[EM] “Monotonic” Binomial STV

[Kristofer Munsterhjelm]

On 28.02.2022 01:38, Kevin Venzke wrote:
> Hi Kristofer,
> 
> Le dimanche 27 février 2022, 15:53:46 UTC−6, Kristofer Munsterhjelm <km_elmet at t-online.de> a écrit :
>> (You could try to add this method to the simulator we've been
>> discussing, I guess, and see where it ends up :-) Though it has the same
>> ambiguity as Antiplurality about what to do with truncation and equal-rank.)
> 
> I can do a plot with no truncation allowed. One may have to go to:
> http://lists.electorama.com/pipermail/election-methods-electorama.com/2022-February/date.html
> in order to see this in a fixed-width font:

I'm using a dedicated mail program, so no problem there :-)

> ......................IRV....................................................
> .............................................................................
> ..............................................BPW............................
> .............................................................................
> ............IFPP....................CIRV.....................................
> .....................ChainRO.................................................
> ...................................fpAfpC....................................
> .............................................................................
> .............................................................................
> ..................................MinMax.....................................
> ..................................CFPP.......................................
> ..............................................Bucklin........................
> .............................................................................
> FPP............DAC/DSC.......................................................
> .............................................................................
> .............................................................................
> .........................................Borda...............................
> .............................................................................
> .............................................................................
> .............................................................................
> .........................................................................Anti
> .........................................................................plur
> ......................................................BinSTV.............alit
> 
> I have 3-candidate Binomial STV as slightly closer to Borda than to Antiplurality,
> but still pretty distant from either.

That makes sense. As I remarked to Forest, although the vast majority of
 election methods that have been proposed have win regions that are
unions of convex polytopes, I think this one might be an exception.
Using, in effect log(fpA)-log(lpA) > max over other candidates X:
log(fpX)-log(lpX) might well induce a curved win region.

It's an interesting question if there's some (property based) reason
that most methods are linear in this sense. Perhaps there's some
property that can only be passed by such methods. But if there is, I
don't know what it is.

I did mention some nonlinear methods of my own a long time ago, and how
they might be even more strategy resistant than the linear ones.
However, I'm not sure I was right back then, because I thought I found a
method that was much better than fpA-fpC, yet the optimal method finding
program returns a method that's very close to fpA-fpC. So something
could easily be off.

-km