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

Kristofer Munsterhjelm km_elmet at t-online.de
Thu Oct 2 09:02:50 PDT 2014

```On 10/01/2014 10:47 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.

I think that shows that the desired outcome depend on the circumstances.

In an assembly, you want proportionality in part so that there's balance
between the factions according to the balance between them in the real
world. So AB gives disproportionally more power to the [AB] faction, AC
gives disproportionally more power to the [AC] faction, and so you only
have AA (a compromise/majoritarian approach) and BC left.

But in the pizza example, it's different. For the sake of simplicity,
I'll assume each person has preference 1 for the stuff he approved, and
0 for the stuff he didn't. Furthermore, we can assume some kind of
decreasing returns, so that having the same thing twice in a row is not
twice as appealing as having it once. Say it's 0.5 the second time.

Simple enumeration then gives:

[pizza, pizza]: 20 * 1 + 20 * 0.5 = 30
[pizza, curry]: 20 * 1 + 10 * 1 = 30
[pizza, fry-up]: 30
[curry, fry-up]: 10 * 1 + 10 * 1 = 20

So the difference is that power sharing is zero sum, but the enjoyment
from foods is not.

Well, power sharing isn't really zero-sum because electing good
politicians is better than electing bad ones (whatever their stripe),
but the proportionality aspect of it is. The analogous case would be
that a good representative who takes into the account the view of many
before decides may be equal to, or better than, a number of more narrow
representatives. But in elected officials, there's also the temptation
of factionalism and corruption over time; the representative might come
to represent more narrowly at the end of his term than in the beginning.
Such concerns would push the tradeoff in the proportionality direction,
away from the majoritarian support one.

For foods, the decision is going to be somewhat arbitrary because we
don't have "the answer" about how often you can eat something and still
like it. It probably depends. For politics, it's also going to be
somewhat arbitrary. It would depend on, among other things, the dynamics
of the legislature, how corrupt the representatives become, and how
divided the people itself is.
```