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

[Jameson Quinn]

You can also rework the numbers so that a strategic centrist beats an
unstrategic majority-top candidate:
20% voters: 10 Ader, 7 Bore, 0 Cush
20% voters: 0 Ader, 10 Bore, 8 Cush
60% voters: 0 Ader, 6 Bore, 10 Cush

Now the Bore voters can win, if they use strategy and Cush doesn't. But Cush
has 60% first-choice support, and wins an honest Range vote!

2010/1/26 Jameson Quinn <jameson.quinn at gmail.com>

>
> ... 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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>
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