is good, it just happens it was already invented. It also does have some problems/failed properties, though (like any method).

For example, it isn’t Condorcet compliant or Condorcet loser compliant, and it fails participation. It doesn’t satisfy independence of clones either, and it fails various other binary criteria. That doesn’t mean it’s a bad method, but it means it can occasionally produce pathological results. It satisfies the majority winner and majority loser criterion, and later-no-help.

There’s a “mind map” I made some years ago of some of the best-known/characterized voting systems in terms of the binary criteria they satisfy and fail in that discussion above. Probably nowadays I would make a better one (I might at some point). I should have done something like PCA or a graph embedding, but I tried to make that map before I knew about those analysis methods.

@cse4129 I took a brief look and will check in more detail, but from the initial look it reminds me of Bucklin voting:
https://en.wikipedia.org/wiki/Bucklin_voting

This is an exploratory discussion about mapping out voting systems, I think it’s good to be familiar with the major systems described there and generally what kinds of properties they have:
https://www.votingtheory.org/forum/topic/280/map-of-voting-systems?_=1775264773769

@toby-pereira your interpretation is correct, and yes with an even number of voters and non-strict rankings, ties can occur and that can induce non-uniqueness. For example there may be two separate, disconnected Condorcet cycles of different sizes in the Smith set for instance. The proof of uniqueness in general is probably less straightforward than just the intuition, I haven’t dug into it.

With ties in other methods, the resolution of ties is typically standard because the set over which the ties occur is discrete—uniformly sample one from among the tied candidates. But for maximal lotteries, when non-uniqueness holds there is a continuum of admissible lotteries as you indicated. The analog of a uniform distribution in this case would be using Jeffrey’s prior, which is why I think that’s the “right” way to go.

But yes it ultimately doesn’t really matter how the maximal lottery used is chosen since they are all maximal, but that’s also kind of the issue, because a choice has to be made.