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

[Toby Pereira]

From: Kathy Dopp <kathy.dopp at gmail.com>

>>  What I'm saying is
>> that in your system, adding C changes which out of A or B is more deserving
>> of the final seat, which seems wrong to me.
>First, adding more voters (group C) means that the denominator of the
>ratio (proportion) for each (every) voting group changes.>How could I change the denominator of the quantity v_i/v (the
>proportion of each voting group)  without changing the proportion of
>seats that each group should have?
Well, it changes the overall proportion they should have, but it does not change the 5:3 correct ratio of A to B seats. I would argue that if
Faction 1: w seatsFaction 2: x seatsFaction 3: y seats
is more proportional than
Faction 1: w+1 seatsFaction 2: x-1 seatsFaction 3: y seats
then with the same voting patterns
Faction 1: w seatsFaction 2: x seatsFaction 3: z seats
is more proportional than
Faction 1: w+1 seatsFaction 2: x-1 seatsFaction 3: z seats
for any x, y, w, z. Sainte-Laguë, D'Hondt and my system fit this criterion.


>> When [AFTER] the first three seats are
>> allocated, with C as part of the election, according to your system, the
>> order of how deserving each group is to the next seat is C>B>A. B is more
>> deserving than A.
>Yes.
>> However, if C is not there, you get A=B.
>No. I think what you mean to say is that after allocating 2 winning
>seats to group A and 1 to group B, group A and group B both are owed
>1/2 a seat each to be proportionately fair, so that  2 candidates
>each for group A and group B would be equally proportionately fair as
>3 candidates for group A and 1 for group B.
So you mean "yes". That's what I meant for A=B in this context.
>> But why should
>> the presence/absence of C make a difference to whether 3 seats to faction A
>> and 1 to faction B or two seats each to A and B is the more proportional
>> result?
>C's presence makes a difference because group C wins one of the 4
>seats, so that only 3 seats are divied up between group A and B.  C's
>leaving does not change (by one iota) the division of the first 3
>winning seats. Group C's absence merely makes a 4th seat available to
>divy up between two groups rather than between three groups!
No. I was talking about which of A and B was more deserving of the fourth seat even if C was more deserving than both, so assuming C has no seats.
>> It shouldn't. In that sense, C is irrelevant. Specifically, C is
>> irrelevant to which out of A and B is furthest from their proportional
>> allocation.
>AGAIN, you are using a perverted definition of "irrelevant" that I
>know of no one else who agrees with you. Group C is awarded 1 WINNING
>CANDIDATE, so if group C is absent, there is one (1) more candidate to
>award to the remaining groups.
See above.
>
>
>Given your prior example:
>>5: A1, A2, A3, A4
>>3: B1, B2, B3, B4
>>1: C1, C2, C3, C4
>How are you redefining the word "irrelevant" to label voting group C
>as "irrelevant"?
>
>> It's irrelevant to whether A or B is more deserving of the final seat
>> (regardless of whether C is more deserving than both).
>Obviously not.  If group C does not exist, there are only 8 voters in
>your example, not 9 voters. Therefore, the relative proportions MUST
>change between the two remaining groups unless you think magically
>reducing the denominator in the proportion of voters calculation
>should not alter the proportion of voters that each group comprises.>Again, you seem to have difficulty with the way the arithmetic of
>fractions work, as I believe I observed in the first of your emails I
>responded to in this thread.
You admitted you'd misunderstood what I was saying about fractions earlier. You can't then retrospectively wipe that from history because you don't like what I'm saying now. Sainte-Laguë and D'Hondt both fit the criterion I'm talking about, so it's not obviously wrong.
>I think we're just going around in circles, so I'm ignoring the rest
>of your response.
Well, the last example that you ignored was the simplest and probably example of why Sainte-Laguë and D'Hondt have this superior property that your method doesn't.
Toby
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