[EM] MaxMinPA

[Kristofer Munsterhjelm]

On 10/17/2016 10:49 PM, Forest Simmons wrote:
> Kristofer,
> 
> Perhaps the way out is to invite two ballots from each voter. The first
> set of ballots is used to narrow down to two alternatives.  It is
> expected that these ballots will be voted with all possible manipulative
> strategy ... chicken defection, pushover, burial, etc.
> 
> The second set is used only to decide between the two alternatives
> served up by the first set.
> 
> A voter who doesn't like strategic burden need not contribute to the
> first set, or could submit the same ballot to both sets.
> 
> If both ballots were Olympic Score style, with scores ranging from blank
> (=0) to 10, there would be enough resolution for all practical
> purposes.  Approval voters could simply specify their approvals with 10
> and leave the other candidates' scores blank.
> 
> There should be no consistency requirement between the two ballots. 
> They should be put in separate boxes and counted separately.  Only that
> policy can guarantee the sincerity of the ballots in the second set.
> 
> In this regard it is important to realize that optimal perfect
> information approval strategy may require you to approve out of order,
> i.e. approve X and not Y even if you sincerely rate Y higher than X. 
> [We're talking about optimal in the sense of maximizing your
> expectation, meaning the expectation of your sincere ratings ballot,
> (your contribution to the second set).]

That's a kind of virtual runoff. So let's call the initial determination
of the two winners "the first round", and the decision between those two
"the second round".

Suppose now that we make a DSV method for this. For each voter, this
method takes a second round ballot and strategizes on behalf of the
voter for the first round based on that second round ballot. As you've
said yourself, the strategizer can't know the second round ballots of
anyone but the voter that it's strategizing on behalf of. The method
would consist of finding strategic votes for each voter and then running
the first round method on these, and determining the winner based on the
second round balllots.

The DSV method would then be a mapping from ballot sets to candidates,
i.e. an election method. And if there is a theorem to the effect that
"either certain criterion failures like FBC, or a smooth slope towards
Approval strategy being optimal" that applies to every election method,
then it will also apply to that DSV method.

I suspect that it would land in the "criterion failures" camp, which I
guess is my way of saying (in many words) what Benham said:

> [...] the cost is that the overall method becomes a festival of
> fairly easy and obvious Push-over strategising.

The DSV method would be inferior to the original virtual runoff proposal
in the sense that some voters would benefit from lying on their input
ballots (inevitable due to Gibbard-Satterthwaite). However, my point is
more that if there's a fundamental limit to the behavior of the whole
system, then "manual DSV" can't break the rules any more than "automatic
DSV" can -- unless minds are hypercomputational or something similar.

We can also run the argument in reverse. If a virtual runoff method with
(say) MMPO and Approval resists both CD and center squeeze while not
failing other criteria too badly, and if automatic DSV can be made at
least as good at the game of strategy as manual DSV is, then there
exists an ordinary election method that also resists both CD and center
squeeze.

The only exception is where manual DSV permits methods to avoid certain
criterion failures. Suppose you had a method of this form:

- Everybody gets into a room.
- They stay there until there's a majority decision.
- Then everybody exits and the majority decision winner wins.

The election method (majority rule) is strategy-proof and all the
strategizing happens outside of the method itself, in the minds of the
participants. But a DSV analog:

- Everybody submits a ranking to their personal robot (with some common
codebase).
- The robots enter the room and stay there until there's a majority
decision.
- The decision winner wins.

is just an ordinary election method (depending on what codebase the
robots run), and so is subject to G-S etc.

> Nobody expects sincerity on the first set of ballots.  If some of them
> are sincere, no harm done, as long as the methods for choosing the two
> finalists are reasonable.
> 
> On the other hand, no rational voter would vote insincerely on hir
> contribution to the second set.  The social scientist has a near perfect
> window into the sincere preferences of the voters.

That's right, but beware Campbell's law. If you use the sincere
preferences for anything serious, that may introduce an incentive to
distort them.

> Suppose the respective finalists are chosen by IRV and Implicit
> Approval, respectively, applied to the first set of ballots.  People's
> eyes would be opened when they saw how often the Approval Winner was
> sincerely preferred over the IRV winner.

Right - I don't think the pressure would distort the sincere ballots in
that case. I have a hard time seeing the IRV voters as devious enough to
try to manipulate their second-round ballots to make the IRV winner look
better.

> Currently my first choice of methods for choosing the respective
> finalists would be MMPO for one of them and Approval for the other, with
> the approval cutoff at midrange (so scores of six through ten represent
> approval).
> 
> Consider the strategical ballot set profile conforming to
> 
> 40  C
> 32  A>B
> 28  B
> 
> The MMPO finalist would be A, and the likely Approval finalist would be
> B, unless too many B ratings were below midrange.
> 
> If the sincere ballots were
> 
> 40 C
> 32 A>B
> 28 B>A
> 
> then the runoff winner determined by the second set of ballots would be
> A, the CWs.  The chicken defection was to no avail.  Note that even
> though this violates Plurality on the first set of ballots, it does not
> on the sincere set.
> 
> On the other hand, if the sincere set conformed to
> 
> 40 C>B
> 32 A>B
> 28 B>C
> 
> then the runoff winner would be B, the CWs, and the C faction attempt to
> win by truncation of B would have no effect.  A burial of B by the C
> faction would be no more rewarding than their truncation of B.
> 
> So this idea seems to take care of the tension between methods that are
> immune to burial and methods that are immune to chicken defection.
> 
> Furthermore, the plurality problem of MMPO evaporates.  Even if all of
> the voters vote approval style in either or both sets of ballots, the
> Plurality problem will automatically evaporate; on approval style
> ballots the Approval winner pairwise beats all other candidates,
> including the MMPO candidate (if different from the approval winner).

So strategies that would work on either method alone but not on both are
no longer effective. But is it possible to execute pushover-type
strategy on the new method?