[EM] A monotonic DSV method for Range

[Jameson Quinn]

> The classical example is
>
> x:ABC
> y:BCA
> z:CAB
>
> where  max{x,y,z} < (x+y+z)/2 .
>

Yes, that's the one.


>
> Is it possible for the DSV to place the approval cutoff's in such a way
> that all
> of the voters feel like their expressed interests were well cared for by
> the DSV?
>
>
Of course that's impossible, as you say, which is why I didn't suggest it. I
instead suggested a meaninful alternative: to minimize the total of
normalized honest regret minus required strategic dishonesty. Honest regret
means the difference in utility, per voter, between voting honestly and the
best cabal strategy available to that voter (ie, one which actually raises
the utility for all strategists, and all other voters vote honestly).
Required strategic dishonesty means the amount of utility that must be added
and/or subtracted to make the strategic vote; this refers to the input vote
marked by the voter, not the pseudovote created by the system.

That is a clear target. Your response makes me optimistic that your system
will do something like this, but I'd like you to run some scenarios. For
instance, what if the three factions are equal, and two factions give high
approval to the middle candidate while the third gives low approval? What if
there's a fourth candidate, disapproved by two of the factions but favorite
for a third - does the third faction still rate their Condorcet candidate
maximum? You'll never get 0 regret, but it is possible to see if you've
given minimum regret, or maximized the dishonesty required for strategic
voting.

(Why maximize required dishonesty, rather than minimizing it? Because the
greater the dishonesty required for strategy, the more reluctant the voter
will be to vote strategically. That's human nature, but it's also rational:
a highly dishonest vote, geared to a particular strategic situation, could
backfire in a more damaging way if the other votes are not as expected, than
a vote that's only slightly dishonest. Furthermore, if a lot of dishonesty
is required for a strategy to work, voters will correctly surmise that
they're unlikely to pull it off, and thus the incentive to try is less.)

Cheers,
JQ
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