Bayesian regret (executive summary)

  1. "Bayesian regret" is the "gold standard" for comparing single-winner election methods.
  2. Roughly, the "Bayesian regret" of an election method E is the "expected avoidable human unhappiness" caused by using it.
  3. The Bayesian regret of E can be mathematically defined.
  4. It can be measured quantitatively by computer simulations.
  5. No assumption need be made that voters are "sincere" or "well informed." Bayesian regret can be evaluated for any kind of voter strategic behavior and any level of voter informedness.
  6. No simplistic probabilistic assumption need be made such as that we have "random uniform elections" ("impartial culture"); you can put in arbitrarily sophisticated probability distributions, "issue spaces," "utility generators," etc (and we have done quite a lot of that including IEVS features the world's first "reality based" statistics)
  7. Even if utilities for different humans are regarded as inherently unknowable, unmeasurable, and inapproximable by any physical/biological process, that would not affect the validity of the Bayesan Regret methodology and its conclusions one iota.
  8. Those measurements have been done and range voting is robustly the best single-winner voting system (i.e. has the least Bayesian regret) among all commonly proposed alternatives.
  9. Bayesian Regrets values are "meaningless numbers"? Well, no. They're deaths. Wasted money. Illness. Crimes. Devastation. Poverty. Bayesian Regret encapsulates everything you don't want. Yes, it encapsulates it in a number. But that doesn't make it any less real. That makes it more real because it is quantifiable rather than puffery. Bayesian Regret is plenty real. As real as your death.
  10. Pretty picture! (And in black and white.)

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