Rank with cutoff runoff 2.0

[cfrank]

@jack-waugh it is certainly Condorcet (or any other rank-criterion) compliant if the candidate pool is restricted according to the rankings even before the support-based runoff sequence begins.

[Jack Waugh]

@cfrank said in Rank with cutoff runoff 2.0:

restricted according to the rankings

How does that work?

[cfrank]

@jack-waugh before considering the support aspect, you could just ignore all candidates who are not in the Smith or Landau set, for example. This is maybe peculiar though, since in principle it makes it possible that the winner is a candidate who doesn’t have much support at all. And this is perhaps a fair argument against the Condorcet criterion when certain additional information is provided.

[Jack Waugh]

Unless I am mistaken, no restriction is necessary and the system will still find the Condorcet winner if there is one, just like Llull's last system. Any order of elimination would do this.

[cfrank]

@jack-waugh you’re right. No matter what, the runoff will eventually eliminate anybody who is not the Condorcet winner if one exists. It should also eliminate any Condorcet loser. It still leaves open the possibility of electing a candidate with low support, even if they are the Condorcet winner.

Maybe that’s fine? I’m sticking with the philosophy of “if people prefer something else, they should say so.” Aka, they should on the whole provide candidates that represent their preferences and fill the spectrum of feasible options, rather than relying on gamified quantifications of how much they prefer one thing over another.

[Jack Waugh]

Here is a cut at a voting decision-procedure. I rate the candidates on a continuous scale, exaggerating support for the lesser evil (but not past another candidate) if I think the real good candidates are extremely unpopular or unknown. I push the ones at Mussolini-level or below off to the side and consider the rest. I position my cutoff randomly on the scale. The more distance between two adjacent candidates, the more likely the cutoff goes there. I then convert the ratings of all the candidates to ranks and vote.

[cfrank]

@jack-waugh why not simply place the cutoff between the two candidates with the largest difference? Or is it a clustering problem?

I tend to think that preferences are always conditional, and it doesn’t actually make sense to place all preferences on the same scale. You would prefer candidate B if you can’t have candidate A. And if you can have neither, you prefer candidate C, etc.

The “strength” of preferences I think shouldn’t spurn larger numerical differences on a scale, but rather should motivate indicating a larger number of intermediate alternative preferences. Which, in an idealized voting system, would manifest as candidates.

[Jack Waugh]

@cfrank said in Rank with cutoff runoff 2.0:

why not simply place the cutoff between the two candidates with the largest difference?

Because when many voters choose randomly, the effect is the same as though fine-grained Score ballots were being collected and tallied, and I believe that the finer grain has better effect at defeating money and fame effects.

[Jack Waugh]

This is an example system with two distinct aspects in every vote. For which of such systems can we say that it suffices (for an optimal vote) to Gibbard just one of the aspects and vote your values in the other aspect?

[cfrank]

@jack-waugh I’m not sure about this, the most obvious forms of strategy here would be Turkey raising and burial, aka supporting certain candidates or choosing not to support certain candidates tactically. And I think this only helps in the event that there isn’t a Condorcet winner.

[Jack Waugh]

@cfrank said in Rank with cutoff runoff 2.0:

spiral quickly into becoming as convoluted as possible.

An alternative is the opposite: make them as simple and transparent as possible, so everyone engages in them and achieves equal power to everyone else.

[cfrank]

@jack-waugh definitely, I agree.

So this system is basically just a particular Condorcet method. I had a thought to mitigate the high support vs Condorcet issue, which is something possibly complicated like this:

Rather than a majoritarian runoff between A and B occurring across the whole electorate, split the electorate into those who support both A and B, those who support A but not B, those who support B but not A, and those who support neither.

In each group separately, determine the majoritarian rank runoff winner. Then aggregate the victories in each group according to their sizes to determine the overall runoff winner.

For example, if the groups are designated +A+B, +A-B, -A+B, and -A-B, and we have a function N that returns the relative size of the group, say

N(+A+B)=0.4
N(+A-B)=0.1
N(-A+B)=0.2
N(-A-B)=0.3

And a function M that returns the majority runoff winner of each group, say

M(+A+B)=B
M(+A-B)=A
M(-A+B)=B
M(-A-B)=B

Then in this case, B would win the overall runoff by securing 04+0.2+0.3=0.9 points. It’s possible though that if the overall runoff had been majoritarian over the entire electorate without considering support status, then A would win instead.

