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

[Toby Pereira]

From: Kathy Dopp <kathy.dopp at gmail.com>
 >> My
>> system, for example, uses squared rather than absolute deviation (and uses a
>> different measure of deviation anyway) and it gives the results that I
>> wanted it to when I tested it, including stable results for the largest two
>> factions when the size of the third tiny faction changes, and the three-way
>> tie from the other example. It doesn't work by ignoring or eliminating
>> smaller factions;
>Neither does mine (in case you are implying such)  Some party list
>systems do work that way however.
I wasn't implying that but you suggested in one of your posts that it might be desirable. I was just saying that my system deals with it "naturally" - i.e. without manually taking out factions.
>> And I'm still unsure how to translate your method into approval voting with
>> overlapping factions.
>It works exactly the same way with overlapping candidate support in
>different factions. (i.e. v_i and s_i have exactly the same meanings,
>the number of voters in the group and the number of winning candidates
>each group contributes to electing.
But what I mean is that if a large faction (with say 50% of all voters) is divided into two (say 25% each) because of a single controversial candidate who appears on half of that faction's ballots but not the other half, then if that faction receives half the candidates (and the one controversial candidate is not elected), then it will be measured as unproportional because each faction will have each contributed to 50% of the candidates but will only be 25% of the electorate each.
>What is the logic of using squared rather than absolute deviation? and
>are you also selecting the slate of candidates minimizing your formula?
Squared deviation gave better and more consistent results when I tried it. I always come armed with election scenarios where I have an intended result, and I see if the method being tested gives the intended result. My method with squared deviation gave every result I wanted it to. Absolute deviation didn't.
And yes, in my method the winning set would be the one with the lowest sum of the squared deviations. Well, not necessarily, because if candidates could be elected sequentially, which could give a different result.
Toby


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