[EM] Ranked Preferences, example calculations

[Abd ul-Rahman Lomax]

At 06:09 AM 10/30/2006, Chris Benham wrote:

>Abd ul-Rahman Lomax wrote:
>The strongest preference is expressed in range by rating the 
>undesired outcome at the minimum rating and the desired outcome at 
>the maximum rating. If the majority does this, and if they are in 
>agreement about these two things, they will prevail.
>>
>>"Strong preference" means strong preference for a desired outcome. 
>>If they only have a weak preference, and express such a preference, 
>>they might not get it.
>
>CB: This requires them to be coordinated regarding their "desired 
>outcome". What if they agree that X should lose but are split about 
>which individual candidate should get max. rating,
>or  they agree that Y should win but are split about which candidate 
>should get minimum rating? Why shouldn't they also "prevail" in those cases?

Chris is going to argue indefinitely, it does not matter what I 
write. I'm not. If I can't answer an argument by Chris, I won't. I 
won't continue to argue based on an assumption that what I said in 
the past is true, and must be defended to the bitter end.

The line of argument that Chris has presented simply disregards what 
has been written here about the connection between a desired 
"strategic" outcome and the true sincere votes of voters.

Continually, it is assumed that the majority should "prevail," i.e, a 
small preference by a majority should prevail over a large preference 
of a minority, no matter how great the gap in preference, and no 
matter how close the minority is to the majority. His argument here 
applies equally well to Approval Voting, it is just that the matter 
is starker there, and does require strategic considerations on the 
part of the voter. I.e., under Approval, a voter must, to vote with 
full power, determine an approval cutoff which involves knowing who 
the top candidates are likely to be, and then the voter must 
effectively state that both of them are equally preferred.

Approval is a Range method with binary input.

The majority should prevail when it is voting on a single question. 
This is Robert's Rules, actually, and election methods have been 
exempted from it because it was not obvious what would be better than 
the Majority Criterion. The U.S. generally, has an even weaker 
system, not requiring a Majority winner. Systems that have a top-two 
runoff are closer to satisfying the real, informed preference of the majority.

The Majority Criterion is sensible when it is a two-candidate 
election, and both sides are informed about the preference strengths 
of the other. Venzke pointed out that this is what happens with 
pizza, which is why pizza choosers don't actually use Range. They do 
the Range work informally and then use a Supermajority criterion, 
Approval Style, unless nobody has a strong preference, in which case 
they will simply choose the favorite of the majority.

But that informal process breaks down on a large scale. So the 
question is, what methods are going to have the same salubrious 
effects on the unity of the association or society that the informal 
Pizza process produces.

Range gets the closest. Yes, Range does not satisfy the Majority Criterion.

But Range with the safety valve that I have described does. If there 
is a Majority winner, then the majority must consent to the election, 
by one of two methods. The Range winner cannot win with either method 
if the Majority so strongly prefers someone else that they will 
disregard the social consequences. They are willing to go ahead. And 
they have that right, unless we have weighted systems, which is a 
whole other kettle of fish and territory I'm not willing to enter, 
except where the weight comes from the free choice of voters.

Asset Voting is an example of that. Does Asset satisfy the Majority 
Criterion? Isn't that an interesting question?

The Majority Criterion is weak when considering elections with more 
than two candidates.

To repeat, Chris, in his argument, continues to rely on the Majority 
Criterion. He is using the Majority criterion to justify the Majority 
Criterion. He is not deriving the Majority Criterion from generally 
accepted principles that do *not* include the Majority Criterion.

I'll quote again and answer directly:

>What if they agree that X should lose but are split about which 
>individual candidate should get max. rating,
>or  they agree that Y should win but are split about which candidate 
>should get minimum rating? Why shouldn't they also "prevail" in those cases?

They are split about the second-best. The question should be 
reversed. We are examining the Majority Criterion. The question 
should be, "Why should the preference, no matter how weak, of the 
Majority prevail?"

This goes back, if asked, to the foundations of democracy, its 
theoretical underpinnings. It should be remembered that a number of 
the writers we consider the forerunners of democracy *were opposed to 
elections*, as I remember the matter. Their arguments apply most 
strongly to pure preference methods, but they also apply to Range. 
Range works if we make certain assumptions about what it means to 
assign a value to a candidate.

