[EM] Manipulation Resistant Voting
km_elmet at t-online.de
Sun Jul 18 01:48:11 PDT 2021
On 7/18/21 5:30 AM, robert bristow-johnson wrote:
>> On 07/17/2021 5:12 PM Susan Simmons <suzerainsimmons at outlook.com> wrote:
>> The Gibbard–Satterthwaite theorem states roughly that every
>> deterministic voting rule is manipulable, except possibly in two cases:
>> if there is a distinguished voter who has a dictatorial power, or if the
>> rule limits the possible outcomes to two options only.
> Could someone demonstrate here how, well outside a cycle, an
> insincere vote can bring in a tactical advantage with a Condorcet rule?
> Say when would it be advantageous to bump your Number 2 to Number 1?
> Or when would it be advantageous to bury your Number 2?
> And without going anywhere near a cycle.
There are two cases where it would be beneficial to do strategy.
Number one is when there is currently a CW, but a faction can alter its
votes to create a cycle. Then it's beneficial if they prefer the cycle
tiebreaker winner to the CW. (Or vice versa, for that matter)
Number two is where there is a cycle and the tiebreaker itself is
vulnerable to strategy.
If the voters are constrained so that they can only submit ballots which
in aggregate makes a CW, then every Condorcet method passes IIA (since
if the CW is removed, it's not an irrelevant candidate, and if someone
else is removed, the CW remains the CW). I think, though I'm not sure,
that this also makes it strategy-proof.
My point, though, is that you don't just have strategy behavior inside
the cycle domain, you also have strategy by deliberately pushing the
method into (or out of) a cycle.
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