[EM] Novel Electoral System

Sun May 18 16:58:58 PDT 2025

Hi Chris,

I certainly did not mean to cause any offence with that comment. I
understand that the paper itself is not at all simple or accessible, and my
attempt at summarizing it on a busy Sunday afternoon is perhaps not a
paragon of clarity. However, though my explanations are not the best, I do
hold onto the belief that the idea itself, when understood geometrically,
is simple. You choose the candidate whose vote totals are the closest to
unanimous selection when plotted on a graph. I do think that most voters
are familiar with 2-dimensional graphs, from which the core idea can be
understood. I don't think that at its core this method is any more
complicated for the average voter to understand than many of the other
ranked choice electoral methods, some of which can become quite intricate.
Again, I acknowledge that my paper and explanations are not easy to
understand, but I think that is a failure of my communication skills, not
of the method itself. I'll keep working on expressing the idea more simply.

-Dan

On Sun, May 18, 2025 at 3:58 PM Chris Benham via Election-Methods <
election-methods at lists.electorama.com> wrote:

> Daniel,
>
> So according to you, this method is so childishly "simple" that you can't
> understand why no-one has thought of it before, but it can't be explained
> without reference to geometry, graphs, square roots and "the Pythagorean
> theorem".
>
> *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.*
>
>
> I think that there are many people in the US (and elsewhere) who have no
> background in Maths or Geometry and so don't understand any Math-ese , even
> some who are interested in election methods.
>
> Is this really your best attempt to explain how the method works to them??
>
> Chris
>
> On 19/05/2025 3:21 am, Daniel Kirslis via Election-Methods wrote:
>
> 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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