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osmarks 2024-12-26 19:01:05 +00:00 committed by wikimind
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@ -29,6 +29,6 @@ Vengeance is an important mechanism to disincentivize doing bad things to GTech
If the scale of the vengeance relative to the event triggering it (denoted ν) is less than 1 - i.e. the vengeance is smaller than the act causing it - then the resulting vengeance will tend toward 0 over time, a desirable outcome. However, it can be shown that this results in an asymmetrical distribution of vengeance, with the initial party receiving less total badness. ν > 1 leads to increasing total badness over all time, due to the lack of convergence, although there is no asymmetry, and the situation for ν = 1 is nearly identical, although it keeps vengeance per step constant (obviously).
However, more complicated strategies can resolve these problems. Stateful vengeance handling, while possible, is likely impractical for GTech™ employees due to high storage requirements; we instead recommend a stochastic vengeance strategy with ν > 1 but a probability p of not exacting vengeance at any step. It can be shown that vengeance will terminate in a finite number of steps (an expected number of 1/p) with arbitrarily high probability, even though for some values of ν it will lead to an infinite expected quantity of vengeance.
However, more complicated strategies can resolve these problems. Stateful vengeance handling, while possible, is likely impractical for GTech™ employees due to high storage requirements; we instead recommend a stochastic vengeance strategy with ν > 1 but a probability p of not exacting vengeance at any step. It can be shown that vengeance will terminate in a finite number of steps (an expected number of 1/p) almost surely, even though for some values of ν it will lead to an infinite expected quantity of vengeance.
In practice, issues of vengeance quantization and vengeance illegibility/noise can make this difficult. Vengeance quantization derives from the fact that it is not necessarily possible to exact vengeance at a scale of arbitrary real numbers, since many possible actions are highly discretized, and vengeance illegibility is the closely related issue that both parties may not be accurately determining the intended vengeance scale of the other, resulting in greater or lesser retribution than intended. For this reason, it is suggested that vengeance with values of ν very close to 1 not be used.