But full-on deliberative methods with a Yes/No vote to confirm any 
choice are what represent the true majority will.

>>There are value judgements embodied in the language used that 
>>essentially incorporate the conclusion.
>
>CB: No, the language is purely technical.

Yeah, I've heard that argument before. A writer, an academic, states 
that the writings of so-and-so are "racist." Naturally, there are 
objections from supporters of that writer, who think that the writer 
wasn't a racist. But, in fact, if you know the academic, technical 
definition of "racism," it is practically undefensible that the 
writer is racist. Under that definition. But "racist" is loaded with 
highly negative connocations.

And "vulnerable" is loaded with connotations, implying that the 
vulnerability is pathological. We don't use "vulnerable," for 
example, to refer to the Condorcet method as being "vulnerable" to 
selecting a winner that satisfies the Majority Criterion.

Range looks to a different Criterion. We might call it the Range 
Criterion, which is shorter than "Maximizes the Sum of Satisfaction 
with Election Values."

But that criterion is exactly at the foundation of democracy. 
Greatest good for the greatest number. Not tiny good for the greatest 
number, which is what Majority Criterion winners *can* represent.

(Often the Majority Criterion will indicate the best winner, i.e., 
the Range winner, *if the election method is run with preference 
strengths expressed. It appears that the Schulze method, which seems 
to be preferred by Condorcet advocates, infers preference strengths 
from rank sequence, which is about the best you can do with a pure 
ranked ballot, and uses this information to choose a winner when 
there is no Condorcet winner.

Now, question is, why not just choose the candidate with the most 
first-preference votes? I agree that the Schulze method is superior, 
but just making the Plurality choice satisfies the Plurality 
Criterion, which is broadly accepted, though, I think we would agree, 
it is accepted ignorantly.

I don't understand the Schulze method, I just have noticed that it 
makes assumptions about preference strength. (It assumes that the 
voters have voted "linearly," i.e., that all expressed preference 
strengths are equal.

>>He expects that people would engage in a conspiracy to vote 
>>insincerely in order to impose their weak preference on the society.
>CB: What "conspiracy"?

An agreement to vote insincerely. "Strategically."

>>No, if they are actually going to do this, they have a strong 
>>preference. Their so-called "strategic vote" is actually a sincere one.
>
>CB: In my examples, votes that I specify as insincere are insincere.

But this is tantamount to assuming two contradictory conditions. That 
is, the two conditions are unlikely to exist in reality because they 
imply a relatively strong preference (strong enough to motivate the 
voters to distort their expressed votes in the strategic plan to 
thereby "win"), stronger than the supposed "sincere" preference. The 
presumption here is that "insincere" preference will be expressed 
under two conditions. The first here is habit. We have polarized 
political systems that encourage partisan behavior.

This is not so true in local politics. It's a problem of scale. So, 
there is a habit of believing that one's favorite is the greatest 
candidate since Abe Lincoln, and an opposing candidate, since he 
seems to be against Lincoln, must be in favor of slavery; after all, 
the enemy of the good is evil. The system encourages polarization, 
because large shifts in policy can result from tiny differences in 
voting support.

If this were a control system we were engineering, we'd say that it 
suffers from hysteresis. Such control systems can shake an airplane to pieces.

And it *is* a control system we are engineering. The winner-take-all 
nature of preference election systems is quite dangerous, from an 
engineering perspective. Condorcet could make it worse, because the 
Condorcet winner in one election might be from fanatic party A, with 
35% of the vote, and the next one from party B, with 35% of the 
vote.... The society swings. (And this is indeed what I think we are 
seeing in U.S. politics. We'll see. The percentages may be about 
right, if Condorcet were being used.)

>>Right off I'll note that these votes are preposterous. People will 
>>not vote, in such numbers, anything like this.
>
>CB: Completely irrelevant for my demonstration.

But what Chris is demonstrating is that Range does not satisfy the 
Majority Criterion. We already knew that, it is not at issue. What is 
at issue is the social benefit of the Majority Criterion!

