[EM] Range strategy pathological example (was Re: IRV vs Plurality)

[Jameson Quinn]

> ... a lot of hot air about "strategic voting" in Range.
>

Here's the nightmare scenario:

True (normalized) utilities:
20% voters: 10 Ader, 7 Bore, 0 Cush
20% voters: 8 Ader, 10 Bore, 0 Cush
20% voters: 0 Ader, 10 Bore, 8 Cush
40% voters: 0 Ader, 8 Bore, 10 Cush

Bore is the CW by a 60/40 margin over the other candidates, and the true
Range winner (avg 8.4 vs Cush's avg 5.6). However, if the Cush voters all
strategically downrank Bore to 0, then Cush wins (Bore's average drops to
5.4).

Yes, there are potential counterstrategies. But if I can construct a
semi-plausible example where unanimous strategy overcomes giant 3-2 margins
(in terms of both Condorcet and Range), then in real life, smaller margins
in strategy could overcome smaller real-world margins. And the reason I call
it a "nightmare" scenario is that I believe most people would find this
result especially bad, since it "rewards" the "sneaky" Cush voters who "take
advantage of" the "innocent" others. This would be especially divisive if
there were already-explosive ethnic or gender politics behind the division.

Thus, to me, Range's problem with strategy is not merely "hot air". Not that
it's insoluble - for instance, a Range ballot with options of only 0, 1,
998, 999, and 1000 would solve the strategy problem by forcing all voters to
use strategy (and thus would reduce to Approval, with the advantage that it
could be post-analyzed to find a CW). There are other ways to fix the
problem, too. And this one disadvantage of Range should be weighed against
Range's many clear advantages. But it is a real problem.

Jameson
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