[EM] Instant Runoff Voting 3-candidate elections - pathologies considerably more common than you may have thought

[Kristofer Munsterhjelm]

Jonathan Lundell wrote:
> On Aug 29, 2010, at 1:29 AM, Kristofer Munsterhjelm wrote:
>> Jonathan Lundell wrote:
>>> On Aug 27, 2010, at 12:48 PM, robert bristow-johnson wrote:
>>>> with Score and Approval, it's easy to mark your favorite
>>>> candidate (Score=99 or Approval=1).  and we know that Satan
>>>> gets Score=0 or Approval=0.  then what do you do with other
>>>> candidates that you might think are better than Satan?  that
>>>> question has never been answered by Clay.  and any answer must
>>>> be of a strategic nature.
>>> That is, to my mind, a fundamental problem with cardinal-rating 
>>> systems--approval, borda, range, etc. Except for some trivial
>>> cases (notably two-candidate elections), the voting act is
>>> necessarily a strategic exercise. With an ordinal method (IRV,
>>> Condorcet (though one could I suppose specify a non-ordinal cycle
>>> breaker), Bucklin) it's at least possible (and usually a good
>>> idea) to cast a sincere ballot.
>> What do you think of Cardinal Weighted Pairwise? It uses a
>> Condorcet matrix and sets the direction of defeats according to
>> inferred ranking of the rated ballots, but the magnitude according
>> to the rating. James Green-Armytage also suggests that a method
>> that makes use of it normalize the ratings within the Smith set so
>> the voters don't have to guess at what the Smith set will actually
>> be.
> 
> I don't see how it cures the cardinal problem.

If not cure it, CWP does seem to make strategy harder by forcing the 
voter to be consistent. He can't vote Approval style unless he wants his 
ballot to count as an Approval one, as the ranking is inferred from the 
rating; and if the implementation employs the normalize-within-Smith 
suggestion, it's hard to do strategic normalization when the voter's 
unsure of what the Smith set may turn out to be.

>>> Why the latter is a good thing is a separate discussion... ----
>> I think Abd once argued that people will "automatically" vote in
>> the Approval, maximum for all those I like better than the lesser
>> evil, minimum for the rest, manner. IIRC, he called it "Neumann-van
>> Morgenstern utilities".
>> 
>> I don't think so, so I think Approval burdens people with the need
>> to be strategic, but there you go -- that's at least one person
>> arguing that one should (and would) rather use strategic utilities.
>> 
> The strategy problem isn't solved by recommending a "best strategy".
> I agree with you on the subject of Approval, merely point out that
> the same is true for any cardinal-weighted system.

It isn't, but I pointed that out as an example of someone arguing that 
people don't vote honestly to begin with, and that because they don't, 
they gain a better outcome.