[EM] Simplest Condorcet method to hand count?

[Chris Benham]

Etjon,

My favourite Condorcet method,  Margins Sorted Approval, would be 
relatively easy to hand count because it would only very rarely need the 
full pairwise matrix.

First just count the approvals to determine each candidate's approval 
score. Those scores give us our initial order, from highest to least 
approved.  Now we are only interested in the pairwise results between 
pairs of candidates which are adjacent to each other in this order.

(Our goal is to arrange the candidates in a chain where the candidate at 
the head beats the candidate that is second who in turn beats the 
candidate that is third, and so on. Ranked Pairs also does that.)

Next we do the pairwise comparison between the adjacent pair of 
candidates with the smallest difference in their approval scores. (If 
there is a tie for this, then the tied pair lowest in the order.)  If 
they are pairwise out of order (i.e. if the less approved of the two 
pairwise beats the more approved) then the candidates change places in 
the order to give us our new provisional ordering.

We repeat this process to the end.  (The order always stabilises.)   
Then the candidate at the top of the final order is the winner.

There are two versions of this method, MSA (explicit) and MSA 
(implicit).  I prefer the more expressive (and more in the Condorcet 
spirit) explicit version which allows voters to rank among candidates 
they don't want to approve, versus the somewhat simpler (and possibly a 
bit higher SU) implicit version which asks the voters to rank only those 
candidates they approve.

Benham meets Unburiable Mutual Dominant Third and I think this doesn't, 
but Benham does need the full pairwise matrix (just the win-loss-tie 
results) and overall isn't as good. So why put up with relative 
"shortcomings" ?

Chris

On 22/05/2025 8:10 pm, Etjon Basha via Election-Methods wrote:
> Good evening gentlemen,
>
> I've been pondering the above issue, and already consulted Gemini who 
> disagrees with me on the practicality of pairwise matrices, so 
> couldn't help a lot.
>
> I suspect that compiling pairwise matrices in the context of a hand 
> counted election would be very time consuming, and quite prone to 
> errors and challenges from all parties.
>
> Assuming we agree on this (which you might not) is there any practical 
> Condorcet method can can be hand counted?
>
> I suspect Nanson is a reasonable candidate. Yes, it still requires 
> log(candidates,2) counting rounds, and each of those rounds require 
> sending a matrix of how many times each candidate was ranked in which 
> position to a central location, so quite the bother indeed.
>
> Yet, I suspect this task can at least be completed within acceptable 
> timeframes with an acceptable error rate by most volunteers.
>
> (Interestingly, Gemini considers Copeland easier to hand count than 
> Nanson, which I disagree with)
>
> Are there any simpler methods I'm unaware off, despite any other 
> shortcomings such a method might have?
>
> Best regards,
>
> Etjon
>
>
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