[EM] Another Proposed Single-winner Method

[Kristofer Munsterhjelm]

On 17/04/2019 09.53, William WAUGH wrote:
> *Goals*
> 
> My design goals here are:
> 
> 1. The election method I am proposing must (like Score Voting) remove
> the strategic need for candidates to expensively convince voters they
> are one of the "2 most likely to win" <https://rangevoting.org/Cash3.html>.
> 
> 2. The method should be perceived to provide the perceived benefit of
> IRV over Score, at least as well as IRV is perceived to, that a voter
> can support a compromise candidate without diluting the voter's support
> for the voter's favorite candidate.
> 
> To obtain the above two benefits, I am willing to accept the following
> costs:
> 
> - The method need not be precinct-summable.

[snip]

> *Questions*
> 
> 1. Can you point out a simpler election method that you think would work
> at least as effectively as the one I propose above, to unseat oligarchy?
> (Score Voting is simpler, since it is precinct-summable).

A Condorcet perspective:

If a candidate is inside the Smith-set, it is well known, otherwise it
would be beaten by most of the other candidates (either by not being
ranked, or by being ranked below them on a majority of the ballots).
Thus, any election method that passes ISDA ensures that unknown parties
or candidates can't change the outcome.

In other words, there's no need for a candidate to use a lot of money
convincing the voters that he's very important and that voting for him
will not be a waste, because:

- either he's not in the Smith set, and the method passes ISDA, so it
doesn't matter where the voter ranks him, or

- he's in the Smith set, in which case he's well known already and
doesn't need huge amounts of money to promote himself.

More broadly, in FPTP/Plurality, it's important for a candidate to
signal that he's one of the frontrunners because voting for someone who
is not a frontrunner may make the wrong frontrunner win. This is called
compromise incentive: voting for a frontrunner even though you like some
non-frontrunner better is "compromising" for that frontrunner.

James Green-Armytage's paper, "Strategic Voting and Nomination" (e.g.
https://mpra.ub.uni-muenchen.de/32200/1/MPRA_paper_32200.pdf ) shows
that Condorcet methods generally have very low compromising incentive,
and so that won't be a problem.

In all fairness, I should say that the classical Condorcet methods
(Schulze, MAM/RP, etc.) are susceptible to burial. A follow-up paper of
Green-Armytage's, "Four condorcet-hare hybrid methods for single-winner
elections" (e.g.
https://pdfs.semanticscholar.org/49db/a225741582cae5aabec6f1b5ff722f6fedf1.pdf),
shows that Condorcet-IRV hybrids resist burial pretty well, albeit at
the cost of monotonicity and precinct summability.
Burial might not matter, and in that case, MAM/RP or Schulze is good
enough (and is at least somewhat known). But if burial resistance is
important to deter two-party rule, then use Hare (IRV) hybrids instead.

(Incidentally, I'm currently working on finding a method that is
monotone, passes ISDA, and that resists both burial and compromising.)

It's also possible to argue that all forms of election will result in
some sort of rule by the few. I've ignored that here, because getting
into a discussion of how few are too few would distract from the point
above.

> *Analysis*
> 
> You may be wondering why I included the possibility for the voter to
> choose Interpretation Category "B". No doubt when you first read it, it
> sounded strange and arbitrary.

I suspect that the voters will have the same thought. Suppose the
proposed method, when properly used, does what you say it does (that is,
stops oligarchy). Then the ballot format would probably still lead the
voters to scratch their heads going "what's all this stanza and
interpretation category business?". It's not particularly user-friendly.

It might be better suited as a multiple round runoff method. In each
round of the runoff, the voters know precisely who are in the running,
and there's no need for the contingency options of the stanzas and
interpretation categories.

> I believe that in order to remove the strategic need for candidates to
> expensively convince voters they are one of the "2 most likely to win"
> <https://rangevoting.org/Cash3.html>, an election method must meet two
> constraints:
> 
> 1. Frohnmayer balance; and
> 
> 2. Sufficient expressivity.

Random ballot seems to be a counterexample to both of these. Random
ballot uses Plurality-style ballots, and so is neither expressive nor
has the balance property. Yet it is completely strategy-proof. Either
your ballot is chosen to determine the winner or it isn't; if it's
isn't, it doesn't matter what you put on it, and if it is, you're best
off by putting your favorite first. Thus, there's no need for a
candidate to claim to be a frontrunner, because compromising strategy is
pointless.

Asset could also serve as a counterexample to sufficient expressivity,
if the candidates are sufficiently good at negotiating. (Perhaps party
list PR democracies also fit here, but maybe the system is too different
for the constraints to apply.)

The Condorcet-Hare hybrids also resist both burial and compromising, yet
clearly fail Frohnmayer balance since IRV itself fails it.

>From the other end, I doubt the following method is immune to
vote-splitting, even though it obeys both constraints:

- Each voter rates each candidate between 0 and 10, and marks his ballot
either "+" or "-".
To count a ballot:
	- The ballot is normalized so that the sum of scores is 1.
	- If the mark is "+", then for each candidate A, the normalized
ballot's score for A is added to A's total. If the mark is "-", the
normalized ballot's score for A is subtracted.

This is basically cumulative voting with Range ballots, and with a tweak
to make it satisfy 1. Continuous cumulative voting has a serious
vote-splitting problem where the best strategy is to give the preferred
frontrunner 10 and everybody else 0. I don't think adding a subtraction
option removes that incentive.