Rank with cutoff runoff 2.0
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@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.
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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?
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@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.
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@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.
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@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)=0.3And 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)=BThen 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.
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@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.
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@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>AThen 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)=32while
M(+A+B)=B
M(+A-B)=A
M(-A+B)=B
M(-A-B)=Bmeaning 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=Bso again B wins. I may code this system up just to see what happens with more candidates.
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@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.
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@sarawolk You can draw a line between the names of the candidates you support and the rest.
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@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.
score-stratified-condorcet [10] cardinal-condorcet [9] ranked-condorcet [8] score [7] approval [6] ranked-bucklin [5] star [4] ranked-irv [3] ranked-borda [2] for-against [1] distribute [0] choose-one [0]
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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?
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Moved from Single-winner by
SaraWolk
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@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.
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.