[EM] Novel Electoral System

Sun May 18 10:51:54 PDT 2025

Hi all,

Thanks so much for the replies. I’ll respond to everyone in this thread.

*Andy* - I really appreciate your feedback. Your summary is correct, and
your framing of it as one-norm vs. two-norm vs. infinity-norm is a way of
thinking about it that I had not considered. It seems like a potentially
fruitful lens for understanding it. And, as perhaps you have surmised, I
may have been mistaken in the statement about the sincere favorite
criteria, but I am working on an analysis of the issue that I will share.

*Toby*, making a short summary is a great suggestion. The argument in the
paper is admittedly a bit convoluted before it presents the actual method.
Here is the simplified way that I would explain it:

*Each voter ranks their preferences, with ties allowed and unranked
candidates treated as last-place preferences. Then, for each candidate, you
make a plot, where each axis is the total number of times that they were
preferred to each of their opponents. So, if the candidates are A, B, and
C, candidate A’s plot would have “number of times preferred to B” on one
axis and “number of times preferred to C” on the other axis. Candidate B &
C could be plotted similarly in terms of their opponents. The winner is
simply the candidate who is plotted the farthest up and to the right, or
closest to topmost and rightmost point, which is where a candidate who is
the unanimous first-place choice would be plotted. The distance from that
point is calculated using the Pythagorean theorem, which is where
minimizing the sum of squares that Andy referenced comes in.*

The figures in the paper tell the story better than the words, as it is
essentially a geometric idea. And, sections 4, 5, and 6 can really be
skipped - they are more about justifying the approach than explaining it.

*Chris*, you asked “Why should we be interested in the "concerns" of Borda
(whatever they are)? And so much that we should embrace a method that fails
the Condorcet criterion?” Great question. If you look at the Stanford
Encyclopedia of Philosophy’s entry on Social Choice Theory, they list
Condorcet and Borda as the original pioneers of this thinking (
https://plato.stanford.edu/entries/social-choice/). Borda thinks about
majoritarianism in terms of votes, while Condorcet thinks about it in terms
of voters. Obviously, in FPP elections, these are the same, but the heart
of the interest in these questions comes from the tension that arises
between them in a ranked-choice setting, where each voter has multiple
votes and ‘majoritarianism’ is no longer simple to define. Don Saari is a
thinker who studies these issues and has argued most persuasively for
Borda’s approach over Condorcet methods. In section 9 of my paper, I
explain some of my philosophical objections to the Condorcet winner
criterion.

You also asked “Do you propose allowing above-bottom equal ranking or
truncation?” Equal ranking is allowed, and unranked candidates are treated
as last place.

And, I am afraid I may have actually been mistaken about the sincere
favorite property, so will have to disappoint you there.

You asked “Who does your method elect in this example?

46 A
44 B>C
10 C”

If I am understanding your notation correctly, A would win in this example.
The full ranking would be:
A's K-count = 46 = 100-SQRT((100-46)^2+(100-46)^2)/(SQRT(2))
B's K-count = 44 = 100-SQRT((100-44)^2+(100-44)^2)/(SQRT(2))
C's K-count = 28.53 = 100-SQRT((100-54)^2+(100-10)^2)/(SQRT(2))

As you can see, when a candidate only appears as a first-place or
last-place preference, their K-count is simply equal to the number of
voters ranking them first.

Thanks all!

On Sun, May 18, 2025 at 12:10 PM Andrew B Jennings (elections) <
elections at jenningsstory.com> wrote:

> Hi Dan,
>
> Great paper. Thank you for posting!
>
> It seems like the short version is that the winner is the candidate with
> the smallest sum of SQUARES of non-victories (defeats plus ties) against
> their opponents.
>
> Taking the square root and dividing can make it meaningful by scaling it
> to [0,1] or [0,s] (where s is the number of voters), but doesn't change the
> finish order.
>
> It does seem like an interesting attempt to "square the circle" (great
> pun) and compromise between Borda and Condorcet. I hadn't realized that
> Borda and Minimax are minimizing the one-norm and infinity-norm in the same
> geometric space. The two-norm certainly seems like it should be explored.
>
> I would love to see the proof of non-favorite-betrayal.
>
> Best,
>
> ~ Andy
> On Thursday, May 15th, 2025 at 4:25 PM, Daniel Kirslis via
> Election-Methods <election-methods at lists.electorama.com> wrote:
>
> Hello!
>
> I am a newcomer to this mailing list, so please forgive me if this message
> violates any norms or protocols that the members of this list adhere to.
>
> I have recently developed a novel method for tabulating ranked-choice
> elections that attempts to reconcile the concerns of Borda and Condorcet. I
> believe that it maintains the simplicity and mathematical elegance of the
> Borda count while incorporating Condorcet's concern with pairwise
> dominance. Intuitively, it can be understood as ordering candidates by how
> close they come to being unanimously selected when plotted in Cartesian
> coordinate space. Here is a link to the paper:
>
> https://drive.google.com/file/d/152eNheS2qkLHJbDvG4EwW3jdO4I_NwcX/view?usp=sharing
>
> Given its simplicity, I have been very surprised to discover that this
> method has never been proposed before. I am hoping that some of you all
> will take a look at the paper and share your comments, questions, and
> critiques. Ultimately, it is my hope that ranked-choice voting advocates
> can arrive at a consensus about the best method for RCV and thus strengthen
> efforts to adopt it and deliver much needed democratic improvements. But
> even if you don't find the system itself compelling, you may find the
> method of plotting electoral outcomes elucidated in the paper to be useful
> for the analysis of other electoral systems.
>
> Thank you!
>
> -Dan
>
>
>
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