So a preposterous example, one which incorporates assumptions that 
are, in reality, almost certainly mutually contradictory, is what is 
irrelevant. It is a smoke screen, put up to conceal the weakness of 
the argument for the Majority Criterion.

My realization of the depth of the problem with the MC is quite new. 
We ought to make this very explicit, in the Range material and 
elsewhere. Crhis has not even come close to answering these 
objections to the MC, he just keeps presenting evidence that Range violates it!

Which it *must* in order to maximize perceived social benefit. 
"Violation" is also a loaded term. That Range "violates" the Majority 
Criterion, which is technically true, there is no doubt or argument 
about this, carries an impression to an average reader, and even, 
possibly, a subconscious tilt to the thinking of an expert, of some 
kind of defect. It isn't a defect, it is a strength! An optimal 
system *must* violate the Majority criterion under some scenarios.

>>  No election method is going to produce a satisfactory result in 
>> this situation. It is entirely unclear to me which of the three 
>> candidates is actually the best.
>CB: Of course. With a sincere Majority Loser and a sincere Condorcet 
>winner some of us are not so confused.

This is because the example given shows what are clearly two 
radically different factions, in direct opposition to each other, 
with this opposition being as polarized as possible, and, to me, it 
is almost certain that there is a better winner than A, B, or C. It 
is D. Who is not on the ballot. The only way to select D is a process 
which is not a single election.

But Chris is an Election Methods Expert. It does not matter if his 
technical truths have real application to actual societies. He is not 
even concerned if the parties tear each other apart after the 
election. His precious Majority Criterion has been satisfied by the method....

If an election comes up with such equally matched votes, I'll repeat, 
the real situation is None of The Above. Libertarians actually would 
put this on the ballot, it is one of the Libertarian proposals I'd agree with.

"I prefer A, and if not A, then None of the Above. Or, if there is no 
candidate on the ballot who would make me reasonably happen, None of 
the Above, period."





>>Bottom line, though: if I could make a suggestion to this society, 
>>it would be that you need to find a candidate with broader support. 
>>Any winner for this election, among the three presented, will 
>>result in a badly fractured society, an officer who is *detested* 
>>by half the people.
>
>
>>Well, I would have to assume that the serious closeness of this 
>>election would be known. A shift from 98 to 99 is hardly a major shift.
>
>CB: Sufficient to force those voters to stop expressing their B>A preference.

Note how we have a situation where the "sincere preference" is 99 to 
98 in Range. Chris expresses this situation as "forcing" voters to 
vote insincerely. But if they vote sincerely, with the initial 
conditions, they get a candidate who is almost perfect to them, 
relatively speaking. The difference is insignificant. So why are they 
"forced" to vote the extremes, to lie about their rating of their 
second choice? Where does this pressure come from?

Not from strength of preference, for sure! It is coming from the 
Election Methods Expert, who thinks that people *should* always try 
to get their preference, or, at least, that they will always try to 
do so, no matter how slight the preference. It's not true, not even 
the second one. If the preference is as slight as is expressed in the 
example, they would be happy with a coin toss! In fact, in the 
polarized situation described, they will be deliriously happy with 
the election of A, their second choice. After all, C very nearly won!

The problem here is that Chris is assuming some major social benefit 
from selecting the majority winner, when the margin between that 
winner and another is razor-thin. If it is razor-thin, there is no 
substantial advantage to selecting one over the other.

What Chris is going to have to show, if he can, and he wants to use 
examples, is an example where social damage is done by selecting the 
Range winner over the Majority winner, in a pure Range system.

(If the 25% rule is in place, if blanks aren't counted as zeros, 
there is danger, which is why I'd somewhat prefer to toss out the 
disregard of blanks, at least at first. There *is* social value in 
providing some recognition to a winner who has high ratings from 
those who know him, but I think that the time to elect this person is 
the next election, not this one. Or it would be in some kind of 
runoff, say if the 25% criterion is met, though the 25% criterion is 
a quite artificial boundary, I have argued on the Range list that the 
only boundary that is *not* set by some kind of complex balancing 
judgement is the 50% boundary, i.e., that at least 50% of voters must 
have rated a candidate for the candidate to win. I think there is 
more to the rule than that, I forget at the moment.



