[EM] Monotone method inspiration approach?

[Kristofer Munsterhjelm]

On 18.01.2022 01:57, Daniel Carrera wrote:
> On Mon, Jan 17, 2022 at 4:40 PM Kristofer Munsterhjelm
> <km_elmet at t-online.de <mailto:km_elmet at t-online.de>> wrote:
> 
>>     These if-then clauses may be difficult to put into mathematical
>>     expression form, but I found this (which may seem a bit ugly at first):
>>             f(A) = g(H(fpA - fpC) * H(fpB-fpC) * A>B,
>>                      H(fpA - fpB) * H(fpC-fpB) * A>C)
>> 
>>     where H is the step function H(x) = 1 if x > 0, 0 otherwise,
> 
> 
> Btw, if you want to make a plot of that, I recommend you replace the
> Heavyside function with one that is equal to 0.5 when x is exactly 0.
> Otherwise, when fpB == fpC you'll see f(A) suddenly crash to 0 for no
> apparent reason and you'll be left scratching your head.

That's deliberately left unspecified because when fpB == fpC, that means
that two candidates tie for last, and then IRV's in big trouble. I
*think* using second preferences to break the tie would then work, but
as this situation is measure zero I didn't want to further complicate my
expression by including it.

In practice, this tie dependence can further amplify IRV's chaotic
behavior. Warren calls it "near-tie nightmares".

-km