COWPEA and COWPEA Lottery paper on arXiv
I don't know how many of you will be interested in this, but I wrote a paper on the COWPEA and COWPEA Lottery voting methods, which is now available on arXiv here: https://arxiv.org/abs/2305.08857 They're also described on the wiki: https://electowiki.org/wiki/COWPEA
Basically COWPEA is a proportional approval method that elects candidates with different weights to the elected body. COWPEA Lottery elects a fixed number of candidates with equal weight, but it is non-deterministic. The weight a candidate gets in the elected body under COWPEA is the same as its probability of being elected in the following lottery:
Start with a list of all candidates. Pick a ballot at random and remove from the list all candidates not approved on this ballot. Pick another ballot at random, and continue with this process until one candidate is left. Elect this candidate. If the number of candidates ever goes from >1 to 0 in one go, ignore that ballot and continue. If any tie cannot be broken, then elect the tied candidates with equal probability.
COWPEA Lottery just runs this lottery a fixed number of times to elect the candidates. I see these methods as of theoretical interest because of their criterion compliance. As well as being proportional, they are strongly monotonic, and pass Independence of Irrelevant Ballots. COWPEA Lottery also passes Independence of Universally Approved Candidates (this criterion isn't applicable to COWPEA), and as far as I understand, it is the only method that has been shown to pass all of these criteria.
Toby
On 5/19/23 13:56, Toby Pereira wrote:
I don't know how many of you will be interested in this, but I wrote a
paper on the COWPEA and COWPEA Lottery voting methods, which is now
available on arXiv here: https://arxiv.org/abs/2305.08857
https://arxiv.org/abs/2305.08857 They're also described on the wiki:
https://electowiki.org/wiki/COWPEA https://electowiki.org/wiki/COWPEA
In the paper, when describing clone independence, you say:
In a single-winner method, the situation is much simpler: adding a > clone would mean that the winner must not switch between a candidate
outside the clone set and one inside, in either direction.
Doesn't that definition omit crowding? The winner would change from a
candidate outside the clone set to another one.
Basically COWPEA is a proportional approval method that elects
candidates with different weights to the elected body. COWPEA Lottery
elects a fixed number of candidates with equal weight, but it is
non-deterministic. The weight a candidate gets in the elected body under
COWPEA is the same as its probability of being elected in the following
lottery:
Start with a list of all candidates. Pick a ballot at random and remove
from the list all candidates not approved on this ballot. Pick another
ballot at random, and continue with this process until one candidate is
left. Elect this candidate. If the number of candidates ever goes from
1 to 0 in one go, ignore that ballot and continue. If any tie cannot
be broken, then elect the tied candidates with equal probability.
COWPEA Lottery just runs this lottery a fixed number of times to elect
the candidates. I see these methods as of theoretical interest because
of their criterion compliance. As well as being proportional, they are
strongly monotonic, and pass Independence of Irrelevant Ballots. COWPEA
Lottery also passes Independence of Universally Approved Candidates
(this criterion isn't applicable to COWPEA), and as far as I understand,
it is the only method that has been shown to pass all of these criteria.
That's interesting. It reminds me of a ranked method I mentioned on here
once, where you choose a winner from the top of a ranked ballot,
eliminate this winner, and repeat. It tends to party list
proportionality given enough candidates per party, but is either not
very proportional (when determinized) or has a high variance (when not)
with few seats. Unlike COWPEA, it also works by electing candidates
rather than excluding them.
Could anything useful be said about the mode of the COWPEA lottery for a
fixed number of candidates? Or does that lose proportionality the way
random ballot is (in a sense) proportional yet Plurality definitely is not?
-km
On Sunday, 21 May 2023 at 19:34:33 BST, Kristofer Munsterhjelm km_elmet@t-online.de wrote:
In the paper, when describing clone independence, you say:
In a single-winner method, the situation is much simpler: adding a > clone would mean that the winner must not switch between a candidate
outside the clone set and one inside, in either direction.
Doesn't that definition omit crowding? The winner would change from a
candidate outside the clone set to another one.
You're right. I'll make a note of that for any updates to the paper.
That's interesting. It reminds me of a ranked method I mentioned on here
once, where you choose a winner from the top of a ranked ballot,
eliminate this winner, and repeat. It tends to party list
proportionality given enough candidates per party, but is either not
very proportional (when determinized) or has a high variance (when not)
with few seats. Unlike COWPEA, it also works by electing candidates
rather than excluding them.
Could anything useful be said about the mode of the COWPEA lottery for a
fixed number of candidates? Or does that lose proportionality the way
random ballot is (in a sense) proportional yet Plurality definitely is not?
-km
I noticed you'd added the ranked-ballot version of random ballot on the wiki at some point last year. https://electowiki.org/wiki/Random_ballot I think I prefer COWPEA Lottery because although it's still a lottery, it potentially uses more ballots - i.e. not just the same number of ballots as there are candidates to elect - so I see it as a more consensual lottery (unless everyone just bullet votes.) Because of that I think its proportionality might hold up better than the ranked method. Obviously its proportional guarantees aren't as great as the deterministic variable-candidate-weight version though. But if there are several representatives (e.g. 5 or 6) elected per geographical constituency and many of these across a country, then overall it should give better proportionality than a deterministic method. This is because parties/ideologies that have say 10% of the support nationally should still win the right proportion of seats rather than keep missing out. I also think it works well with scores or grades but used as layers of approval rather than as numerical values, and I think this probably reduces the strategic burden on the voters.
Toby
On 5/21/23 20:57, Toby Pereira wrote:
On Sunday, 21 May 2023 at 19:34:33 BST, Kristofer Munsterhjelm
km_elmet@t-online.de wrote:
In the paper, when describing clone independence, you say:
In a single-winner method, the situation is much simpler: adding a
clone would mean that the winner must not switch between a candidate
outside the clone set and one inside, in either direction.
Doesn't that definition omit crowding? The winner would change from a
candidate outside the clone set to another one.
You're right. I'll make a note of that for any updates to the paper.
What would the multiwinner version be - just a straightforward "cloning
a non-winner shouldn't replace one of the winners with someone else?"
Good point about the additional information being incorporated. Strictly
speaking, random ballot also has the proportionality due to
nondeterminism property, but its variance is too high. I suppose more
information being incorporated into the COWPEA lottery would reduce the
variance as well.
-km
On Sunday, 21 May 2023 at 21:05:28 BST, Kristofer Munsterhjelm <km_elmet@t-online.de> wrote:
On 5/21/23 20:57, Toby Pereira wrote:
On Sunday, 21 May 2023 at 19:34:33 BST, Kristofer Munsterhjelm
km_elmet@t-online.de wrote:
>In the paper, when describing clone independence, you say:
>> In a single-winner method, the situation is much simpler: adding a
> clone would mean that the winner must not switch between a candidate
>> outside the clone set and one inside, in either direction.
>Doesn't that definition omit crowding? The winner would change from a
>candidate outside the clone set to another one.
You're right. I'll make a note of that for any updates to the paper.
What would the multiwinner version be - just a straightforward "cloning
a non-winner shouldn't replace one of the winners with someone else?"
Something along those lines. Although I might still frame it in terms of increasing/decreasing probabilities. For a deterministic method it just means 1 or 0 anyway.
Good point about the additional information being incorporated. Strictly
speaking, random ballot also has the proportionality due to
nondeterminism property, but its variance is too high. I suppose more
information being incorporated into the COWPEA lottery would reduce the
variance as well.
Yes. Also I think having multiple representatives per constituency would reduce the variance as well. Certainly very popular candidates would be less on a knife-edge if they have five or six opportunities to get elected.
Toby