[EM] Scientific American and the "Perfect Electoral System"

[Kristofer Munsterhjelm]

On 2023-11-07 05:29, Forest Simmons wrote:
> Rob,
> 
> Thanks for clearing up a lot  of the confusion... and for putting the 
> current status in perspective.
> 
> I like the comparison of the "impossibilities of voting" with the 
> impossibilities of faster than light travel, etc.  The 2nd law of 
> thermodynamics is especially relevant... because as Prigogene showed in 
> the 70's, the impossibility of decreasing entropy in closed systems 
> still allows for local pockets of possibility ... that make life 
> possible .... until the "heat death" of our island space-time big bang 
> remnant ... while miriads of new "inflationary bubbles" appear from 
> random virtual quantum fluctuations.
> 
> We used to "know" that the event horizon was a boundary of no return 
> .... nut now evaporation of black holes through quantum tunneling is 
> taken for granted.
> 
> In the early 1800's Gauss proved the impossibility of trisecting an 
> arbitrarily given angle .... inside the rules of classical geometric 
> ruler and compass constructions.
> 
> But it turns out that (as any first year topology student can show) any 
> angle can be transformed into atrisectable one by an arbitrarily small 
> perturbation.

One of my favorites in this respect is that the FLP impossibility 
theorem says that deterministic asynchronous consensus of a distributed 
system is impossible. However, by using randomization, you can get close 
enough to certainty quickly enough that it doesn't matter.

If anything distinguishes voting method impossibility theorems, it would 
be that many are surprisingly robust. For instance, perhaps we'd try to 
circumvent Gibbard-Satterthwaite by going to cardinal voting. But then 
Gibbard's stronger theorem shows that strategy can pay off even there.

Or perhaps we'd want to escape it by going to multiwinner, because G-S 
only applies to elections of single candidates. But then Duggan-Schwartz 
generalizes it to every method that elects a set of candidates (e.g. 
multiple winners). Or we'd try to circumvent G-S or Arrow by using 
random dictatorship or random pair. But their general performance - 
expected VSE or similar - sucks.

But we won't find stronger generalizations unless we try. And we won't 
find exceptions either.

-km