[EM] Plurality-order principle

[Tom Ruen]

I'm interested in opinions on these thoughts:

I see there's two major conflicting principles that we want in a single 
winner election winner:
1. Plurality Principle - we want the winner who is can beat all others in 
the full set of candidates. (Intensity of support)
2. Condorcet Principle - we want a winner who can beat all other 
head-to-head (Breadth of support)

I'm not interested in a debate whether either or both of these are valuable 
(or even fully defined) principles, and I accept opinions will vary which 
principle should rule exclusively or both or neither.

Our current single-winner elections are largely done by plurality, so this 
suggests to me that any reform done must be consistent with valuing the 
plurality count.

Runoffs (with a majority winner constraint) are a sort of compromise between 
these two principles. In the final round you know that the chosen winner 
will also be the Condorcet winner for that final set of surviving 
candidates. That's a nice little piece of knowledge.

The "problem" (for me) with runoffs are when different elimination rules can 
sometimes result in a different final set of candidates AND possibly find a 
different winner.

Specifically I consider "top-two runoff" versus "bottom-up runoff" as two 
extremes - the first most "harsh", and the last most "careful". Looking at 
these extremes I see that a runoff has the "original top-two" and the 
bottom-up-elimination "final top-two" as a different set of candidates, then 
we know different elimination rules can possibly pick different winners, BUT 
runoffs don't allow us to "peek" at alternative winners.

For me this is the #1 feature of IRV which I think will cause politicians to 
reject IRV. If I'm a candidate and I reach first or second in the first 
round, I EXPECT I should NEVER have to face elimination except to be 
defeated by a united majority against me. However IRV can have this result 
in a race where second and third place are close. (Like A=39%, B=30%, C=28%, 
D=3%)

I call this general idea as: Respecting Plurality Order. This is what 
candidates see in their expectations for success. (I accept that "plurality 
order" is not a stable measure since it can change if you change the 
original set of candidates, but there's nothing to be done about this except 
completely abandon plurality counts as valuable.)

I've never seen this "respect plurality order" idea expressed in this way, 
but I find it useful - most of all to reject bottom-up IRV.

I considered which election methods can satisfy this "respecting plurality 
order" principle. The general idea comes down to disallowing more than 1 
elimination round. AND it makes sense in terms of fairness. In the first 
round candidates KNOW their competitors, KNOW preelection poll data, and can 
judge their chances. However when the second round competition is 
unpredictable voters and candidates are put at a disadvantage to know how 
long to "stand tall", and when it is time to "compromise down" for a 
stronger candidate against an unexpected common enemy. Mechanized sequential 
rules are fine when elimination order is predictable, but unacceptable when 
voters might CHANGE their vote based on who was eliminated.

Limiting elimination to one round means candidates are partitioned into two 
sets "top set", "bottom set". All candidates in the top set have more votes 
in the plurality count than all candidates in the bottom set. Whatever rules 
are used to make this "top set", everyone will agree the winner should come 
from the top set of candidates, and the lower set can be eliminated. (IRV 
proponents will gladly say an elimination process can continue into a second 
elimination round, but I disagree because candidates will find themselves 
competing in a different field, and it becomes unfair to force elimination 
mechanically from rank ballots.)

The methods that follow this "plurality order" approach are:
    1. Plurality. (Top 1 wins)
    2. Top-two runoff. (Stronger of top-two wins)
    3. Condorcet. (No elimination)

All of these could be considered special cases of a general 
Plurality-Condorcet method:

Plurality-Condorcet:
    Round 1: Perform a plurality count, and eliminate a bottom set of 
candidates by predetermined criteria.
    Round 2: Perform a Condorcet count to find the winner. (Neglecting cases 
of no Condorcet Candidate)

I've considered different rules for elimination. My current "pet rule" is to 
eliminate all candidates with less than half as many votes as the plurality 
leader. It is "generous" without usually allowing too many candidates 
passing to the second round. I'd probably add a minimum top-two survivor 
rule as well to retain a final majority winner. We might also add an 
additional safety net rule "all candidates above 15% survive to round 2" to 
have a clear threshold for candidates (and supporters) to strive for in 
preelection polls.

I like this set of methods because they seem to respect both plurality and 
condorcet. Plurality supporters will accept the elimination sets as fair 
(forced mass-elimination from a known set of competitors). And Condorcet 
supporters ought to be willing to compromise and accept this "primary" round 
to reduce the candidates and they might even be happy for a smaller pairwise 
victory table.

This single-elimination round continues to have a spoiler effect. 
Introducing a new candidate similar to an otherwise winner, with less votes 
than that otherwise winner, could help knock out that winner in the first 
round. I only justify the continuation in that a "generous" survival rule 
can offset this fear, AND to the degree candidates FEAR their own 
elimination, it will encourage them to talk with like-minded candidates to 
compromise BEFORE the election (as plurality encourages). I consider that a 
positive aspect of the "spoiler effect". I often wonder that without any 
spoiler effect, that candidates would too easily multiple beyond the ability 
of voter to make an informed choice.

For me this also suggests a "progress" of methods from existing plurality 
towards "spoiler free" Condorcet. And until the Condorcet pairwise process 
becomes accepted legally as a valid counting method within "one person, one 
vote", I see the best we can do is a Top-two Runoff. (OR Top-two Instant 
Runoff)

This is my argument against (bottom-up) IRV as a useful reform. In reality I 
see IRV as "mostly harmless" and perhaps 99.9% of the time in practice 
top-two and bottom-up IRV will agree (IRV and Condorcet as well!), but I 
really fear a single nasty election where the original top-two and final 
top-two differ that it will sour people towards IRV and ALL election 
reforms.

As I've long said "Plurality is the enemy". It is "default" when people 
can't agree on anything else.

I like to visualize a "progression" of single-winner methods because this 
sequence doesn't say better/worse - just different compromises between two 
competing contradictory principles. In any given circumstance, we can ask: 
Do we "compromise towards Condorcet more", or "Compromise towards Plurality 
more"? I like that.

Tom Ruen