# [EM] COWPEA and COWPEA Lottery paper on arXiv

Kristofer Munsterhjelm km_elmet at t-online.de
Sun May 21 11:33:45 PDT 2023

```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
```