[EM] NPVIC and voting systems

[Jameson Quinn]

There is understandably an increased interest in the National Popular Vote
Interstate compact right now. How would that interact with other voting
systems, and how could an improved compact do so?

First off, the basics. The NPVIC is an attempt to effectively abolish the
US electoral college by a kind of constitutional end run: states in the
compact agree that, as soon as the compact gets enough states to control
the winner, they will all give all their electoral votes to the winner of
the national popular vote. The relevant bit of legal text in the compact
is: "Prior to the time set by law for the meeting and voting by the
presidential electors, the chief election official of each member state
shall determine the number of votes for each presidential slate in each
state of the United States and in the District of Columbia in which votes
have been cast in a statewide popular election and shall add such votes
together to produce a national popular vote total for each presidential
slate."

IANAL, but I believe that the above text would work with approval voting,
as is. The question is, how could it work with other voting systems?

I believe that the "ideal" interstate compact would allow different states
to use different voting systems, and then combine the results in some way.
What would that mean, and how would we decide that such a system was "fair"?

I've thought about it, and basically I think that the substrate for
combining results from two different voting systems has to be a lowest
common denominator. I think approval totals is clearly the right answer
here. It's compatible with plurality, it's natural, and it works with the
existing NPVIC.

What if some state used some non-approval ballot format, and then output
numbers that it claimed were compatible with approval totals? How could we
decide if that process was fair? There are cases that are obvious — a state
that said "our procedure is to run a Condorcet election, and then claim
that the winner had 100% approval and everyone else had 0%" would not be
playing within the NPVIC rules. But are there general rules for when a
system is or isn't fair?

First question: if a system has some kind of built-in logic that's
conditional on overall totals (as pretty much any system except approval
and score do), are they allowed to use the nationwide totals? If they are,
who gets to "go first"? Wouldn't that be giving an unfair advantage at
states with a more sophisticated system, given that they get to peek at the
results of other states before declaring their own?

One proposal would be to require each state to immediately report the
"highest possible" and "lowest possible" number for each candidate from
their ballots. Essentially: how many top-votes and how many bottom-votes
each candidate got. Then the local procedure could peek at these totals
nationally, but would not be allowed to peek at anything else across state
lines.

But I think that kind of thinking ultimately doesn't work. There are too
many questions it opens up. For just one instance: that would create all
kinds of strategic incentives, where two states could be using voting
systems that had good strategic properties but the combined system could be
absolutely horrible.

So I think that in the end, each state system would have to produce nominal
approval totals based only on their own ballots.

Let's say, for the sake of generality, that a state uses score ballots.
(It's pretty easy to translate these into preferential or graded ballots if
need be.)

To be "fair", a system for turning those ballots into approval totals must
obey the following criteria:
-applies monotonic functions to each ballot to map scores into the range
0-1, including both endpoints. For instance, for a given ballot, you could
say "scores above this threshold count as approval, below count as 0"
-These functions should be monotonic globally as well as locally. That is,
raising a candidate C's score on ballot X while leaving everything else
equal is allowed to change the function applied to ballot Y, but not in
such a way that C's overall approval total is reduced.
-The overall system must still be neutral and anonymous.

I think that these criteria are simple and desirable. They cover Bucklin
variants, including PAR. But... the second criterion would rule out IRV,
and it's not even obvious how to make a Condorcet method that would pass it.

I think that under the above rules, the most powerful way to assign votes
for a given state would be:


   - Use some neutral and anonymous system to determine a winner and a
   'threat' based on the ballots within the state, and decide which is more
   important.
   - If the winner is more important,
   - for every ballot which ranks put the winner above bottom, put the
      threshold just below the winner;
      - then, for every remaining ballot which rates the threat below top,
      put the threshold just above the threat;
      - then, put the threshold just below top on the remaining ballots.
   - if the threat is more important, do the first two steps as above in
   the opposite order, then put the threshold just above bottom on the
   remaining ballots.

I think the above procedure is fair, presuming the system for finding the
winner and threat is fair. In PAR, the winner would be the winner, and the
'threat' would be the disqualified candidate with the highest preference
total, and helping the winner would be more important than hurting the
threat.

...

I'll continue to discuss this later, but I want to see what others think
about this too.

Note: I'm not actually proposing any of the above as at all "ready for
prime time" as a way to rework the NPVIC. I'm just exploring possibilities
at the moment.
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