>>I've recommended that Range elections include a facility for 
>>expressing Favorite *without* giving a higher rating. I've also 
>>recommended that Range be coarser, not 0 to 99, I'd rather see 0 to 10.
>
>CB: The fact that the range was so large (99-0) is what forced me to 
>make the difference in size between the two factions so small.

Yes. However, with a larger step size (i.e, 0.1 rather than 0.01, 
comparing Range 11 with Range 101), it is more likely that candidates 
would rate equally. The Favorite expression option makes this less 
painful to partisans. A 10% difference in preference strength is 
probably still down in the noise in terms of what it means to human 
beings. It is still a slight preference.

>>Now, note that I proposed, in these and concurrent threads, a 
>>safety feature, a runoff if the preference winner were different 
>>from the Range winner.
>
>CB: Yes *you* did, but that isn't the CRV proposal.

That's right. CRV has *not* in my opinion developed, yet, a consensus 
definition of Range, as far as the details are concerned.

>  I have been addressing the pure Range method, not some as yet not 
> even fully defined "Range with Runoff" or "Range with Ratification" 
> scheme of yours.

Yes. Note that these "schemes" would be normal in standard 
deliberative process. "Shall so-and-so take office" is a not uncommon 
motion. I'd insist on it, where I have the choice!

In other words, the context of a method matters. A method which is 
vulnerable to some possible malfunction can actually be the optimal 
method if the context deals with that and prevents it from actually 
causing damage.


>>I don't consider that a vulnerability. Vulnerability implies that 
>>there is something wrong with it.
>
>CB: Again, the language is technical.

Yes. So what we see here is that Chris effectively acknowledges that 
the technical language is misleading to the ordinary reader.


>>Remember, the "sincere" vote here was A99>B98.
>>
>CB: The ranking was sincere but as I explained, the ratings maybe not.

We can't understand what the rankings actually mean if we do not know 
what the sincere ranking would actually be. What Chris was allegedly 
examining was the vulnerability of Range to strategic voting. But we 
can't examine strategic voting unless we understand what sincere 
voting was. The first results, 99 to 98, were presumably in the 
absence of strategic considerations. We can do nothing other than 
assume that these are sincere.

If the preference were stronger than that, why would the Range voters 
not want to express it? That, without some plan, with voters going to 
the polls naked, as it were, they agreed on 99 to 98 is just about a 
proof to me that they don't actually have a preference between A and 
B, it is *way* down in the noise.

Control systems that radically change output based on noise.... not a 
great idea.

>The 18 B voters have "defected" from the AB coalition by insincerely 
>changing from B99>A98
>>>to B99>B0=C0, and Range rewards their dishonesty (and disloyalty) 
>>>by electing B.
>>
>>
>>Now, why would they do this? Only if they strongly prefer B to A. 
>>But this contradicts the initial conditions.
>
>CB: Range only allows voters to express one "strong" (by your 
>definition) preference (between two candidates or two sets of
>equally-ranked candidates).

*Range is not about expressing preference, it is about expressing 
value. That Chris puts so much weight on preference is simply coming 
from his *assumption* that preference is what matters.

>  In "the initial conditions"
>the B supporters strongest preference was B>C. Of course their 
>sincere B>A preference doesn't have to be all that strong for them 
>to want to make B win.

Again, the contradiction is hidden in the word "make." Make implies 
effort and force. And one does not try to force decisions on a group 
unless one has a strong preference (or has a disorder that causes 
them to behave as if small preferences were commands from God. 
Properly, such people need medication. I know, I have a son who had 
this disorder.)

How far would these voters go to get what they prefer? Would they 
spend, say, $100 each to put into campaign funds to attempt to elect 
B? From my point of view, that is not a particularly strong 
preference for an average citizen in first-world countries. But it is 
far higher than what citizens actually spend.

Personally, looking back, how much *should* I have spent to try to 
elect Al Gore in 2000?

