[EM] Condorcet/Score

[Abd ul-Rahman Lomax]

On 1/4/2019 2:47 PM, Curt wrote:
> Hi, I was wondering what you all thought of the following reasoning.
>
> 1) Start with the assumption that for a single-winner election, if one candidate would defeat all others head-to-head, that candidate must be the winner. This requires the method to be Condorcet-compliant, and, I believe, disregards the later-no-harm criterion.

Actually, you are starting with a prior assumption, perhaps several of 
them. You assume a deterministic voting system, you assume a fixed 
candidate list. Then "must be the winner" may allow a candidate to win 
without being specifically approved for that by a majority of the 
electorate, which is a basic principle of democracy for *any decision 
binding on the membership.* It's where democracy begins.

I have never seen a study of when and where this was abandoned. It is 
still followed in deliberative bodies

LNH is a voting system criterion, that, if passed, disallows compromise. 
Imagine neighbors voting to decide what colors to paint fences. Neighbor 
A has a favorite. The voting system they use satisfies LNH. LNH 
compliant systems must hide all lower preferences from consideration 
until the first preference is actually eliminated. Then and only then 
can another color be voted for. In fact, neighbors will probably use an 
ancient system, negotiation, and will seek supermajority, not mere 
majority. Majority is a fall-back position, but if majority decisions 
are not at least accepted at some level, the neighborhood will be in 
trouble.

People will agree, in real situations, that such a winner is not always 
the best choice. And this points to a possible fundamental voting system 
criterion: can the system distinguish preference level from acceptance, 
which is binary, and there is a simple way to do this with score voting, 
which is to define a particular score or above as the minimum acceptance 
level.

In promoting Approval Voting, votes have been called, no surprise, 
"approvals." "Do you approve of candidate A?" That is an ontological 
error, where "approve" has a narrow meaning, different from the 
emotional reaction. In a runoff voting system (which I argue is 
fundamentally necessary), approval means "do you prefer the election of 
this candidate over the election being repeated?" That is a binary choice.

>
> 2) Acknowledge the “one-person one-vote” principle that means that if, in a two-candidate election, candidate A has 50 votes and candidate B has 49 votes, then candidate A *must* win, even if B’s voters are wildly more enthusiastic.

Which, of course, makes sense only because we are accustomed to voting 
systems that don't consider preference strength, except in one way: 
turnout. Turnout is biased in some election by the level of preference 
the voter actually holds. "Wildly more enthusiastic" does not encompass 
the possibilities. How about "49 people are ready to destroy the 
organization if the candidate mildly preferred by 50 is elected?" 
Preference strength matters. Only if the two factions are similarly 
"enthusiastic" would choosing a bare majority candidate make sense. In 
reality, the probability is high that the best person for the office was 
not on the ballot. A simple vote-for-one ballot seems simple, but does 
not collect enough information to allow better social choices to be made.\

So, then, should B win? No, of course not, not just with that 
information. However, I suggest this basic principle, to make *and 
continue* any decision, majority approval is required. This can be 
expressed as a ratification or the lack of a motion for reconsideration.

> 3) Acknowledge that score or range voting *does* have an advantage in recognizing overall utility society when taking into account voter enthusiasm - *if* the enthusiasm is scored/recorded honestly.

This issue of "honesty" vastly distorts the reality. Voting is like 
tossing weights on a balance. Score voting is just voting, tossing 
weights on a balance. Generally, score systems do not reward reversal of 
preference, optimal strategy will rank candidates in order of 
preference, but, then, the decision of how to rate those candidates 
(equally or not, or with what difference in score) is made generally, 
and optimally,. according to the voters' estimation of the effect of the 
vote. There may be such a thing as absolute preference strength, but 
it's quite a complex issue. To test it requires some kind of metric. 
Bottom line and in practice, people have varying preference strength and 
it is expressed according to probabilities, not according to absolutes.

When there is a real-world consequence, affecting the voter, that leads 
the voter to make accept/reject choices, this can nail the score votes 
to a minimum of three levels. Suppose there is a score system allowing 
three ratings: Prefer, Accept, and Reject. "Prefer" has an obvious 
meaning, Accept means "prefer the election of this person to a repeated 
election," and Reject again has an obvious meaning: "I prefer another 
election."

Ballots, I suggest, as far as is practical, should collect preference 
information and acceptance information. So I would have a score ballot 
with enough rating resolution to allow meaningful preferences to be 
expressed. Below a certain level of preference strength, votes are not 
particularly meaningful. My general sense is that ratings of 0-9 would 
be quite adequate. Then 5 could represent acceptance. Because equal 
rating would be allowed, the voter would still have 4 acceptance levels 
and 6 rejection levels.

