Yee Diagramm - Strong monotonicity failure resistance

Below you will find examples of Yee diagrams regarding some voting methods.
The list of used systems is as follows (from left to right):
FAIR-V, STAR, CB, SV, STARV, STLR, DV, IRV
Systems that don’t satisfy monotony:
FAIR-V, CB, DV, IRV

Formula used in the simulation to calculate utility:
utility = 1 / sqrt (12000.0 + distance^2)
The extremes of the utility range are found: [worst utility, best utility] and then the range is stretch to [0, MAX], for the voting system.

10000 voters, 200 standard deviation



10000 voters, 200 standard deviation



Another comparison, between the following 3 systems:
Extended DV, DV, IRV

10000 voters, 100 standard deviation


In this post I want to discuss the failure of monotonicity.
IRV (weak resistance to failure of monotonicity): it is certainly the method that fails monotonicity most of all, and this failure takes the form of a big bifurcation in some vertex.
DV (medium resistance to monotonic failure): fails much less than IRV, but such failure is still visible.
FAIR, CB, Extended DV (strong resistance to monotonicity failure): there doesn’t appear to be any visible effect of monotonicity failure, to the point that they are the same than other methods that satisfy monotonicity.

I think it’s necessary evaluating how much a voting method fails a certain criterion, and in this context I would say that:
a method that have strong resistance to monotonicity failure (like FAIR-V, CB, Extended DV) can in practice be considered immune to the problems about failure of monotony (although, at a theoretical level, failure is possible).

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