[EM] General PR question (from Andy Jennings in 2011)

[Toby Pereira]

Richard, there may have been come confusion because my examples have been assuming an approval ballot, so A, C and C, A are the same. Obviously if these are ranked ballots this changes things.
And in terms of the fair outcome (with approval ballots), I would argue that BC is the most proportional outcome, and it's an open question whether or not you think that makes it the fairest or best. It could depend on the circumstances. But that's also why I gave the food example as well and was wondering if there is a system that gives a non-arbitrary trade-off between proportionality and overall support, and also suggested using my system sequentially, which would elect A and one of B/C.
I also tend to think that the argument for score or approval ballots gets stronger for proportional representation than for single-winners. And I don't think Kemeny is the best ranked-ballot single-winner method to start from anyway!
 
      From: Richard Fobes <ElectionMethods at VoteFair.org>
 To: election-methods at lists.electorama.com 
 Sent: Friday, 3 October 2014, 1:37
 Subject: Re: [EM] General PR question (from Andy Jennings in 2011)
   
On 10/1/2014 1:47 PM, Toby Pereira wrote:
 >
 > 10 voters: A, B
 > 10 voters: A, C
 >
 > With two to elect, I would argue that BC is the most proportional.
 > ...
 > So the question is - what is the best election method in cases such 
as this? ...

The above example produces a tie for the second seat, and a tie requires 
some other way to resolve it.

Here is a more revealing example:

50 voters: A, B
49 voters: A, C
1 voter: C, A

In this case the fair outcome would be A and C.

Notice this is _not_ B and C, as Toby would probably "argue."

Although I have not run the numbers, I expect that VoteFair ranking 
would provide these results.

So my answer to the question "what is the best election method in cases 
such as this?" is ... "VoteFair ranking"

Details about VoteFair _representation_ ranking, which is the 
semi-proportional part of VoteFair ranking, are here:

  http://www.votefair.org/calculation_details_representation.html

Basically it proportionally reduces the influence of the voters whose 
first choice wins the first seat, and then does VoteFair popularity 
ranking (which is equivalent to the Condorcet-Kemeny method) to identify 
the winner of the second seat.

Of course the same approach of proportional reduction could be used with 
a different voting method.

Yet my expectation is that when voting criteria failures are 
_quantified_ by how often each method fails each criterion -- instead of 
using the current simplistic yes/no checklist approach -- then the 
Cordorcet-Kemeny method will be recognized as failing the criteria less 
often than all the other voting methods.

If some other voting method least-often fails all the voting criteria 
(roughly weighted by importance, and not corrupted by including 
variations of a minor criterion), then I would be happy to see the 
proportional reduction method applied to that method.

(Fairness is very important to me.)

Richard Fobes





On 10/1/2014 1:47 PM, Toby Pereira wrote:
> There are arguably situations where proportionality is desirable but not
> at the cost of overall support. I gave this example:
>
> 10 voters: A, B
> 10 voters: A, C
>
> With two to elect, I would argue that BC is the most proportional.
> However, imagine a group of people are deciding what to have for dinner
> on various days. They only have enough to have each particular meal
> once. For simplicity, Let's say there's 20 people and they have to
> decide for two days, and they vote approval style on the meals they like.
>
> 10 voters: pizza, curry
> 10 voters: pizza, fry-up
>
> This is effectively exactly the same vote as the other example.
> Curry/fry-up might be more "proportional" but it seems absurd not to
> have pizza on one of the days. Nothing is gained by preventing the other
> group from getting more enjoyment at no cost to yourself.
>
> So the question is - what is the best election method in cases such as
> this? I've struggled with this for a while because it requires a
> non-arbitrary trade-off between proportionality and positive support. I
> think my system of proportionality used sequentially would generally
> give good results, but it's a bit of a cop out and basically hides from
> the problem. There should be a reasonable non-sequential solution.
>
> Forrest Simmons's PAV would work reasonably well here (although I would
> argue with Sainte-Laguë rather than D'Hondt divisors), but it still
> fails independence of commonly rated candidates, and I don't know how to
> fix it.

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