But such systems require very substantial voter knowledge and 
participation. There is a far easier solution that hybridizes voting 
with represented voting, first suggested by Charles Dodgson (Lewis 
Carroll) in the 1880s, for use with Single Transferable Vote, now called 
Asset Voting, the term invented, if I'm correct, by Warren Smith. More 
about that below.

> 4) Acknowledge the occasional (and probably rare) phenomenon of A->B->C->A loops in Condorcet-style voting, which must be resolved somehow.

Once we accept that an election can fail, which is standard democratic 
process in voluntary organizations, there is no "must be resolved." Does 
the voting system allow explicit acceptance, in addition to mere 
preference? If so, that is a possible resolution. This is approached and 
possibly implied by the use of a score ballot. This would be handled in 
a ranked ballot by having a dummy candidate called "Repeat the 
election," which the voter would rank at the appropriate position in the 
list of candidates.

And compared to Asset, it's all unnecessary complication, that 
perpetuates the isolation between voters and the collective. Asset 
creates public voters (I call them electors) and the collection of 
electors fully represents the entire voting electorate. The electors 
then make the necessary compromises, etc,. on behalf of the electorate. 
Contrary to what is often assumed, these are not necessarily 
"candidates" for the office. This is like the original U.S. electoral 
college, but the writers of the Constitution punted on voting system. 
It's clear that the intention was not, however, "pledged electors, from 
a slate pledged, and not even named on the ballot." It became that 
because of a loophole in the Constitution, allowing each state 
legislature to determine how the electors from each state would be 
chosen. Thus, in fact, the Electoral College ended up representing the 
States, not the voters. They did not factor for the development of the 
party system.

> 5) Accept that the presence of such loops is not a “bug”, but instead the measurement of some level of indecisiveness among the electorate, such that further voter data is required.
Indeed. What is missed is "a better list of candidates."
>
> And end up with the following:
>
> 1) Present the ballots as score/range ballots
Score ballots allow ranking. If the score resolution is limited, not 
full ranking, but full ranking with small preference strength (or donkey 
voting in systems that require full ranking, as in some Australian 
elections) is largely meaningless. If there are as many ratings as 
candidates, it allows full ranking. Such ballots would collect valuable 
information, even if it is not used for the instant election. It could, 
for example, provide for ballot eligibility, it could affect campaign 
funding. I am opposed to public campaign financing (but in favor of 
measures that would reduce or even eliminate the need for major election 
spending, which are possible, and Asset would do it), but if there is 
such financing, ratings could affect it. At substantial cost and effort, 
information is gathered from the voting electorate, but it's primitive, 
black and white, unsophisticated.
> 2) When tabulating, use the scores/ranges to deduce an ordinal (ranked-choice) ranking for each ballot, ignoring the scores/ranges otherwise
Yes, basic in designing a hybrid system. This was proposed long ago.
> 3) Use the rankings to determine if there is a Condorcet Winner. If so, STOP HERE. This makes the voting method Condorcet-Compliant.

I would not stop there. I would require explicit approval. This can be 
easily specific on a score ballot as a particular rating. On a score 9 
ballot, half rating would be 4.5 which can't be expressed, so 5 becomes 
the accepted rating level. The actual rules could be come quite 
sophisticated, with practice and experience. I would "err" in the 
direction of repeated election where there is doubt about the result.

I would have write-in votes be allowed in all elections (which is 
standard practice in many places in the U.S.), including run-offs. I 
would then use an "advanced ballot" for both a primary and a runoff. The 
runoff ballot would then have at least two candidates on it, plus 
write-in. Under some conditions, it might have three on the ballot.

A Condorcet winner, if not winning directly, would be on the runoff 
ballot, for sure. This is why "must win" is a Bad Idea. The runoff will 
test preference strength! If you voted for the CW, but it was a weak 
preference, you might not turn out to vote in runoff, because *you don't 
care enough to spend the time.* So the "enthusiastic" Score voting 
winner might well prevail. There are indications from study of runoff 
election results to indicate that this effect actually happens. A dark 
horse becomes the runner-up in a primary and then goes on to win in the 
runoff. That rarely happens with IRV.

> 4) If not, determine the Smith Set
> 5) Use the scores/ranges to determine the winner from within the Smith Set. This makes the method Smith-compliant.

The Score voting winner would also be on a runoff ballot.

If the Score winner is the same candidate as the Cordorcet winner, and 
if a majority of the electorate has also approved of the candidate, 
there is no runoff.

Then we start to deal with rarer situations: my view is that no election 
should complete without majority approval. A point to keep in mind, 
mentioned by Roberts' Rules of Order, is that repeating the election 
would allow new nominations. In fixed runoff systems, this is still 
respected by allowing write-in votes in the runoff. (and it has happened 
that a write-in candidate won a runoff.) Ah, but can a candidate win a 
runoff with a mere plurality? This is at the edge of democracy, and it's 
hazardous to discard the majority principle. But the example I know of, 
it was very clear that the winner was the choice of the electorate, 
given the obstacles she faced and overcame.