The fact is that though I strongly preferred Gore, my preference was 
not great enough to get me out working for him, or sending in 
significant money. I think I *did* contribute to his campaign, which 
is, I think, a first for me. Or maybe I have that campaign confused 
with Kerry 2004. By 2004 I had realized, however, that the most 
efficient place for me to put my efforts was in the metastructure, 
not in trying to control the identities of the players in the 
existing system. If a significant number of others were doing the 
same, actually a tiny percentage of the population, we'd change the 
whole thing, I believe, in a fairly short time.

This is because FA/DP is *not* goal-oriented. It is 
intelligence-oriented. Instead of trying to get society to take this 
or that measure, to protect the environment, to avoid war, to ensure 
economic and social justice, and so forth (or, from another point of 
view, to protect the world from the incursions of Communism, Secular 
Humanism, and the predations of feminazis and gay activists), we are 
trying to develop the tools which could examine and solve social 
problems, with minimal institutional bias. FA/DP organizations do not 
determine outcomes, other than reporting the level of consensus that 
exists. When consensus levels have risen high enough, people will 
act. FA/DP does not tell them how high is appropriate, it is entirely 
up to them, which, in practice, would mean that it is up to the 
leaders they have chosen, caucus leaders, high-level proxies, 
depending on how much trust has been given these leaders. Some might 
have appropriation authority. But the FA/DP organization stays out of 
this. As to decisions, it only makes those decisions necessary for 
its own housekeeping, it has no opinion on "outside issues," even if, 
in this case, outside issues are exactly what it is considering every day.

>>. And yet we imagine that the B voters are going to lie about their 
>>preference, in cahoots with each other, in order to elect B?
>CB: Who (besides you) mentioned anything about them being "in 
>cahoots with each other"?

You did. You mentioned an agreement to vote in a certain way, as I recall.

>   No coordination is needed. As long as the other factions vote the 
> same way, individual members of the B faction can try the strategy 
> without any risk of it back-firing (and it can work if only some of 
> them do it.)

And, again, what is strange in a practical sense about this is 
supposing that a behavior will, *without some kind of party 
discipline*, spontaneously result in all voters preferring the party 
candidate voting the same allegedly insincere pattern, while the 
supporters of a candidate *who is practically identical in acceptance 
to the preference of these voters* don't vote similarly at all.

Once again, the suggested behavior makes no sense. It has been 
constructed artificially just in order to show a characteristic of 
Range Voting that we all agree is true. It does not satisfy the 
Majority Criterion, and, further, a group of voters voting in highly 
coherent patterns can push an outcome the way they want.

Yes, they can. However, the point I've been making is that this is 
essentially stupid behavior. And there is no reason to suppose that, 
if Range Voting is implemented, such behavior will be common enough 
to significant affect outcomes, *plus* if it *does* affect outcomes, 
it seems that it does so in a way that is not offensive to the majority.

The examples given all show election outcomes that are satisfactory 
to the majority. *Quite* satisfactory. So where is the beef?

>>The Majority Criterion properly applies (i.e., is desirable) to 
>>binary elections. It gets dicey when there are more than two choices.
>
>CB: Why on earth is that, in your book?  "Strength of preference" is 
>all-important when there are three candidates, but not two?

Range methods are actually superior even in the two-candidate case, 
and this is easy to show.

Chris is correct here. I was not thinking clearly about this.

I had not said, by the way, that "strength of preference is 
all-important," but I will now. Weak preferences aren't important. 
Important preferences are not weak.

There is some value to weak preferences when other things are equal. 
We may suspect that weak preferences are somehow more intuitively 
correct. But a society has not deviated from democracy merely because 
some selections being made are not worshipping at the temple of whim.

It deviates from democracy when the government is not accepted by the 
majority. It deviates even when it *is* majority-accepted, but 
minorities are or consider themselves oppressed.

Democracy is an ideal that is unattainable in its perfection, but it 
can be approached. Social decisions, binding on all, which are not 
accepted by a majority rather obviously violate basic principles of 
democracy. But decisions which are not consensus decisions still are 
offensive to a degree. It is just that the degree declines with the 
percentage of citizens who are offended. You cannot please everyone, 
certainly, but being content with 50% is surely inadequate.