# [EM] A few papers on election science I'd like to point out to y'all

Kristofer Munsterhjelm km_elmet at t-online.de
Sun Feb 4 09:22:03 PST 2018

```On 01/29/2018 02:43 PM, Arthur Wist wrote:
> Hello,
>
> Sorry in advanced for the huge load of information all at once, but I
> think you'll highly likely find the following quite interesting:
>
> On how people misunderstood the Duggan-Schwartz theorem:
> https://arxiv.org/abs/1611.07105 - Two statements of the Duggan-Schwartz
> theorem
> https://arxiv.org/abs/1611.07102 -  Manipulability of consular election
> rules
>
> EVERYTHING here:
>
> Some key highlights from that last link above:
>
> https://arxiv.org/abs/1708.07580 - Achieving Proportional Representation
> via Voting [ On which a blog post exists:
> https://medium.com/@haris.aziz/achieving-proportional-representation-2d741871e78.
> Better than STV and STV derivatives in all criteria? You decide! ]

From a cursory look at the latter, that looks like Bucklin with a
STV-style elect-and-reweight system. I wrote some posts about a
vote-management resistant version of Bucklin at
http://lists.electorama.com/pipermail/election-methods-electorama.com/2016-December/001234.html
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2017-September/001584.html,
and found out that the simplest way of breaking a tie when more than one
candidate exceeds a Droop quota is nonmonotonic.

The simplest tiebreak is that when there are multiple candidates with
more than a quota's worth of votes (up to the rank you're considering),
you elect the one with the most votes. This can be nonmonotone in th
following way:

Suppose in the base scenario, A wins by tiebreak, and B has one vote
less at the rank q, so A is elected instead of B. In a later round, say,
q+1, E wins. Then suppose a few voters who used to rank A>E decides to
push E higher.

Then B wins at rank q. If now most of the B voters vote E at rank q+1,
it may happen that the deweighting done to these voters (since they got
what they wanted with B being elected instead of A) could keep the
method from electing E.

E.g. A could be a left-wing candidate, B be a right-wing candidate, and
E a center-right candidate. In the base scenario, A wins and then the B
voters get compensated by having the center-right candidate win. But
when someone raises E, the method can't detect the left wing support and
so the right-wing candidate wins instead. Afterwards, the right-wing has
drawn weight away from E (due to E not being a perfect centrist, but
instead being center-right), and so E doesn't win.

Achieving monotonicity in multiwinner rules is rather hard; it's not
obvious how a method could get around the scenario above without
considering later ranks.

I'm not sure if rank-maximality solves the problem above. If it doesn't,
then the above is an example of CM failure but not RRCM failure.

http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/094876.html
and
http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-February/095188.html
for another Bucklin PR method that seemed to be monotone.

It's also unknown whether Schulze STV is monotone, though it seems to do
much better than IRV-type STV in this respect. And I'd add that there's
yet another (very strong) type of monotonicity not mentioned in the
paper as far as I could see. Call it "all-winners monotonicity" -
raising a winner on some ballot should not replace any of the candidates
on the elected council with anyone ranked lower on that ballot.

(There's a result by Woodall that you can't have all of LNHelp, LNHarm,
mutual majority and monotonicity. Perhaps, due to the difficulty of
stopping the monotonicity failure scenario above, the equivalent for
multiwinner would turn out to be "you can't have either LNHelp or
LNHarm, and both Droop proportionality and monotonicity"...)
```