This may be too convoluted, but it’s essentially the way we vote by district. In this case the “districts” are classes of voters determined by their support status for A and for B (rather than, say, gerrymandering).

Let me also say, this kind of thing may make people “put their money where their mouth is,” since if they support both A and B, for example, they implicitly agree by the mechanism to effectively support whichever of A or B wins the +A+B runoff.

[Jack Waugh]

@cfrank, using the grouping that you describe in 2881, votes that look formally "opposite" would be separated into different groups wrt ea pair of candidates, and so I'm pretty sure it would break the balance.

basically just a particular Condorcet method.

It collects more information than most, and goes beyond mere ranking.

[cfrank]

@jack-waugh yes it does break the balance. I’ve argued before that this may not actually matter very much, but who knows. You could also formally impose the cancellation by exactly the method described above before districting, or some other form of “preprocessing rectification” that forces balance.

The only reason I’m considering this kind of districting system is that I want to see what happens in a system that satisfies independence of clones while incorporating the support aspect more strongly than a Condorcet method can and incorporating the preference aspect more strongly then approval voting can.

I’m not sure if there are mathematical guarantees on the level of support an existing Condorcet winner must have, but I feel like the Condorcet winner could still have very low support, which I think is somewhat peculiar.

I’d be interested to examine the comparison against the Condorcet winner in terms of support.

If we have:

35: A|B>C
18: B|A>C
25: B>A|C
32: C|B>A

Then the Condorcet winner is B. I think in this case B will also win the “districted” election. A and B have the top support, and

N(+A+B)=25
N(+A-B)=35
N(-A+B)=18
N(-A-B)=32

while

M(+A+B)=B
M(+A-B)=A
M(-A+B)=B
M(-A-B)=B

meaning that B surely wins the runoff, so A is eliminated. And we then find

N(+B+C)=0
N(+B-C)=43, M=B
N(-B+C)=32, M=C
N(-B-C)=35, M=B

so again B wins. I may code this system up just to see what happens with more candidates.

[SaraWolk]

@cfrank How would you propose doing a ranked ballot with a support cutoff? This sounds simple but I'm not visualizing an elegant or simple way to do that.

[Jack Waugh]

@sarawolk You can draw a line between the names of the candidates you support and the rest.

[cfrank]

@sarawolk I do understand what you mean, the issue being that on a ballot, candidates may not be lined up in order. One could indicate the ranking position at which support begins. Rank order ballots in general are another topic.

I’m not pining for this or any related method, I’m just trying to think of possible “reasonable” ways to combine support and ranking that are distinct from existing methods.

The prospect of combining the two though begs the question of how exactly to do so, and the ones I’ve considered introduce several somewhat complicated tactical dilemmas, so I’m not sure it’s any kind of promising direction.

[SaraWolk]

Right, at a glance this detail makes the system not viable or practical for scaled or official elections, imo.

Also, there are a number of ways to find the top two candidates, (Borda, Condorcet, IRV, etc..) Quantity of support isn't explicit enough.

Another point is that a given voter's support cut-off (ie. Approval Threshold) is absolutely relative to the other options. It's not a concrete thing.

What is the intention behind the proposal? Just a thought experiment?

[cfrank]

@sarawolk yes more or less a thought experiment, trying to address some dissonance between the possibility of a Condorcet winner having low support and a support (approval) winner being different from the Condorcet winner even when one exists.

In this case, I mean that a candidate is either supported or not supported by a voter according to the support cutoff of their ballot. I’m using the word “support” rather than “approval,” because I don’t think approval is an appropriate word philosophically (or mathematically). The positive emotional connotation of “approve” is all that bothers me. “Support” seems more emotionally neutral and has a mathematical meaning that aligns well with what is happening in the system, for example, “the support of a distribution.”

https://en.m.wikipedia.org/wiki/Support_(mathematics)

The quantity of support of a candidate is simply the number of voters who formally support that candidate on their ballot.

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Here is another attempt at a modification. In sequence, if there is a Condorcet loser, they are eliminated. If there is no Condorcet loser, a candidate with the least quantity of support is eliminated, with ties broken by rank runoff if possible. Repeat until one candidate remains.