[EM] The Last Temptation of David Catchpole- rated R

[David Catchpole]

On Thu, 28 Oct 1999, Donald E Davison wrote:

> Dear David Catchpole,
> 
>      You surprise me. I should think that a person who is into mathematics
> as you seem to be, would have made a few calculations and determined that
> my claims are indeed possible. In other words: You should know the answers
> before you make the charges.
> 
>      I am going to give you a chance to redeem yourself. In this letter, I
> am going to make the few calculations that prove my claims to be possible.
> And then I am going to ask you to give an example that show my claims to be
> true.

I didn't ask for "calculations-" I asked for a single example which
demonstrates the phenomenon you insist can occur.

>      This is how you can redeem yourself. Fear not, your task will be easy
> - `A Piece of Cake'. I have already constructed such an example.

As the priest says in Casper, "piece of carrot cake."

>      I will now say the same in a different way, in order to help you
> understand. If only 80% of the votes elect all the members, then a 48%
> group has 60% of the votes that are electing the members (48/80=60%)
>      My claim of 58% falls inside this range of 60%, therefore my claim is
> possible.

However, this 60% will not be reflected in 60% of the elected members.
Rather, in the given 4 winner example, with a Droop quota of 20, the 48%
group will receive 2 members- that's 50%, not 58%. Hare has
precisely the same result for the same situation (If not worse- consider
A1 20, A2 20, A3 8, B1 25, B2 7, B3 7, B4 7, B5 6 for some Hare quota
systems). Nihilism and ignoring the issue of how votes go into _seats_
(not how votes fit into quotas) don't get nowhere.

>      If you chose not to take this assignment, you will not be redeemed,

uh huh.

> your computer will self destruct, and your first born will be taken from
> you. (he's kidding)

Damnit. Where's a Cohen when you need him?

> Note: It is the feature of having small districts that stop an eight
> percent group from electing any members, which was included in my claims.

Yeah, but I was discussing the Droop quota, not the problem of small
electorates.