[EM] Novel Electoral System

[Chris Benham]

Dan,

The new short version of your paper I also find opaque. Earlier you 
agreed with Andrew that

> 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.

And then you told me that in this example

46 A
44 B>C
10 C

your  K-count method elects A.

C>A 54-46,   A>B  46-44,   B<C 44-10

Each candidate has only one "non-victory".  So then I take it then, 
using Andrew's version  the winner is C, because squaring the pairwise 
non-victory scores of  C44,  B46,  A54 doesn't change their order and 
C's is the smallest.

Obviously one of us has it wrong.

Chris


On 20/05/2025 8:58 am, Daniel Kirslis via Election-Methods wrote:
> Hi Chris,
>
> Yes, that is correct. I have created a simplified version of the paper 
> that attempts to explain the method in the most concise possible way. 
> It's only two pages: 
> https://drive.google.com/file/d/1F_I2ZBUKXKbmcS-uSvMAf_gNdNO8m0GB/view?usp=drive_link
>
> It skips over a lot of the background that explains why I view this as 
> a compromise between the Borda count and Condorcet methods and just 
> focuses on explaining the method itself. Once you see how the plotting 
> works, it is like Bocce Ball - closest to the target ball wins.
>
> Thank you for your engagement on this. I should have started with this 
> version of the paper!
>
> On Mon, May 19, 2025 at 12:32 PM Chris Benham via Election-Methods 
> <election-methods at lists.electorama.com> wrote:
>
>>
>>     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.
>
>     I take that these numbers you are squaring are the candidate's
>     opposing and tying vote scores, and not simply the number of such
>     results. Is that right?
>
>     Because otherwise that would often be very indecisive, like Copeland.
>
>
>     On 19/05/2025 1:40 am, Andrew B Jennings (elections) via
>     Election-Methods 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>
>>     <mailto: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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