[EM] Proxy-style hybrids with other voting methods

[Jameson Quinn]

The advantage of proxy systems such as Asset Voting is that they scale well
to a large number of candidates or voting options. An individual voter need
not study all possibilities; the proxy holder acts as their trusted
representative in that sense. Yet this same advantage can be seen as a
disadvantage, if a voter wants to be able to explicitly mark their own
individual preferences. Hybrid systems could give the best of both worlds in
this sense.

The principal advantages of the systems described below (particularly hybrid
Proxy/Bucklin) are:
- relatively easy to administer. Most are precinct-summable, and, while this
letter is to short to explain it, I can think of a trick to count the
ballots on plurality-only equipment by running the ballots through once per
candidate.
- Very easy to vote - a simple bullet vote loses you no voting power at all,
provided you trust your candidate to represent your interests.
- Expressive - If you don't fully trust your first-choice candidate, you can
express further likes and dislikes
- Tend to elect a true-majority winner, and if not, allow for a runoff
- Scale well for large numbers of candidates
- Give reasonable balance between slight advantages to "frontrunner"
candidates and enough openness to "insurgents".
- While strategy is definitely possible, it is not an overwhelming factor.
Naive voters will not unwittingly have significantly less voting power than
sophisticated ones. (Unless, of course, the basis for the hybrid system is
Range Voting, for which uneven strategy is the principal defect).

Basically, my idea for hybridizing is simple. A voter may explicitly rate or
rank any candidates he or she chooses to, but may leave some or all
candidates unrated. Then votes are counted and, if there is no majority
winner, the candidates can "fill in the blanks" on those ballots where they
are the first choice.

For example, consider hybridizing Range or Bucklin voting. To count, you'd
keep tallies of the range scores, and also a matrix of what number of X-top
votes left Y unranked. Then each candidate X would make a public vote
(separate from their private ballot), and their public score for each Y
would be multiplied by that number and added to the totals. Blanks on
ballots with ties at the top ranking would be divided equally. So if I vote
A=100, B=99, C=0 and candidate A voted A=100, B=0, C=0, D=60, then my ballot
would effectively count as A=100, B=99, C=0, D=60.

If using either Range or Bucklin, I would advocate having a 50% "majority"
cutoff for winning. If no candidate met that threshold, even after counting
proxy votes, then the election would go to a top-two runoff, and proxies
would NOT count in determining the top two. This motivates candidates to
seriously use their "proxy" capacity, instead of just voting 0 for all
others in the hopes of a miraculous win. If they don't use their proxy
power, they lose it.

Hybridizing a Condorcet-style system creates some more complicated issues.
Say a voter votes A>B>C (leaving D unranked) and then candidate A votes
A>C>D>B. This ballot, when filled in with the candidate's preferences, would
be contradictory; it would have a cycle B>C>D>B. Still, any Condorcet system
has a means of resolving such cycles, even though in normal circumstances
they cannot exist on a single ballot. (Allowing equalities would allow other
"paradoxical" ballots).

These proxies, by reducing the effective number of voters, could make
"condorcet tie" situations somewhat more common when there is not a single
majority winner. Without the proxy hybrid, I'd say any Condorcet system is
just about as good as any other, since condorcet ties are so rare; with the
proxies, a good tiebreaker is more important. Still, with a good tiebreaker
system, and with the number of proxies in each candidate's hands a known
factor, strategy is a minor factor, and is mostly about legitimate choices
of whether or not to compromise.

In IRV, the "proxy" votes could occur only after the ballot was otherwise
exhausted. Unlike the examples above, this case would not be
precinct-summable - but then, IRV is already not precinct-summable, so it
just adds a marginal additional complexity to an already-complex system.

In elections with known frontrunners, this would make little difference.
Even if many simply bullet voted for their favorite, the frontrunners would
have a majority or close to it, and so either the election would need no
proxies or some minor candidate(s) would just act as kingmakers.

Yet it does have some advantages. Because voters could, if they trusted
their first choice, decide not to rank "dark horse" candidates, the "dark
horse plus 3" pathology would probably be avoided. This is when a polarized
electorate consistently ranks a nonentity candidate second, allowing a
potentially disastrous, unscrutinized candidate to become an apparent
Condorcet. When voting their proxies, presumably the "frontrunner"
candidates themselves would recognize the real chance of electing such a
person, and give sufficient consideration to that choice.

....

Hybridizing a PR system is harder. My only idea along these lines is
"Approval-restricted Asset Voting". You vote a proxy and a (dis)approval
ballot, where blanks count as approval. A matrix is kept to ensure that your
vote will never be transferred to a candidate you explicitly disaprove of.
So, if candidate A was the proxy for 10K ballots, 3K of which disapproved of
B and 8K of which disapproved of C, candidate A could transfer 7K votes to B
-OR- 2K votes to C. The rest of the ballots would become untransferrable
(exhausted). Transferred blocs of votes would retain their "disapproval"
percentages, so you could guarantee that your vote would never go to a
candidate you disapprove. (If remaining ballots did not become
untransferrable, you'd lose precinct summability because you'd have to keep
each ballot to make such a guarantee.)

I'd like to figure out a way to use the approval ballot to determine order
of candidate elimination, but anything I can think of is vulnerable to
strategy. Note that as ballots became exhausted, the win quota would have to
be lowered proportionally, because no later runoff could hope to enfranchise
only those whose ballots had not yet achieved representation.

.....

I'd love to hear what others think of these proposals. Personally, my
favorite basis for a hybrid system is Bucklin with equal-rankings and gaps
allowed. (Bucklin does poorly on criteria, but relatively well in practice.
Obviously, hybrid systems are never going to be the best on pure criteria
anyway.)

Regards,
Jameson Quinn
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