[EM] Re: Condorcet's strategy problem, ICA

[Rob Lanphier]

Hi Kevin,

Thanks for the response.  I've had to cut my response short, because I
want to get back to a project I'm working on.  More inline.

On Sun, 2005-09-18 at 23:00 +0200, Kevin Venzke wrote:
> --- Rob Lanphier <robla at robla.net> a écrit :
> > My understanding based on your previous descriptions of ICA is that
> > explicit approval is problematic in ICA, since there's a lot of gaming
> > that can be done below the cut line.
> 
> This is the difference:
> Implicit approval: Burying strategy is always too risky.
> Explicit approval: Burying strategy only backfires when the other voters
> try to use burying strategy also.
> 
> The latter would probably lead to some equilibrium that we could live with.
> If it's really easy to bury, then everyone will try, and then it will
> always backfire, so fewer people will try.
> 
> My feeling is: Why not throw out burying strategy altogether?

I think implicit approval punishes honest voters.  You're asking that
voters opt out of races between candidates that they don't approve of,
even though they could very well have an opinion.

If the approval question is actually tied to something substantive (e.g.
term length), does that help remove the incentive to bury?

> > All things considered, I'm not sure how this doesn't count as "favorite
> > betrayal".  A voters gave the election away by "approving" B.  Their
> > favorite (A) lost the election as the result of a lower ranking.
> 
> "Favorite betrayal" means lower ranking *of your favorite*, not higher 
> ranking of a *different* candidate.
> 
> The issue here is truncation incentive, which WV methods have also.
> 
> Example:
> 
> 49 A
> 24 B
> 27 C>B
> 
> B wins. Now the B voters add another preference:
> 
> 49 A
> 24 B>C
> 27 C>B
>
> C wins. Has "one person, one vote" been violated? If you say no, I guess
> I haven't understood what you mean by "one person, one vote."

Well, the effect is the same, so I guess you could argue "yes".  Both
cases (the approval example and this one) are examples of the peril in
accepting a plurality in the absence of a majority.

I don't think this is a problem with "one person, one vote".  Instead,
this particular case is an "independence from irrelevant alternatives"
criteria (IIAC) violation, combined with severe apathy among A voters,
rearing its ugly head.  What's really happening is this set of ballots:
49 A>B=C
24 B>C=A
27 C>B>A

...is now:
49 A>B=C
24 B>C>A
27 C>B>A

If A is eliminated from this contest, both sets of ballots would be:
49:abstain
24:B>C
27:C>B

...and C would win, and there's no way that B voters could truncate
their way to victory.  So, at least in a head-to-head race, WV methods
behave in a relatively predictable way.  Your approval example doesn't
require a third candidate to produce a peculiar result.

IIAC is a tough problem to solve when there's no Condorcet winner,
especially when nearly half of the electorate (A voters) opt out of the
important race (B vs C) entirely.

I can't say I'm thrilled with how WV handles this problem, but accept
that the result is never going to be perfect when there is no Condorcet
winner.

I'd be willing to concede that both this:
40 A>B
35 A=B
25 B

...and this:
49 A>B=C
24 B>C=A
27 C>B>A

...constitute cases where no candidate can claim majority support, and
thus, there's really no "good" answer.

I'll have to do some more thinking on this.  It appears as though ICA is
a variant of CDTT//Approval.  Am I getting that right, and if so, can
you explain the difference and why it's different?  If this was
discussed before, just let me know the rough timeframe and I'll try to
dig up the reference.

Thanks
Rob