The runoff ballot should also allow multiple "accept" votes, in addition 
to ranking. This would allow a write-in to also express an opinion on 
the frontrunners.

Asset trumps all this complication. Asset shines with proportional 
representation, with the entire assembly being a single district, which, 
then allows flexible and full representation. I would expect that 
electors would mostly be elected locally, so they would, to that extent, 
represent districts. And then the Assembly would elect officers, i.e,. a 
parliamentary system, the officers serving at the pleasure of the 
public, expressed through the Assembly, elected by the Electoral 
College, each set representing a quota of votes, all traceable to 
electors, and voters know whom they voted for.

However, the Electoral College could also elect officers, single-winner. 
Simple. Ballots could even be vote-for-one, majority required. But there 
is no reason to avoid more sophisticated, more efficient ballot designs, 
expecially given that the electors are public voters. So the standard 
result that a decision can be moved for reconsideration by anyone who 
supported it can function (with a secret ballot, there is no way to 
know). A motion for reconsideration must be seconded and is then put to 
a vote immediately. No debate, no discussion. Thus every election must, 
in effect, be, at least, implicitly approved.

> I am not well-versed in voting criteria, but it seems to me this bypasses the worst criticisms of score/range voting, while also taking in account some of their advantage. While score/range voting is susceptible to strategic voting, there should be little incentive for a voter to strategically adjust their scores *to the point of changing their ordinal ranking*, due to the emphasis on finding the Condorcet Winner first.
Right. Equal ranking must be allowed, though. It means "no *significant* 
preference.
>   And so then, since people will be scoring/rating relatively honestly, greater social utility is met in the case where there is not a Condorcet Winner. Finally, we know that the winner is (ordinally) preferred over all other candidates outside of the Smith Set, making it Smith-compliant. Score/Range/Star voting are not Condorcet-compliant (nor Smith-compliant, I think), but this voting method is.

But it does not satisfy the generalized "negative majority criterion" 
(for lack of a better name, "if a candidate does not receive an 
acceptance vote from a majority of voters, the candidate cannot win.". 
Even though this is standard practice in deliberative bodies, voting 
systems theorists, designing voting systems criteria, have apparently 
neglected it.

Task for a student: how did we end up in this fix?

The most advanced voting system in current practice in the U.S. is 
runoff voting. It has a problem, for sure, center squeeze. Curt should 
look at Bucklin voting, which was almost what he wants. A Score ballot 
could be used for Bucklin. Bucklin was rejected, in the end, because not 
many voters in primary elections still using it, were adding additional 
approvals. It's obvious why. It was a friggin' *primary*. It was 
replaced by runoff voting, if I'm correct, instead of keeping the 
Bucklin ballot for the primary and using it to feed a runoff if there 
was no majority winner, they dropped the advanced ballot.

So FairVote is going around, killing the most advanced method in use 
(runoff voting), in favor of the "instant" version that then fails to 
allow flexibility in runoffs. Even with top-two runoff, the runner-up in 
the primary often wins, about a third of the time, whereas it is rare 
with "instant runoff." FairVote then argues that this result is 
"unfair," because of lower turnout in runoffs, which is a knee-jerk 
response that assumes there is something wrong with low *voluntary* turnout.

> I conjecture that if scores/rankings were measured for all other Condorcet methods (and then similarly ignored to deduce ordinal rankings), this method would offer greater social utility as measured by the scores, by definition. And, I believe this is superior to pure range/score/star voting *when* starting with the axiom that the voting method must be Condorcet-compliant.

The Condorcet criterion is intuitively satisfying only in a world which 
does not consider *actual preference strength. The negative majority 
criterion is more fundamental. I agree that hybrid systems are the 
possible future of voting systems, but the fact is that very primitive 
voting systems work with the negative majority criterion respected.

For the present, the most obvious voting system reform is what I call 
"*Count All the Votes*." This slogan or name for it represents how 
simple the system is, it requires no ballot changes except a changed 
instruction. This is what is more commonly called Approval Voting, and 
it is a Score voting system, Score 1, i.e, votes from 0-1, with 0 being 
assumed if the voter does not mark the candidate. It is then a simple 
step to add more score levels, Score 2 having obvious meaning, as stated 
above. (but I defined a vote of 1 as being "accept." It could be 
neutral, an abstention, which then would be more likely to require a 
runoff.)

Asset's slogan could then ride on this: "*Make All Votes Count*." Asset 
wastes no votes, period.

Asset is radical, it would, my opinion, transform politics entirely, 
into the science of how we communicate, collaborate, and cooperate.

The system is the message.

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