[EM] Yee Diagrams of IRV
suzerainsimmons at outlook.com
Wed Jul 7 20:19:58 PDT 2021
When you look at IRV under the "electoscope" of Yee diagrams, what do you see? Fragmented win regions shot full of holes, even complicated fractals. Sometimes a candidate's position is isolated outside of its own win region What do these fragmented pictures mean? They mean that as the center of a smooth, regular gaussian distribution of voters moves in a straight line through issue space, the IRV winner changes chaotically, a manifestation of extreme sensitivity to small variations in voter preferences, the more candidates, the more chaos, but even with only four candidates on the corners of a square you start to see this chaos.
Condorcet methods show none of this strange, erratic, geometry ... because when voters are distributed with central symmetry in issue space (as the electoscope assumes) the candidate closest to the center of symmetry will be a Condorcet winner. The electoscope is very easy on methods, it throws all easy pitches ... the voter distributions are not only centrally symmetric ... they are Gaussian! Thrown softball pitches like that, who could make a bad showing? ... not Borda, not Range, not STAR, not Majority Judgment, not BRGL, not CSSD, not RP, not Nanson, not River, not Approval, etc ... among all well known methods only IRV seems capable of making a really bad mess out of it.
It is well worth the time to study the Yee diagrams on Warren Smith's website, for example. It gave me a whole new insight into IRV's shoddy performance. These examples are not based on weird distrbutions of voters in high dimensional issue spaces... they are two dimensional Gaussian distributions with circular symmetry, for Pete's sake!
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