[EM] Borda Done Right

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[EM] Borda Done Right

Forest Simmons
It is a very small step from Copeland done right to Borda done right because in a certain sense Borda can be thought of as Copeland applied to each ballot separately and then summed over ballots. 

Let's start with Copeland and change it into Borda.

Copeland: The score of alternative X is the total probability of the alternatives beaten pairwise by X minus the total probability of the alternatives that beat X pairwise.

Borda: The contribution of ballot B to the Border score by alternative X is the total probability of the alternatives ranked below X on B minus the total probability of the alternatives ranked above X on ballot B.

That's it!

 What do you think?

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Re: [EM] Borda Done Right

Kevin Venzke
Hi Forest, these are interesting... I have a new rank ballot sim currently and that Copeland one seems like an interesting one to try. Do you think it's actually cloneproof? Clearly if a faction tries to flood the race with additional candidates, the total score they can achieve across all those candidates should stay constant.

Kristofer has been studying low-manipulability methods where, often, observing the first preference count is a key component. So I wonder if the decloned Copeland would end up with similar properties.

I have a method similar to your DSV approval method. My primary issues (differences?) are just that I don't think truncated rankings can be allowed, and that I don't really see it as a single-round method. Very minor issues. I think this method gives strange results, but has its place. It doesn't feel to me like an automated approval method, but a method that forces voters to provide approval to enough candidates to represent a majority of the voters. Since this resembles proposing a coalition to govern, I have just been calling this "the coalition method."

Kevin


Le mercredi 2 décembre 2020 à 18:04:50 UTC−6, Forest Simmons <[hidden email]> a écrit :

>It is a very small step from Copeland done right to Borda done right because in a certain sense Borda can be 
>thought of as Copeland applied to each ballot separately and then summed over ballots. 
>
>Let's start with Copeland and change it into Borda.
>
>Copeland: The score of alternative X is the total probability of the alternatives beaten pairwise by X minus the 
>total probability of the alternatives that beat X pairwise.
>
>Borda: The contribution of ballot B to the Border score by alternative X is the total probability of the alternatives 
>ranked below X on B minus the total probability of the alternatives ranked above X on ballot B.
>
>That's it!
>
> What do you think?
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Re: [EM] Borda Done Right

Forest Simmons
Greetings Kevin,

I experimented with random favorite probability like Kristofer, and more generally random approval ballot probability for the probability component of this DSV method. The approval cut off could be just below top, or it could be at the truncation line, or it could be voter specified, etcetera. 

As long as the truncated candidates on the ballot represent less than 50% of the probability, it would not mess up the one pass method.

These choices of winning probability estimates, that is the ones based on random approval ballot probabilities, in general fail mono-raise, which is why I switched over to the quick-and-dirty direct estimate of the winning probability distribution.

In any case, a multi round version would probably at least mildly fail monotonicity, so it wouldn't be a big loss to just go back to the simpler and more familiar random approval probabilities.

The one pass version has a non-negligible chance of producing tied approvals ... which is additional motivation for going over to multi pass.

The truth is I'm more interested in (de-cloned) Copeland and Borda right now, though I always come back DSV Approval eventually.

Best,

Forest

On Wednesday, December 2, 2020, Kevin Venzke <[hidden email]> wrote:
Hi Forest, these are interesting... I have a new rank ballot sim currently and that Copeland one seems like an interesting one to try. Do you think it's actually cloneproof? Clearly if a faction tries to flood the race with additional candidates, the total score they can achieve across all those candidates should stay constant.

Kristofer has been studying low-manipulability methods where, often, observing the first preference count is a key component. So I wonder if the decloned Copeland would end up with similar properties.

I have a method similar to your DSV approval method. My primary issues (differences?) are just that I don't think truncated rankings can be allowed, and that I don't really see it as a single-round method. Very minor issues. I think this method gives strange results, but has its place. It doesn't feel to me like an automated approval method, but a method that forces voters to provide approval to enough candidates to represent a majority of the voters. Since this resembles proposing a coalition to govern, I have just been calling this "the coalition method."

Kevin


Le mercredi 2 décembre 2020 à 18:04:50 UTC−6, Forest Simmons <[hidden email]> a écrit :

>It is a very small step from Copeland done right to Borda done right because in a certain sense Borda can be 
>thought of as Copeland applied to each ballot separately and then summed over ballots. 
>
>Let's start with Copeland and change it into Borda.
>
>Copeland: The score of alternative X is the total probability of the alternatives beaten pairwise by X minus the 
>total probability of the alternatives that beat X pairwise.
>
>Borda: The contribution of ballot B to the Border score by alternative X is the total probability of the alternatives 
>ranked below X on B minus the total probability of the alternatives ranked above X on ballot B.
>
>That's it!
>
> What do you think?

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Election-Methods mailing list - see https://electorama.com/em for list info